uld certainly not want to be an outright buyer of options. For him, covered call
writing might be the best strategy. Not only would it accomplish his financial aims
moderate profit potential with reduced risk-but it would be much more appealing
to him psychologically. The conservative investor normally understands and accepts
the risks of stock ownership. It is only a small step from that understanding to the
covered call writing strategy. The aggressive investor would most likely not consider
covered call writing to be the best strategy, because he would consider the profit
potential too small. He is willing to take larger risks for the opportunity to make larg
er profits. Outright option purchases might suit him best, and he would accept, by
his aggressive stature, that he could lose nearly all his money in a relatively short time
Chapter 42: The Best Strategy? 935
period. ( Of course, one would hope that he uses only 15 to 20% of his assets for spec
ulative option buying.)
Many investors fit somewhere in between the conservative description and the
aggressive description. They might want to have the opportunity to make large prof
its, but certainly are not willing to risk a large percentage of their available funds in
a short period of time. Spreads might therefore appeal to this type of investor, espe
cially the low-debit bullish or bearish calendar spreads. He might also consider occa
sional ventures into other types of strategies-bullish or bearish spreads, straddle
buys or writes, and so on-but would generally not be into a wide range of these
types of positions. The T-bill/option strategy might work well for this investor also.
The wealthy aggressive investor may be attracted by strategies that offer the
opportunity to make money from credit positions, such as straddle or combination
writing. Although ratio writing is not a credit strategy, it might also appeal to this type
of investor because of the large amounts of time value premium that are gathered in.
These are generally strategies for the wealthier investor because he needs the "stay
ing power" to be able to ride out adverse cycles. If he can do this, he should be able
to operate the strategy for a sufficient period of time in order to profit from the con
stant selling of time value premiums.
In essence, the answer to the question of "which strategy is best" again revolves
around that familiar word, "suitability." The financial needs and investment objectives
of the individual investor are more important than the merits of the strategy itself. It
sounds nice to say that he would like to participate in strategies with limited risk and
potentially large profits. Unfortunately, if the actual mechanics of the strategy involve
risk that is not suitable for the investor, he should not use the strategy, no matter how
attractive it sounds.
Example: The T-bill/option strategy seems attractive: limited risk because only 10%
of one's assets are subjected to risk annually; the remaining 90% of one's assets earn
interest; and if the option profits materialize, they could be large. What if the worst
scenario unfolds? Suppose that poor option selections are continuously made and
there are three or four years of losses, coupled with a declining rate of interest earned
from the Treasury bills (not to mention the commission charges for trading the secu
rities). The portfolio might have lost 15 or 20% of its assets over those years. A good
test of suitability is for the investor to ask himself, in advance: "How will I react if the
worst case occurs?" If there will be sleepless nights, pointing of fingers, threats, and
so forth, the strategy is unsuitable. If, on the other hand, the investor believes that he
would be disappointed (because no one likes to lose money), but that he can with
stand the risk, the strategy may indeed be suitable.
936 Part VI: Measuring and Trading Volatility
MATHEMATICAL RANKING
The discussion above demonstrates that it is not possible to ultimately define the best
strategy when one considers the background, both financial and psychological, of the
individual investor. However, the reader may be interested in knowing which strate
gies have the best mathematical chances of success, regardless of the investor's per
sonal feelings. Not unexpectedly, strategies that take in large amounts of time value
premium have high mathematical expectations. These include ratio writing, ratio
spreading, straddle writing, and naked call writing (but only if the "rolling for cred
its" follow-up strategy is adhered to). The ratio strategies would have to be operated
according to a delta-neutral ratio in order to be mathematically optimum. Unfor
tunately, these strategies are not for everyone. All involve naked options, and also
require that the investor have a substantial amount of money ( or collateral) available
to make the strategies work properly. Moreover, naked option writing in any form is
not suitable for some investors, regardless of their protests to the contrary.
Another group of strategies that rank high on an expected profit basis are those
that have limited risk with the potential of occasionally attaining large profits. The T
hill/option strategy is a prime example of this type of strategy. The strategies in which
one attempts to reduce the cost of longer-term options through the sale of near-term
options fit in this broad category also, although one should limit his dollar commit
ment to 15 to 20% of his portfolio. Calendar spreads such as the combinations
described in Chapter 23 (calendar combination, calendar straddle, and diagonal but
terfly spread) or bullish call calendar spreads or bearish put calendar spreads are all
examples of such strategies. These strategies may have a rather frequent probability
of losing a small amount of money, coupled with a low probability of earning large
profits. Still, a few large profits may be able to more than overcome the fre


r 23 (calendar combination, calendar straddle, and diagonal but
terfly spread) or bullish call calendar spreads or bearish put calendar spreads are all
examples of such strategies. These strategies may have a rather frequent probability
of losing a small amount of money, coupled with a low probability of earning large
profits. Still, a few large profits may be able to more than overcome the frequent, but
small, losses. Ranking behind these strategies are the ones that offer limited profits
with a reasonable probability of attaining that profit. Covered call writing, large debit
bull or bear spreads (purchased option well in-the-money and possible written option
as well), neutral calendar spreads, and butterfuly spreads fit into this category.
Unfortunately, all these strategies involve relatively large commission costs.
Even though these are not strategies that normally require a large investment, the
investor who wants to reduce the percentage effect of commissions must take larger
positions and will therefore be advancing a sizable amount of money.
Speculative buying and spreading strategies rank the lowest on a mathematical
basis. The T-bill/option strategy is not a speculative buying strategy. In-the-money
purchases, including the in-the-money combination, generally outrank out-of-the
money purchases. This is because one has the possibility of making a large percent
age profit but has decreased the chance of losing all his investment, since he starts
Chapter 42: The Best Strategy? 937
out in-the-money. In general, however, the constant purchase of time value premi
ums, which must waste away by the time the options expire, will have a burdensome
negative effect. The chances of large profits and large losses are relatively equal on a
mathematical basis, and thus become subsidiary to the time premium effect in the
long run. This mathematical outlook, of course, precludes those investors who are
able to predict stock movements with an above-average degree of accuracy. Although
the true mathematical approach holds that it is not possible to accurately predict the
market, there are undoubtedly some who can and many who try.
SUMMARY
Mathematical expectations for a strategy do not make it suitable even if the expect
ed returns are good, for the improbable may occur. Profit potentials also do not
determine suitability; risk levels do. In the final analysis, one must determine the
suitability of a strategy by determining if he will be able to withstand the inherent
risks if the worst scenario should occur. For this reason, no one strategy can be des
ignated as the best one, because there are numerous attitudes regarding the degree
of risk that is acceptable.
Postscript
Option strategies cannot be unilaterally classified as aggressive or conservative.
There are certainly many aggressive applications, the simplest being the outright pur
chase of calls or puts. However, options can also have conservative applications, most
notably in reducing some of the risks of common stock ownership. In addition, there
are less polarized applications, particularly spreading techniques, that allow the
investor to take a middle-of-the-road approach.
Consequently, the investor himself-not options--becomes the dominant force
in determining whether an option strategy is too risky. It is imperative that the
investor understand what he is trying to accomplish in his portfolio before actually
implementing an option strategy. Not only should he be cognizant of the factors that
go into determining the initial selection of the position, but he must also have in mind
a plan of follow-up action. If he has thought out, in advance, what action he will take
if the underlying entity rises or falls, he will be in a position to make a more rational
decision when and if it does indeed make a move. The investor must also determine
if the risk of the strategy is acceptable according to his financial means and objec
tives. If the risk is too high, the strategy is not suitable.
Every serious investor owes it to himself to acquire an understanding of listed
option strategies. Since various options strategies are available for a multitude of pur
poses, alrrwst every money manager or dedicated investor will be able to use options
in his strategies at one time or another. For a stock-oriented investor to ignore the
potential advantages of using options would be as serious a mistake as it would be for
a large grain company to ignore the hedging properties available in the futures mar
ket, or as it would be for an income-oriented investor to concentrate only in utilities
and Treasury bills while ignoring less well known, but equally compatible, alterna
tives such as GNMAs.
938
Postsaipt 939
Moreover, in today's markets, with options being available on futures, equities,
and indices, the strategist in any one field should familiarize himself with the others,
because any of them will provide profit opportunities at one time or another.

Appendices

Strategy Sullllllary
Except for arbitrage strategies and tax strategies, the strategies we have described
deal with risk of market movement. It is therefore often convenient to summarize
option strategies by their risk and reward characteristics and by their market out
look-bullish, bearish, or neutral. Table A-1 lists all the risk strategies that were dis
cussed and gives a general classification of their risks and rewards. If a strategist has
a definite attitude about the market's outlook or about his own willingness to accept
risks, he can scan Table A-1 and select the strategies that most closely resemble his
thinking. The number in parentheses after the strategy name indicates the chapter in
which the strategy was discussed.
Table A-1 gives a broad classification of the various risk and reward potentials
of the strategies. For example, a bullish call calendar spread does not actually have
unlimited profit potential unless its n

eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf


an Table A-1 and select the strategies that most closely resemble his
thinking. The number in parentheses after the strategy name indicates the chapter in
which the strategy was discussed.
Table A-1 gives a broad classification of the various risk and reward potentials
of the strategies. For example, a bullish call calendar spread does not actually have
unlimited profit potential unless its near-tenn call expires worthless. In fact, all cal
endar spread or diagonal spread positions have limited profit potential at best until
the near-term options expire.
Also, the definition of limited risk can vary widely. Some strategies do have a
risk that is truly limited to a relatively small percentage of the initial investment-the
protected stock purchase, for example. In other cases, the risk is limited but is also
equal to the entire initial investment. That is, one could lose 100% of his investment
in a short time period. Option purchases and bull, bear, or calendar spreads are
examples.
Thus, although Table A-1 gives a broad perspective on the outlook for various
strategies, one must be aware of the differences in reward, risk, and market outlook
when actually implementing one of the strategies.
943
944
TABLE A-1.
General strategy summary.
Strategy (Chapter)
Bullish strategies
Call purchase (3)
Synthetic long stock (short put/long call) (21)
Bull spread-puts or calls (7 and 22)
Protected stock purchase (long stock/long put) ( 17)
Bullish call calendar spread (9)
Covered call writing (2)
Uncovered put write ( 19)
Bearish Strategies
Put purchase ( 16)
Protected short sale (synthetic put) (4 and 16)
Synthetic short sale (long put/short call) (21)
Bear spread-put or call (and 22)
Covered put write ( 19)
Bearish put calendar spread (22)
Naked call write (5)
Neutral strategies
Straddle purchase ( 1 8)
Reverse hedge (simulated straddle buy) (4)
Fixed income + option purchase (25)
Diagonal spread (14, 23, and 24)
Neutral calendar spread-puts or calls (9 and 22)
Butterfly spread ( 10 and 23)
Calendar straddle or combination (23)
Reverse spread ( 13)
Ratio write-put or call (6 and 19)
Straddle or combination write (20)
Ratio spread-put or call ( 11 and 24)
Ratio calendar spread-put or call (12 and 24)
Risk
Limited
Unlimited 0
Limited
Limited
Limited
Unlimited 0
Unlimited 0
Limited
Limited
Unlimited
Limited
Unlimited
Limited
Unlimited
Limited
Limited
Limited
Limited
Limited
Limited
Limited
Limited
Unlimited
Unlimited
Unlimited
Unlimited
Appendix A
Reward
Unlimited
Unlimited
Limited
Unlimited
Unlimited
Limited
Limited
Unlimited 0
Unlimited 0
Unlimited 0
Limited
Limited
Unlimited 0
Limited
Unlimited
Unlimited
Unlimited
Unlimited
Limited
Limited
Unlimited
Unlimited
Limited
Limited
Limited
Unlimited
0 Wherever the risk or reword is limited only by the fact that o stock cannot foll below zero in price,
the entry is marked. Obviously, although the potential may technically be limited, it could still be quite
large if the underlying stock did foll a large distance.
APPENDIX B
Equivalent Positions
Some strategies can be constructed with either puts or calls to attain the same prof
it potential. These are called equivalent strategies and are given in Table B-1. They
do not necessarily have the same potential returns, because the investment required
may be quite different. However, equivalent positions have profit graphs with exact
ly the same shape.
Other equivalences can be determined by combining any two strategies in the
left-hand column and setting that combination equivalent to the two corresponding
strategies in the right-hand column.
945
946
TABLE B-1.
Equivalent strategies.
This Strategy is equivalent to
Call purchase
Put purchase
Long stock
Short stock
Naked call write
Naked put write
Bullish call spread
(long call at lower strike/
short call at higher strike)
Bearish call spread
(long call at higher strike/
short call at lower strike)
Ratio call write
(long stock/short calls)
... and is also equivalent to ...
Straddle buy (long call/long put)
Appendix B
This Strategy
Long stock/long put
Short stock/long call (synthetic put)
Long call/ short put (synthetic stock)
Long put/ short call (synthetic short sale)
Short stock/short put
Covered call write (long stock/ short call)
Bullish put spread
(long put at lower strike/
short put at higher strike)
Bearish put spread
(long put at higher strike/
short put at lower strike)
Straddle write (short put/short call)
Ratio put write (short stock/ short puts)
Reverse hedge (short stock/long calls)
or buy stock/buy puts
Butterfly call spread Butterfly put spread
(long 1 call at each outside strike/ (long one put at each outer strike/
short 2 calls at middle strike) short two calls at middle strike)
All four of these "butterfly" strategies are equivalent
Butterfly combination Protected straddle write
(bullish call spread at two (short straddle at middle strike/
lower strikes/bearish put spread
at two higher strikes)
long call at highest strike/
long put at lowest strike
APPENDIX C
Formulae
Chapter references are given in parentheses. The following notation is used through
out this appendix.
X = current stock price
s = striking price
C = call price
p = put price
r = interest rate
t = time (in years)
B = break-even point
u = upside break-even point
D = downside break-even point
p = maximum profit potential
R = maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three
striking prices in a formula. The formulae are arranged alphabetically by title or by
strategy.
948
Annualized Risk (Ch. 26)
Annualized risk = L INV 360
i
1
Hi
where INVi = percent of total assets invested in options
with holding periods, Hi
length of holding period in days
Bear Spread
-Calls (Ch. 8)
-Puts (Ch. 22)
p = Cl - C2
R = s2 - s1 - P
B = s1 + P
R = P2 - Pl
p = S2


e three
striking prices in a formula. The formulae are arranged alphabetically by title or by
strategy.
948
Annualized Risk (Ch. 26)
Annualized risk = L INV 360
i
1
Hi
where INVi = percent of total assets invested in options
with holding periods, Hi
length of holding period in days
Bear Spread
-Calls (Ch. 8)
-Puts (Ch. 22)
p = Cl - C2
R = s2 - s1 - P
B = s1 + P
R = P2 - Pl
p = S2 - S1 - R
B = s1 + P = s2 + Pl - P2
Black Model (Ch. 34):
X
s
C
p
r
Theoretical futures call price= e-rt x BSM[r = 0%]
where BSM[r = O) is the Black-Scholes Model
using r = 0% as the short-term interest rate
Put price = Call price - e-rt x (f - s)
where f = futures price
current stock price
striking price
call price
put price
interest rate
time (in years)
B
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
f futures price
Appendix C
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula.
The formulae are arranged alphabetically by title or by strategy.
Appendix C
Black-Scholes Model (Ch. 28)
where d1
andd2
ln
N()
V
Delta
Bull Spread
=
=
=
=
=
=
Theoretical call price= xN(d 1) - se-rtN(d2)
ln(x/s) + (r + ½v2)t
vTt
d1 -v-ft
natural logarithm
cumulative normal density function
annual volatility
N(d1)
-Calls ( Ch. 7)
-Puts (Ch. 22)
Butterfly Spread
R = C1 - C2
P = s2- s1 - R
B = s2 - P = s 1 - c2 + c1
P = P2 -p1
R = s2- s1 - P
B = s2- P
949
A butterfly spread combines a bull spread using strikes s1 and s2 with a bear
spread using strikes s2 and s3.
-if using all calls (Ch. 10)
R = c1 + c3 - 2c2
-if using all puts ( Ch. 23)
R =PI+ P2 - 2p2
-if using put bull spread and call bear spread ( Ch. 23)
p = C2 + P2 - C3 - p 1
950
-if using call bull spread and put bear spread ( Ch. 23)
R = P2 + c2 - PI c3 - s3 + s2
Then
P = s3 - s2 - R or R = s3 - s2 - P
D = s1 + R
U = S3-R
Combination Buy (Ch. 18)
S1 < S2
Out-of-the-money: R = c2 + PI
In-the-money: R = c1 + p2 - s2 + s1
D = s1 -P
U = s2 + P
Combination Sale (Ch. 20)
X
s
C
p
r
Out-of-the-money: P = c2 + PI
In-the-money: P = c1 + p2 - s2 + s1
D = s1 -P
current stock price
striking price
call price
put price
interest rate
time (in years)
B
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
f futures price
Appendix C
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a fonnula.
The formulae are arranged alphabetically by title or by strategy.
950
-if using call bull spread and put bear spread ( Ch. 23)
R = p2 + c2 - Pl - c3 - s3 + s2
Then
P = s3 - s2 - R or R = s3 - s2 - P
D = s1 + R
U = S3-R
Combination Buy (Ch. 18)
S1 < S2
Out-of-the-money: R = c2 + Pl
In-the-money: R = c1 + p2 - s2 + s1
D = s1 -P
U = s2 + P
Combination Sale (Ch. 20)
Out-of-the-money: P = c2 + PI
In-the-money: P = c1 + p2 s2 + s1
D = s1 - P
X
s
C
p
current stock price
striking price
call price
put price
r interest rate
t ~ time (in years)
f futures price
U = s2 + P
B
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Appendix C
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula.
The formulae are arranged alphabetically by title or by strategy.
950
-if using call bull spread and put bear spread ( Ch. 23)
R = P2 + c2 - PI - c3 - s3 + s2
Then
P = s3 - s2 - R or R = s3 - s2 - P
D =SI+ R
U = S3-R
Combination Buy (Ch. 18)
S1 < S2
Out-of-the-money: R = c2 + PI
In-the-money: R = cI + p2 - s2 + sI
D = SI -P
U = s2 + P
Combination Sale (Ch. 20)
Out-of-the-money: P = c2 + PI
In-the-money: P = cI + P2 - s2 + sI
D = sI -P
X
s
C
p
current stock price
striking price
call price
put price
r interest rate
t = time ( in years)
f futures price
U = s2 + P
B
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Appendix C
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula.
The formulae are arranged alphabetically by title or by strategy.
Appendix C
Conversion and Reversal Profit (Ch. 27)
Conversion: P = s + c - x - p + dividends - carrying cost
Reversal: P = x + p - c - s - dividends + carrying cost
where
951
. t {srt (simple interest) carrymg cos =
s[l- (1 + r)-t] (compound interest, present worth)
Covered Call Write (Ch. 2)
P=s+c-x
B =X-C
Covered Straddle Write (Ch. 20)
P=s+c+p x
B = s - ½P = ½(x + s - p - c)
Cumulative Normal Density Function (Ch. 28)
Approximation by fifth-order polynomial
a= 1- z(l.330274y 5 - l.821256y 4 + l.781478y 3 - .3565638y2
+ .3193815y)
1
where y = l + .23164191crl
z = .3989423e--0212
Then
N(cr) = fa
U-a
Delta-see Black-Scholes Model
Delta Neutral Ratio:
-stock versus option (Ch. 6)
ifcr>O
ifcr<O
Neutral ratio = 1 ~ De ta o option
-spread (Chs. 11 and 24)
952
N t l t. Delta of long option eu ra ra 10 = -----=---=--Delta of short option
Equivalent Futures Position (Ch. 34)
EFP = Delta x Number of options
Equivalent Stock Position (Ch. 28)
ESP = Unit of trading x Delta x number of options
Appendix C
where unit of trading is the number of shares of the underlying stock that
can be bought or sold with the option (normally 100).
Futures Contract Fair Value (Ch. 29)
-Stock index futures
Index value x (1 + rt) + Present worth (dividends)
Also see Present worth.
Future Stock Price (Ch. 28)
where
-lognormal distribution, assuming a movement of a fixed number of stan
dard deviations
q = future stock price
Vt = volatility for the time period
a = number of standard deviations of movement
(normally-3.0::; a::; 3.0)
Gamma (Ch. 40)
X
s
C
p
r
let z =


)
-Stock index futures
Index value x (1 + rt) + Present worth (dividends)
Also see Present worth.
Future Stock Price (Ch. 28)
where
-lognormal distribution, assuming a movement of a fixed number of stan
dard deviations
q = future stock price
Vt = volatility for the time period
a = number of standard deviations of movement
(normally-3.0::; a::; 3.0)
Gamma (Ch. 40)
X
s
C
p
r
let z = In [ x ] /v --ft + v --ft
S X (1 + r)t 2
Then (-x212)
r- __ e-===--
- xv ✓ 2nt
current stock price B
striking price
call price
put price
interest rate
time (in years)
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula.
The formulae are arranged alphabetically by title or by strategy.
Appendix C
Probability of Stock Movement (Ch. 28)
-lognormal distribution
P(below q) = N {1:~q/x)}
P(above q) = 1- P(below q)
where
q = stock price in question
N() = cumulative normal density function
In = natural logarithm
Vt = volatility for the time period
Present Worth of a Future Arrwunt (Ch. 28)
p t rth _ Future amount resen wo - (l + r)t
Put Pricing Model-Arbitrage Model (Ch. 28)
where
Theoretical put price = Theoretical call price + s - x + dividends
- carrying cost
. t { srt (simple interest) carrv1ng cos =
· r s [1- (1 + r)-t] (compound interest, present worth)
Ratio Call Write (Ch. 6)
General case: long m round lots of stock, short n calls
P = m(s -x) + nc
U=s+-P __
n-m
p
D=s-m
2:1 ratio (straddle sale)
P=s-x+2c
U=s+p
D=s-p=x-2c
953
954 Appendix C
Ratio Spread
-Calls (Ch. 11): buy n1 calls at lower strike, s1, and sell n2 calls at higher
strike, s2
S1 < s2
n1 < n2
R = n1c1 - n2c2
P = (s2-s1)n1 -R
p
U=s2+ --n2-n1
Break-even cost of long calls for follow-up action (Ch. 11)
Break-even cost = n2(s2 - si) - R
n2 n1
-Puts (Ch. 24): buy n2 puts at higher strike, s2, and sell n1 puts at lower
strike, s1
S1 < S2
n2 < n1
R = n2p2 - n1p1
P = n2(s2 - s1) - R
p
D =S1 ----n1 -n2
Reversal-See Conversion and Reversal Profit
Reverse Hedge (Ch. 4)-simulated straddle purchase
General case: short m round lots of stock and long n calls
R = m(s -x) + nc
U=s+-R-n-m
R D=s--m
X
s
C
current stock price
striking price
call price
p put price
r interest rate
t = time (in years)
B
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula.
The formulae are arranged alphabetically by title or by strategy.
Appendix C
2:1 ratio (straddle buy):
R=s+2c-x
U=s+R
D=s-R=x 2c
Using puts (long 100 stock, long 2 puts) (Ch. 18)
R = x + 2p-s
Straddle Buy (Ch. 18)
Straddle Sale ( Ch. 20)
U = s + R = x + 2p
D =s-R
R=p+c
U = s + R
D=-R
P=p+c
U=s+p
D =s-p
Synthetic Put Purchase-short stock and long call ( Ch. 4)
R=s+c-x
B = s-c
Variable Ratio Write (Ch. 6)
-long 100 shares of stock, short one call at strike s1, short one call at
strike s2
p = Cl + C2 + S1 - X
D = s1 - P = x - c1 - c2
U = s2 + P
955
954 Appendix C
Ratio Spread
-Calls (Ch. 11): buy n1 calls at lower strike, s1, and sell n2 calls at higher
strike, s2
s1 < s2
n1 < n2
R = n1c1 - n2c2
P = (s2 - s1)n1 -R
p
U=s 2 +--n2-n1
Break-even cost oflong calls for follow-up action (Ch. 11)
Break-even cost = n2(s2 - si) - R
n2-n1
-Puts (Ch. 24): buy n2 puts at higher strike, s2, and sell n1 puts at lower
strike, s1
S1 < S2
n2 < n1
R = n2p2 - n1p1
P = n2(s2 - s1) - R
p D =S1----
n1 -n2
Reversed-See Conversion and Reversal Profit
Reverse Hedge (Ch. 4)-simulated straddle purchase
General case: short m round lots of stock and long n calls
R = m(s -x) + nc
U=s+-R-n-m
R D=s--m
X
s
C
current stock price
striking price
call price
p put price
r interest rate
t = time (in years)
B
u
D
p
R
break-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula.
The formulae are arranged alphabetically by title or by strategy.
Appendix C
2:1 ratio (straddle buy):
R=s+2c-x
U = s + R
D=s-R=x-2c
Using puts (long 100 stock, long 2 puts) (Ch. 18)
R = x + 2p -s
Straddle Buy (Ch. 18)
Straddle Sale ( Ch. 20)
U = s + R = x + 2p
D=s-R
R=p+c
U = s + R
D=-R
P=p+c
u = s +p
D =S-p
Synthetic Put Purchase-short stock and long call ( Ch. 4)
R=s+c-x
B = s-c
Variable Ratio Write (Ch. 6)
-long 100 shares of stock, short one call at strike s1, short one call at
strike s2
p = Cl + C2 + S 1 - X
D = S1 - p = X - C1 - C2
U = S2 + p
955
956 Appendix C
Volatility-Standard Deviation (Ch. 28)
Where
n
L (xi - x)2
i l
V2=----
n-l
xi = daily stock closing price
x = mean (average) of the x/s
n = number of observations
-if vis the annual volatility, then the volatility for a time period, t, is
Vt= V ..ft
Graphs
Chapter references are in parentheses.
A. Intrinsic Value-Call (Ch. 1)
C. Call Option Pricing Curve
(Ch. 1)
B. Intrinsic Value-Put (Ch. 15)
D. Put Option Pricing Curve
(Ch. 15)
957
958
E. Time Value Premium Decay
(Ch. 1)
G. Call Purchase (Ch. 1)
(long stock/long put-Ch. 17)
I. Covered Call Write (Ch. 2)
Naked Put Write (Ch. 19)
F. Lognormal Distribution
(Ch. 28)
H. Put Purchase (Ch. 16)
(short stock/long call-Ch. 4)
J. Naked Call Write (Ch. 5)
(short stock/sh01t put
Ch. 19)
Appendix D
Appendix D
K. Bull Spread (Chs. 7 and 22)
( covered call write + long put
out-of-the-money-Ch. 17)
1_, /
M. Calendar Spread (Chs. 9 and
22)
0. Naked Straddle Write (Ch. 20)
Ratio Call Write (long 100
stock, short 2 calls-Ch. 6)
Ratio Put Write (short 100
stock, short 2 puts-Ch. 19)
IA
L. Bear Spread (Chs. 8 and 22)
N.


ed Call Write (Ch. 5)
(short stock/sh01t put
Ch. 19)
Appendix D
Appendix D
K. Bull Spread (Chs. 7 and 22)
( covered call write + long put
out-of-the-money-Ch. 17)
1_, /
M. Calendar Spread (Chs. 9 and
22)
0. Naked Straddle Write (Ch. 20)
Ratio Call Write (long 100
stock, short 2 calls-Ch. 6)
Ratio Put Write (short 100
stock, short 2 puts-Ch. 19)
IA
L. Bear Spread (Chs. 8 and 22)
N. Butterfly Spread ( Chs. 10 and
23)
P. Straddle Purchase (Ch. 18)
Reverse hedge (short 100
stock, long 2 calls-Ch. 4)
Put Hedge (long 100 stock,
long 2 puts-Ch. 18)
959
960
Q. Combination Sale (Ch. 20)
Variable Ratio Write (long 100
stock, short 2 calls with
different strikes-Ch. 6)
7
S. Ratio Call Spread (Ch. 11)
U. Reverse Calendar Spread
(Ch. 13)
I~
Appendix D
R. Combination Purchase (Ch. 18)
(short 100 stock, long 2 calls
with different strikes-Ch. 4)
T. Ratio Put Spread (Ch. 24)
Qualified Covered Calls
For tax purposes, there is no effect on the holding period of the stock when one
writes an out-of-the-money call. However, when one writes an in-the-money call,
he eliminates the holding period on his common stock unless the stock is already
held long-term. The only exception to this is that if the covered call is deemed to
be qualified, then the holding period is merely suspended rather than eliminated.
Table E-1 shows the lowest striking price that may be written if the stock is in the
price range shown.
961
TABLE E-1. ~
Qualified covered call options.
~
Call is not "deep-in-the-money" Call is not
II
deep-in-the-money"
Applicable if Strike Price2 is at least: Applicable if Strike Price2 is at least:
Stock More than Stock More than
Price1 31-90-Day Call 90-Day Call Price1 31-90-Day Call 90-Day Call
5.13-5.88 5 5 75.13-80 75 70
6-10 None None 80.13-85 80 75
10.13-11.75 10 10 85.13-90 85 80
11.88-15 None None 90.13-95 90 85
15.13-17.63 15 15 95.13-100 95 90
17.75-20 None None 100.13-105 100 95
20.13-23.50 20 20 105.13-110 100 100
23.63-25 None None 110.13-120 110 110
25.13-30 25 25 120.13-130 120 120
30.13-35 30 30 130.13-140 130 130
35.13-40 35 35 140.13-150 140 140
40.13-45 40 40 150.13-160 150 140
45.13-50 45 45 160.13-170 160 150
50.13-55 50 50 170.13-180 170 160
55.13-60 55 55 180.13-190 180 170
60.13-65 60 55 190.13-200 190 180
65.13-70 65 60 200.13-210 200 190
70.13-75 70 65 210.13-220 210 200
1 Applicable stock price is either the closing price of the stock on the day preceding the date the option was granted, or the opening price on
t the day the option is granted if such price is greater than 100% of the preceding day's closing price.
2Assumption is that strike prices are only at $5 intervals up to $ 100 and $10 intervals over $100. Note: If the stock splits, option strike prices 5:c·
will have smaller intervals for a period of time. ""'
Glossary
American Exercise: a feature of an option that indicates it may be exercised at any
time. Therefore, it is subject to early assignment.
Arbitrage: the process in which professional traders simultaneously buy and sell the
same or equivalent securities for a riskless profit. See also Risk Arbitrage.
Assign: to designate an option writer for fulfillment of his obligation to sell stock (call
option writer) or buy stock (put option writer). The writer receives an assignment
notice from the Options Clearing Corporation. See also Early Exercise.
Assignment Notice: see Assign.
Automatic Exercise: a protection procedure whereby the Options Clearing
Corporation attempts to protect the holder of an expiring in-the-money option by
automatically exercising the option on behalf of the holder.
Average Down: to buy more of a security at a lower price, thereby reducing the
holder's average cost. (Average Up: to buy more at a higher price.)
Backspread: see Reverse Strategy.
Bear Spread: an option strategy that makes its maximum profit when the underly
ing stock declines and has its maximum risk if the stock rises in price. The strate
gy can be implemented with either puts or calls. In either case, an option with a
higher striking price is purchased and one with a lower striking price is sold, both
options generally having the same expiration date. See also Bull Spread.
Bearish: an adjective describing an opinion or outlook that expects a decline in
price, either by the general market or by an underlying stock, or both. See also
Bullish.
963
964 Glossary
Beta: a measure of how a stock's movement correlates to the movement of the entire
stock market. The beta is not the same as volatility. See also Standard Deviation,
Volatility.
Black Model: a model used to predict futures option prices; it is a modified version
of the Black-Scholes model. See Model.
Board Broker: the exchange member in charge of keeping the book of public
orders on exchanges utilizing the "market-maker" system, as opposed to the "spe
cialist system," of executing orders. See also Market-Maker, Specialist.
Box Spread: a type of option arbitrage in which both a bull spread and a bear spread
are established for a riskless profit. One spread is established using put options and
the other is established using calls. The spreads may both be debit spreads ( call
bull spread vs. put bear spread), or both credit spreads (call bear spread vs. put
bull spread).
Break-Even Point: the stock price (or prices) at which a particular strategy neither
makes nor loses money. It generally pertains to the result at the expiration date of
the options involved in the strategy. A "dynamic" break-even point is one that
changes as time passes.
Broad-Based: generally referring to an index, it indicates that the index is composed
of a sufficient number of stocks or of stocks in a variety of industry groups. Broad
based indices are subject to more favorable treatment for naked option writers.
See also Narrow- Based.
Bull Spread: an option strategy that achieves its maximum potential if the underly
ing security rises f


s as time passes.
Broad-Based: generally referring to an index, it indicates that the index is composed
of a sufficient number of stocks or of stocks in a variety of industry groups. Broad
based indices are subject to more favorable treatment for naked option writers.
See also Narrow- Based.
Bull Spread: an option strategy that achieves its maximum potential if the underly
ing security rises far enough, and has its maximum risk if the security falls far
enough. An option with a lower striking price is bought and one with a higher strik
ing price is sold, both generally having the same expiration date. Either puts or
calls may be used for the strategy. See also Bear Spread.
Bullish: describing an opinion or outlook in which one expects a rise in price, either
by the general market or by an individual security. See also Bearish.
Butterfly Spread: an option strategy that has both limited risk and limited profit
potential, constructed by combining a bull spread and a bear spread. Three strik
ing prices are involved, with the lower two being utilized in the bull spread and the
higher two in the bear spread. The strategy can be established with either puts or
calls; there are four different ways of combining options to construct the same
basic position.
Calendar Spread: an option strategy in which a short-term option is sold and a
longer-term option is bought, both having the same striking price. Either puts or
Glossary 965
calls may be used. A calendar combination is a strategy that consists of a call cal
endar spread and a put calendar spread at the same time. The striking prices of
the calls would be higher than the striking prices of the puts. A calendar straddle
consists of selling a near-term straddle and buying a longer-term straddle, both
with the same striking price.
Calendar Straddle or Combination: see Calendar spread.
Call: an option that gives the holder the right to buy the underlying security at a
specified price for a certain, fixed period of time. See also Put.
Call Price: the price at which a bond or preferred stock may be called in by the issu
ing corporation; see Redemption Price.
Capitalization-Weighted Index: a stock index that is computed by adding the cap
italizations (float times price) of each individual stock in the index, and then divid
ing by the divisor. The stocks with the largest market values have the heaviest
weighting in the index. See also Divisor, Float, Price-Weighted Index.
Carrying Cost: the interest expense on a debit balance created by establishing a
position.
Cash- Based: Referring to an option or future that is settled in cash when exercised
or assigned. No physical entity, either stock or commodity, is received or delivered.
CBOE: the Chicago Board Options Exchange; the first national exchange to trade
listed stock options.
Circuit Breaker: a limit applied to the trading of index futures contracts designed
to keep the stock market from crashing.
Class: a term used to refer to all put and call contracts on the same underlying secu
rity.
Closing Transaction: a trade that reduces an investor's position. Closing buy trans
actions reduce short positions and closing sell transactions reduce long positions.
See also Opening Transaction.
Collateral: the loan value of marginable securities; generally used to finance the
writing of uncovered options.
Combination: (1) any position involving both put and call options that is not a strad
dle. See also Straddle. (2) the name given to the trade at expiration whereby an
arbitrageur rolls his options from one month to the next. For example, if he sells
his synthetic long stock position in June and reestablishes it by buying a synthetic
long stock position in September, the entire four-sided trade is called a combina
tion by floor traders. See also Straddle, Strangle.
966 Glossary
Commodities: see Futures Contract.
Contingent Order: an order whose execution or price is dependent on the align
ment or price of the underlying security and/or its options. Most commonly it is an
order to buy stock and sell a covered call option that is given as one order to the
trading desk of a brokerage firm. Also called a "net order." This is a "not held"
order. See also Market Not Held Order.
Conversion Arbitrage: a riskless transaction in which the arbitrageur buys the
underlying security, buys a put, and sells a call. The options have the same terms.
See also Reversal Arbitrage.
Conversion Ratio: see Convertible Security.
Converted Put: see Synthetic Put.
Convertible Security: a security that is convertible into another security. Generally,
a convertible bond or convertible preferred stock is convertible into the underly
ing stock of the same corporation. The rate at which the shares of the bond or pre
ferred stock are convertible into the common is called the conversion ratio.
Cover: to buy back as a closing transaction an option that was initially written, or
stock that was initially sold short.
Covered: a written option is considered to be covered if the writer also has an oppos
ing market position on a share-for-share basis in the underlying security. That is, a
short call is covered if the underlying stock is owned, and a short put is covered
(for margin purposes) if the underlying stock is also short in the account. In addi
tion, a short call is covered if the account is also long another call on the same secu
rity, with a striking price equal to or less than the striking price of the short call. A
short put is covered if there is also a long put in the account with a striking price
equal to or greater than the striking price of the short put.
Covered Call Write: a strategy in which one writes call options while simultane
ously owning an equal number of shares of the underlying stock.
Covered Put Write: a strategy in which one sells put options and simultaneously is
short an equal number of shares of the underlying security.
Covered Straddle Write: the term use


ing price
equal to or greater than the striking price of the short put.
Covered Call Write: a strategy in which one writes call options while simultane
ously owning an equal number of shares of the underlying stock.
Covered Put Write: a strategy in which one sells put options and simultaneously is
short an equal number of shares of the underlying security.
Covered Straddle Write: the term used to describe the strategy in which an
investor owns the underlying security and also writes a straddle on that security.
This is not really a covered position.
Credit: money received in an account. A credit transaction is one in which the net
sale proceeds are larger than the net buy proceeds ( cost), thereby bringing money
into the account. See also Debit.
Glossary 967
Cycle: the expiration dates applicable to various classes of options. There are three
cycles: January/April/July/October, February/May/ August/November, and
March/J une/Septem ber/Decem ber.
Debit: an expense, or money paid out from an account. A debit transaction is one in
which the net cost is greater than the net sale proceeds. See also Credit.
Deliver: to take securities from an individual or firm and transfer them to another
individual or firm. A call writer who is assigned must deliver stock to the call hold
er who exercised. A put holder who exercises must deliver stock to the put writer
who is assigned.
Delivery: the process of satisfying an equity call assignment or an equity put exer
cise. In either case, stock is delivered. For futures, the process of transferring the
physical commodity from the seller of the futures contract to the buyer.
Equivalent delivery refers to a situation in which delivery may be made in any of
various, similar entities that are equivalent to each other (for example, Treasury
bonds with differing coupon rates).
Delta: (1) the amount by which an option's price will change for a corresponding 1-
point change in price by the underlying entity. Call options have positive deltas,
while put options have negative deltas. Technically, the delta is an instantaneous
measure of the option's price change, so that the delta will be altered for even frac
tional changes by the underlying entity. Consequently, the terms "up delta" and
"down delta" may be applicable. They describe the option's change after a full 1-
point change in price by the underlying security, either up or down. The "up delta"
may be larger than the "down delta" for a call option, while the reverse is true for
put options. (2) the percent probability of a call being in-the-money at expiration.
See also Hedge Ratio.
Delta Neutral Spread: a ratio spread that is established as a neutral position by uti
lizing the deltas of the options involved. The neutral ratio is determined by divid
ing the delta of the purchased option by the delta of the written option. See also
Delta, Ratio Spread.
Depository Trust Corporation (OTC): a corporation that will hold securities for
member institutions. Generally used by option writers, the DTC facilitates and
guarantees delivery of underlying securities when assignment is made against
securities held in DTC.
Diagonal Spread: any spread in which the purchased options have a longer matu
rity than do the written options, as well as having different striking prices. Typical
968 Glossary
types of diagonal spreads are diagonal bull spreads, diagonal bear spreads, and
diagonal butterfly spreads.
Discount: an option is trading at a discount if it is trading for less than its intrinsic
value. A future is trading at a discount if it is trading at a price less than the cash
price of its underlying index or commodity. See also Intrinsic Value, Parity.
Discount Arbitrage: a riskless arbitrage in which a discount option is purchased
and an opposite position is taken in the underlying security. The arbitrageur may
either buy a call at a discount and simultaneously sell the underlying security
(basic call arbitrage), or buy a put at a discount and simultaneously buy the under
lying security (basic put arbitrage). See also Discount.
Discretion: see Limit Order, Market Not Held Order.
Dividend Arbitrage: in the riskless sense, an arbitrage in which a put is purchased
and so is the underlying stock. The put is purchased when it has time value pre
mium less than the impending dividend payment by the underlying stock. The
transaction is closed after the stock goes ex-dividend. Also used to denote a form
of risk arbitrage in which a similar procedure is followed, except that the amount
of the impending dividend is unknown and therefore risk is involved in the trans
action. See also Ex-Dividend, Time Value Premium.
Divisor: a mathematical quantity used to compute an index. It is initially an arbitrary
number that reduces the index value to a small, workable number. Thereafter the
divisor is adjusted for stock splits (price-weighted index) or additional issues of
stock (capitalization-weighted index).
Downside Protection: generally used in connection with covered call writing, this
is the cushion against loss, in case of a price decline by the underlying security, that
is afforded by the written call option. Alternatively, it may be expressed in terms
of the distance the stock could fall before the total position becomes a loss (an
amount equal to the option premium), or it can be expressed as percentage of the
current stock price. See also Covered Call Write.
Dynamic: for option strategies, describing analyses made during the course of
changing security prices and during the passage of time. This is as opposed to an
analysis made at expiration of the options used in the strategy. A dynamic break
even point is one that changes as time passes. A dynamic follow-up action is one
that will change as either the security price changes or the option price changes or
time passes. See also Break-Even Point, Follow-Up Action.
Early Exercise (assignment): the exercise or assign


ssage of time. This is as opposed to an
analysis made at expiration of the options used in the strategy. A dynamic break
even point is one that changes as time passes. A dynamic follow-up action is one
that will change as either the security price changes or the option price changes or
time passes. See also Break-Even Point, Follow-Up Action.
Early Exercise (assignment): the exercise or assignment of an option contract
before its expiration date.
968 Glossary
types of diagonal spreads are diagonal bull spreads, diagonal bear spreads, and
diagonal butterfly spreads.
Discount: an option is trading at a discount if it is trading for less than its intrinsic
value. A future is trading at a discount if it is trading at a price less than the cash
price of its underlying index or commodity. See also Intrinsic Value, Parity.
Discount Arbitrage: a riskless arbitrage in which a discount option is purchased
and an opposite position is taken in the underlying security. The arbitrageur may
either buy a call at a discount and simultaneously sell the underlying security
(basic call arbitrage), or buy a put at a discount and simultaneously buy the under
lying security (basic put arbitrage). See also Discount.
Discretion: see Limit Order, Market Not Held Order.
Dividend Arbitrage: in the riskless sense, an arbitrage in which a put is purchased
and so is the underlying stock. The put is purchased when it has time value pre
mium less than the impending dividend payment by the underlying stock. The
transaction is closed after the stock goes ex-dividend. Also used to denote a form
of risk arbitrage in which a similar procedure is followed, except that the amount
of the impending dividend is unknown and therefore risk is involved in the trans
action. See also Ex-Dividend, Time Value Premium.
Divisor: a mathematical quantity used to compute an index. It is initially an arbitrary
number that reduces the index value to a small, workable number. Thereafter the
divisor is adjusted for stock splits (price-weighted index) or additional issues of
stock (capitalization-weighted index).
Downside Protection: generally used in connection with covered call writing, this
is the cushion against loss, in case of a price decline by the underlying security, that
is afforded by the written call option. Alternatively, it may be expressed in terms
of the distance the stock could fall before the total position becomes a loss (an
amount equal to the option premium), or it can be expressed as percentage of the
current stock price. See also Covered Call Write.
Dynamic: for option strategies, describing analyses made during the course of
changing security prices and during the passage of time. This is as opposed to an
analysis made at expiration of the options used in the strategy. A dynamic break
even point is one that changes as time passes. A dynamic follow-up action is one
that will change as either the security price changes or the option price changes or
time passes. See also Break-Even Point, Follow-Up Action.
Early Exercise (assignment): the exercise or assignment of an option contract
before its expiration date.
968 Glossary
types of diagonal spreads are diagonal bull spreads, diagonal bear spreads, and
diagonal butterfly spreads.
Discount: an option is trading at a discount if it is trading for less than its intrinsic
value. A future is trading at a discount if it is trading at a price less than the cash
price of its underlying index or commodity. See also Intrinsic Value, Parity.
Discount Arbitrage: a riskless arbitrage in which a discount option is purchased
and an opposite position is taken in the underlying security. The arbitrageur may
either buy a call at a discount and simultaneously sell the underlying security
(basic call arbitrage), or buy a put at a discount and simultaneously buy the under
lying security (basic put arbitrage). See also Discount.
Discretion: see Limit Order, Market Not Held Order.
Dividend Arbitrage: in the riskless sense, an arbitrage in which a put is purchased
and so is the underlying stock. The put is purchased when it has time value pre
mium less than the impending dividend payment by the underlying stock. The
transaction is closed after the stock goes ex-dividend. Also used to denote a form
of risk arbitrage in which a similar procedure is followed, except that the amount
of the impending dividend is unknown and therefore risk is involved in the trans
action. See also Ex-Dividend, Time Value Premium.
Divisor: a mathematical quantity used to compute an index. It is initially an arbitrary
number that reduces the index value to a small, workable number. Thereafter the
divisor is adjusted for stock splits (price-weighted index) or additional issues of
stock (capitalization-weighted index).
Downside Protection: generally used in connection with covered call writing, this
is the cushion against loss, in case of a price decline by the underlying security, that
is afforded by the written call option. Alternatively, it may be expressed in terms
of the distance the stock could fall before the total position becomes a loss (an
amount equal to the option premium), or it can be expressed as percentage of the
current stock price. See also Covered Call Write.
Dynamic: for option strategies, describing analyses made during the course of
changing security prices and during the passage of time. This is as opposed to an
analysis made at expiration of the options used in the strategy. A dynamic break
even point is one that changes as time passes. A dynamic follow-up action is one
that will change as either the security price changes or the option price changes or
time passes. See also Break-Even Point, Follow-Up Action.
Early Exercise (assignment): the exercise or assignment of an option contract
before its expiration date.
Glossary 969
Equity Option: an option that has common stock as its underlying security. See also
Non-Equity Option.


ic follow-up action is one
that will change as either the security price changes or the option price changes or
time passes. See also Break-Even Point, Follow-Up Action.
Early Exercise (assignment): the exercise or assignment of an option contract
before its expiration date.
Glossary 969
Equity Option: an option that has common stock as its underlying security. See also
Non-Equity Option.
Equity Requirement: a requirement that a minimum amount of equity must be
present in a margin account. Normally, this requirement is $2,000, but some bro
kerage firms may impose higher equity requirements for uncovered option writing.
Equivalent Positions: positiohs that have similar profit potential, when measured
in dollars, but are constructed with differing securities. Equivalent positions have
the same profit graph. A covered call write is equivalent to an uncovered put write,
for example. See also Profit Graph.
Escrow Receipt: a receipt issued by a bank in order to verify that a customer ( who has
written a call) in fact owns the stock and therefore the call is considered covered.
European Exercise: a feature of an option that stipulates that the option may be
exercised only at its expiration. Therefore, there can be no early assignment with
this type of option.
Exchange-Traded Fund (ETF): an index fund that is listed on a stock exchange.
Options are listed on some ETFs. See also Index Fund.
Ex-Dividend: the process whereby a stock's price is reduced when a dividend is
paid. The ex-dividend date (ex-date) is the date on which the price reduction takes
place. Investors who own stock on the ex-date will receive the dividend, and those
who are short stock must pay out the dividend.
Exercise: to invoke the right granted under the terms of a listed options contract.
The holder is the one who exercises. Call holders exercise to buy the underlying
security, while put holders exercise to sell the underlying security.
Exercise Limit: the limit on the number of contracts a holder can exercise in a fixed
period of time. Set by the appropriate option exchange, it is designed to prevent
an investor or group of investors from "cornering" the market in a stock.
Exercise Price: the price at which the option holder may buy or sell the underlying
security, as defined in the terms of his option contract. It is the price at which the
call holder may exercise to buy the underlying security or the put holder may exer
cise to sell the underlying security. For listed options, the exercise price is the
same as the striking price. See also Exercise.
Expected Return: a rather complex mathematical analysis involving statistical dis
tribution of stock prices, it is the return an investor might expect to make on an
investment if he were to make exactly the same investment many times through
out history.
970 Glossary
Expiration Date: the day on which an option contract becomes void. The expiration
date for listed stock options is the Saturday after the third Friday of the expiration
month. All holders of options must indicate their desire to exercise, if they wish to
do so, by this date. See also Expiration Time.
Expiration Time: the time of day by which all exercise notices must be received on
the expiration date. Technically, the expiration time is currently 5:00 P.M. on the
expiration date, but public holders of option contracts must indicate their desire
to exercise no later than 5:30 P.M. on the business day preceding the expiration
date. The times are Eastern Time. See also Expiration Date.
Facilitation: the process of providing a market for a security. Normally, this refers
to bids and offers made for large blocks of securities, such as those traded by insti
tutions. Listed options may be used to offset part of the risk assumed by the trad
er who is facilitating the large block order. See also Hedge Ratio.
Fair Value: normally, a term used to describe the worth of an option or futures con
tract as determined by a mathematical model. Also sometimes used to indicate
intrinsic value. See also Intrinsic Value, Model.
First Notice Day: the first day upon which the buyer of a futures contract can be
called upon to take delivery. See also Notice Period.
Float: the number of shares outstanding of a particular common stock.
Floor Broker: a trader on the exchange floor who executes the orders of public cus
tomers or other investors who do not have physical access to the trading area.
Follow-Up Action: any trading in an option position after the position is established.
Generally, to limit losses or to take profits.
Fundamental Analysis: a method of analyzing the prospects of a security by observ
ing accepted accounting measures such as earnings, sales, assets, and so on. See
also Technical Analysis.
Futures Contract: a standardized contract calling for the delivery of a specified
quantity of a commodity at a specified date in the future.
Gamma: a measure of risk of an option that measures the amount by which the delta
changes for a I-point change in the stock price; alternatively, when referring to an
entire option position, the amount of change of the delta of the entire position
when the stock changes in price by one point.
Gamma of the Gamma: a mathematical measure of risk that measures by how
much the gamma will change for a I-point move in the stock price. See Gamma.
Glossary 971
Good Until Canceled (GTC): a designation applied to some types of orders, mean
ing that the order remains in effect until it is either filled or canceled. See also
Limit, Stop-Limit Order, Stop Order.
Hedge Ratio: the mathematical quantity that is equal to the delta of an option. It is
useful in facilitation in that a theoretically riskless hedge can be established by tak
ing offsetting positions in the underlying stock and its call options. See also Delta,
Facilitation.
Historic Volatility: See Volatility.
Holder: the owner of a security.
Horizontal Spread: an option strategy


Stop Order.
Hedge Ratio: the mathematical quantity that is equal to the delta of an option. It is
useful in facilitation in that a theoretically riskless hedge can be established by tak
ing offsetting positions in the underlying stock and its call options. See also Delta,
Facilitation.
Historic Volatility: See Volatility.
Holder: the owner of a security.
Horizontal Spread: an option strategy in which the options have the same striking
price, but different expiration dates.
Implied Volatility: a prediction of the volatility of the underlying stock, it is deter
mined by using prices currently existing in the option market at the time, rather
than using historical data on the price changes of the underlying stock See also
Volatility.
Incremental Return Concept: a strategy of covered call writing in which the
investor is striving to earn an additional return from option writing against a stock
position that he is targeted to sell, possibly at substantially higher prices.
Index: a compilation of the prices of several common entities into a single number.
See also Capitalization-Weighted Index, Price-Weighted Index.
Index Arbitrage: a form of arbitraging index futures against stock If futures are
trading at prices significantly higher than fair value, the arbitrager sells futures and
buys the exact stocks that make up the index being arbitraged; if futures are at a
discount to fair value, the arbitrage entails buying futures and selling stocks.
Index Fund: a mutual fund whose components exactly match the stocks that make
up a widely disseminated index, such as the S&P 500, Dow-Jones, Russell 2000, or
NASDAQ-100. See also Exchange-Traded Fund.
Index Option: an option whose underlying entity is an index. Most index options are
cash-based.
Institution: an organization, probably very large, engaged in investing in securities.
Normally a bank, insurance company, or mutual fund.
Intermarket Spread: a futures spread in which futures contracts in one market are
spread against futures contracts trading in another market. Examples: Currency
spreads (yen vs. deutsche mark) or TED spread (T-Bills vs. Eurodollars).
972 Glossary
In-the-Money: a term describing any option that has intrinsic value. A call option is
in-the-money if the underlying security is higher than the striking price of the call.
A put option is in-the-money if the security is below the striking price. See also
Intrinsic Value, Out-of-the-Money.
Intramarket Spread: a futures spread in which futures contracts are spread against
other futures contracts in the same market; example, buy May soybeans, sell
March soybeans.
Intrinsic Value: the value of an option if it were to expire immediately with the
underlying stock at its current price; the amount by which an option is in-the
money. For call options, this is the difference between the stock price and the
striking price, if that difference is a positive number, or zero otherwise. For put
options it is the difference between the striking price and the stock price, if that
difference is positive, and zero otherwise. See also In-the-Money, Parity, Time
Value Premium.
Last Trading Day: the third Friday of the expiration month. Options cease trading
at 3:00 P.M. Eastern Time on the last trading day.
LEAPS: Long-term Equity Anticipation Securities. These are long-term listed
options, currently having maturities as long as two and one-half years.
Leg: a risk-oriented method of establishing a two-sided position. Rather than enter
ing into a simultaneous transaction to establish the position (a spread, for exam
ple), the trader first executes one side of the position, hoping to execute the other
side at a later time and a better price. The risk materializes from the fact that a
better price may never be available, and a worse price must eventually be accept
ed.
Letter of Guarantee: a letter from a bank to a brokerage firm stating that a cus
tomer (who has written a call option) does indeed own the underlying stock and
the bank will guarantee delivery if the call is assigned. Thus, the call can be con
sidered covered. Not all brokerage firms accept letters of guarantee.
Leverage: in investments, the attainment of greater percentage profit and risk
potential. A call holder has leverage with respect to a stockholder-the former will
have greater percentage profits and losses than the latter, for the same movement
in the underlying stock.
Limit: see Trading Limit.
Limit Order: an order to buy or sell securities at a specified price (the limit). A limit
order may also be placed "with discretion" -a fixed; usually small, amount such as
1/s or ¼ of a point. In this case, the floor broker executing the order may use his
Glossary 973
discretion to buy or sell at 1/s or ¼ of a point beyond the limit if he feels it is nec
essary to fill the order.
Listed Option: a put or call option that is traded on a national option exchange.
Listed options have fixed striking prices and expiration dates. See also Over-the
Counter Option.
Local: a trader on a futures exchange who buys and sells for his own account and
may fill public orders.
Lognormal Distribution: a statistical distribution that is often applied to the move
ment of the stock prices. It is a convenient and logical distribution because it
implies that stock prices can theoretically rise forever but cannot fall below zero-
a fact which is, of course, true.
Margin: to buy a security by borrowing funds from a brokerage house. The margin
requirement-the maximum percentage of the investment that can be loaned by
the broker firm-is set by the Federal Reserve Board.
Market Basket: a portfolio of common stocks whose performance is intended to
simulate the performance of a specific index. See Index.
Market-Maker: an exchange member whose function is to aid in the making of a
market, by making bids and offers for his account in the absence of public buy or
sell orders. Several market-makers are


oaned by
the broker firm-is set by the Federal Reserve Board.
Market Basket: a portfolio of common stocks whose performance is intended to
simulate the performance of a specific index. See Index.
Market-Maker: an exchange member whose function is to aid in the making of a
market, by making bids and offers for his account in the absence of public buy or
sell orders. Several market-makers are normally assigned to a particular security.
The market-maker system encompasses the market-makers and the board bro
kers. See also Board Broker, Specialist.
Market Not Held Order: also a market order, but the investor is allowing the floor
broker who is executing the order to use his own discretion as to the exact timing
of the execution. If the floor broker expects a decline in price and he is holding a
"market not held" buy order, he may wait to buy, figuring that a better price will
soon be available. There is no guarantee that a "market not held" order will be
filled.
Market Order: an order to buy or sell securities at the current market. The order
will be filled as long as there is a market for the security.
Married Put and Stock: a put and stock are considered to be married if they are
bought on the same day, and the position is designated at that time as a hedge.
Model: a mathematical formula designed to price an option as a function of certain
variables-generally stock price, striking price, volatility, time to expiration, divi
dends to be paid, and the current risk-free interest rate. The Black
Scholes model is one of the more widely used models.
974 Glossary
Monte Carlo Simulation: a model designed to simulate a real-world event that can
not be approximated merely with a mathematical formula. The Monte Carlo sim
ulation approximates such an event (the movement of the stock market, for exam
ple) and then it is simulated a great number of times. The net result of all the sim
ulations is then interpreted as the result, generally expressed as a probability of
occurrence. For example, a Monte Carlo simulation can be used to determine how
stocks might behave under certain stock price distributions that are different from
the lognormal distribution.
Naked Option: see Uncovered Option.
Narrow-Based: Generally referring to an index, it indicates that the index is com
posed of only a few stocks, generally in a specific industry group. Narrow-based
indices are not subject to favorable treatment for naked option writers. See also
Broad-Based.
"Net" Order: see Contingent Order.
Neutral: describing an opinion that is neither bearish or bullish. Neutral option
strategies are generally designed to perform best if there is little nor no net change
in the price of the underlying stock. See also Bearish, Bullish.
Non-Equity Option: an option whose underlying entity is not common stock; typi
cally refers to options on physical commodities, but may also be extended to
include index options.
"Not Held": see Market Not Held Order.
Notice Period: the time during which the buyer of a futures contract can be called
upon to accept delivery. Typically, the 3 to 6 weeks preceding the expiration of the
contract.
Open Interest: the net total of outstanding open contracts in a particular option
series. An opening transaction increases the open interest, while any closing trans
action reduces the open interest.
Opening Transaction: a trade that adds to the net position of an investor. An open
ing buy transaction adds more long securities to the account. An opening sell
transaction adds more short securities. See also Closing Transaction.
Option Pricing Curve: a graphical representation of the projected price of an
option at a fixed point in time. It reflects the amount of time value premium in the
option for various stock prices, as well. The curve is generated by using a mathe
matical model. The delta ( or hedge ratio) is the slope of a tangent line to the curve
at a fixed stock price. See also Delta, Hedge Ratio, Model.
Glossary 975
Options Clearing Corporation (OCC): the issuer of all listed option contracts that
are trading on the national option exchanges.
Original Issue Discount (O1D): the initial price of a zero-coupon bond. The owner
owes taxes on the theoretical interest, or phantom income, generated by the annu
al appreciation of the bond toward maturity. In reality, no interest is paid by the
zero-coupon bond, but the government is taxing the appreciation of the bond as if
it were interest.
Out-of-the-Money: describing an option that has no intrinsic value. A call option is
out-of-the-money if the stock is below the striking price of the call, while a put
option is out-of-the-money if the stock is higher than the striking price of the put.
See also In-the-Money, Intrinsic Value.
Over-the-Counter Option (OTC): an option traded over-the-counter, as opposed
to a listed stock option. The OTC option has a direct link between buyer and sell
er, has no secondary market, and has no standardization of striking prices and expi
ration dates. See a'lso Listed Option, Secondary Market.
Overvalued: describing a security trading at a higher price than it logically should.
Normally associated with the results of option price predictions by mathematical
models. If an option is trading in the market for a higher price than the model indi
cates, the option is said to be overvalued. See a'/so Fair Value, Undervalued.
Pairs Trading: a hedging technique in which one buys a particular stock and sells
short another stock. The two stocks are theoretically linked in their price history,
and the hedge is established when the historical relationship is out of line, in hopes
that it will return to its former correlation.
Parity: describing an in-the-money option trading for its intrinsic value: that is, an
option trading at parity with the underlying stock. Also used as a point of refer
ence-an option is sometimes said to be trading at a half-point over parity or at a
quart


ry,
and the hedge is established when the historical relationship is out of line, in hopes
that it will return to its former correlation.
Parity: describing an in-the-money option trading for its intrinsic value: that is, an
option trading at parity with the underlying stock. Also used as a point of refer
ence-an option is sometimes said to be trading at a half-point over parity or at a
quarter-point under parity, for example. An option trading under parity is a dis
count option. See a'/so Discount, Intrinsic Value.
PERCS: Preferred Equity Redemption Cumulative Stock. Issued by a corporation,
this preferred stock pays a higher dividend than the common and has a price at
which it can be called in for redemption by the issuing corporation. As such, it is
really a covered call write, with the call premium being given to the holder in the
form of increased dividends. See Call Price, Covered Call Write, Redemption Price.
Physical Option: an option whose underlying security is a physical commodity that
is not stock or futures. The physical commodity itself, typically a currency or
976 Glossary
Treasury debt issue, underlies that option contract. See also Equity Option, Index
Option.
Portfolio Insurance: a method of selling index futures or buying index put options
to protect a portfolio of stocks.
Position: as a noun, specific securities in an account or strategy. A covered call writ
ing position might be long 1,000 XYZ and short 10 XYZ January 30 calls. As a verb,
to facilitate; to buy or sell-generally a block of securities-thereby establishing a
position. See also Facilitation, Strategy.
Position Limit: the maximum number of put or call contracts on the same side of
the market that can be held in any one account or group of related accounts. Short
puts and long calls are on the same side of the market. Short calls and long puts
are on the same side of the market.
Premium: for options, the total price of an option contract. The sum of the intrinsic
value and the time value premium. For futures, the difference between the
futures price and the cash price of the underlying index or commodity.
Present Worth: a mathematical computation that determines how much money
would have to be invested today, at a specified rate, in order to produce a desig
nated amount at some time in the future. For example, at 10% for one year, the
present worth of $ll0 is $100.
Price-Weighted Index: a stock index that is computed by adding the prices of each
stock in the index, and then dividing by the divisor. See also Capitalization
Weighted Index, Divisor.
Profit Graph: a graphical representation of the potential outcomes of a strategy.
Dollars of profit or loss are graphed on the vertical axis, and various stock prices
are graphed on the horizontal axis. Results may be depicted at any point in time,
although the graph usually depicts the results at expiration of the options involved
in the strategy.
Profit Range: the range within which a particular position makes a profit. Generally
used in reference to strategies that have two break-even points-an upside break
even and a downside break-even. The price range between the two break-even
points would be the profit range. See also Break-Even Point.
Profit Table: a table of results of a particular strategy at some point in time. This is
usually a tabular compilation of the data drawn on a profit graph. See also Profit
Graph.
Glossary 917
Program Trading: the act of buying or selling a particular portfolio of stocks and
hedging with an offsetting position in index futures. The portfolio of stocks may be
small or large, but it is not the makeup of any stock index. See also Index Arbitrage.
Protected Strategy: a position that has limited risk. A protected short sale (short
stock, long call) has limited risk, as does a protected straddle write ( short straddle,
long out-of-the-money combination). See also Combination, Straddle.
Public Book (of orders): the orders to buy or sell, entered by the public, that are
away from the current market. The board broker or specialist keeps the public
book. Market-makers on the CBOE can see the highest bid and lowest offer at any
time. The specialist's book is closed ( only he knows at what price and in what quan
tity the nearest public orders are). See also Board Broker, Market-Maker,
Specialist.
Put: an option granting the holder the right to sell the underlying security at a cer
tain price for a specified period of time. See also Call.
Put-Call Ratio: the ratio of put trading volume divided by call trading volume;
sometime~ calculated with open interest or total dollars instead of trading volume.
Can be calculated daily, weekly, monthly, etc. Moving averages are often used to
smooth out short-term, daily figures.
Ratio Calendar Combination: a strategy consisting of a simultaneous position of a
ratio calendar spread using calls and a similar position using puts, where the strik
ing price of the calls is greater than the striking price of the puts.
Ratio Calendar Spread: selling more near-term options than longer-term ones
purchased, all with the same strike, either puts or calls.
Ratio Spread: constructed with either puts or calls, the strategy consists of buying a
certain amount of options and then selling a larger quantity of out-of-the-money
options.
Ratio Strategy: a strategy in which one has an unequal number of long securities
and short securities. Normally, it implies a preponderance of short options over
either long options or long stock.
Ratio Write: buying stock and selling a preponderance of calls against the stock that
is owned. ( Occasionally constructed as shorting stock and selling puts.)
Redemption Price: the price at which a structured product may be redeemed for
cash. This is distinctly different from a "call price," which is the price at which an
issue may be called away by the issuer. See also Call Price, PERCS, Structured
Product.
978 Gloss


d selling a preponderance of calls against the stock that
is owned. ( Occasionally constructed as shorting stock and selling puts.)
Redemption Price: the price at which a structured product may be redeemed for
cash. This is distinctly different from a "call price," which is the price at which an
issue may be called away by the issuer. See also Call Price, PERCS, Structured
Product.
978 Glossary
Resistance: a term in technical analysis indicating a price area higher than the cur
rent stock price where an abundance of supply exists for the stock, and therefore
the stock may have trouble rising through the price. See also Support.
Return (on investment): the percentage profit that one makes, or might make, on
his investment.
Return if Exercised: the return that a covered call writer would make if the under
lying stock were called away.
Return if Unchanged: the return that an investor would make on a particular posi
tion if the underlying stock were unchanged in price at the expiration of the
options in the position.
Reversal Arbitrage: a riskless arbitrage that involves selling the stock short, writing
a put, and buying a call. The options have the same terms. See also Conversion
Arbitrage.
Reverse Hedge: a strategy in which one sells the underlying stock short and buys
calls on more shares than he has sold short. This is also called a synthetic straddle
and is an outmoded strategy for stocks that have listed puts trading. See also Ratio
Write, Straddle.
Reverse Strategy: a general name that is given to strategies that are the opposite of
better-known strategies. For example, a ratio spread consists of buying calls at a
lower strike and selling more calls at a higher strike. A reverse ratio spread, also
known as a backspread, consists of selling the calls at the lower strike and buying
more calls at the higher strike. The results are obviously directly opposite to each
other. See also Reverse Hedge Ratio Write, Reverse Hedge.
Rho: the measure of how much an option changes in price for an incremental mov<'
(generally l % ) in short-term interest rates; more significant for longer-term or i11-
the-money options.
Risk Arbitrage: a form of arbitrage that has some risk associated with it. Commonly
refers to potential takeover situations in which the arbitrageur buys the stock of
the company about to be taken over and sells the stock of the company that is
effecting the takeover. See also Dividend Arbitrage.
Roll: a follow-up action in which the strategist closes options currently in the posi
tion and opens other options with different terms, on the same underlying stock.
See also Roll Down, Roll Forward, and Roll Up.
Roll Down: close out options at one strike and simultaneously open other options al
a lower strike.
Glossary 979
Roll Forward: close out options at a near-term expiration date and open options at
a longer-term expiration date.
Roll Up: close out options at a lower strike and open options at a higher strike.
Rotation: a trading procedure on the open exchanges whereby bids and offers, but
not necessarily trades, are made sequentially for each series of options on an
underlying stock or index.
Secondary M~ket: any market in which securities can be readily bought and sold
after their initial issuance. The national listed option exchanges provided, for the
first time, a secondary market in stock options.
Serial Option: a futures option for which there is no corresponding futures contract
expiring in the same month. The underlying futures contract is the next futures
contract out in time. Example: There is no March gold futures contract, but there
is an April gold futures contract, so March gold options, which are serial options,
are options on April gold futures.
Series: all op,tion contracts on the same underlying stock having the same striking
price, expiration date, and unit of trading.
Skew: See Volatility Skew.
Specialist: an exchange member whose function it is both to make markets-buy
and sell for his own account in the absence of public orders-and to keep the book
of public orders. Most stock exchanges and some option exchanges utilize the spe
cialist system of trading
Spread Order: an order to simultaneously transact two or more option trades.
Typically, one option would be bought while another would simultaneously be
sold. Spread orders may be limit orders, not held orders, or orders with discretion.
They cannot be stop orders, however. The spread order may be either a debit or a
credit.
Spread Strategy: any option position having both long options and short options of
the same type on the same underlying security.
Standard Deviation: a measure of the volatility of a stock. It is a statistical quanti
ty measuring the magnitude of the daily price changes of that stock. See also,
Volatility.
Stop Order: an order, placed away from the current market, that becomes a market
order if the security trades at the price specified on the stop order. Buy stop orders
are placed above the market, while sell stop orders are placed below.
980 Glossary
Stop-Limit Order: similar to a stop order, the stop-limit order becomes a limit
order, rather than a market order, when the security trades at the price specified
on the stop. See also Stop Order.
Straddle: the purchase or sale of an equal number of puts and calls having the same
terms.
Strangle: a combination involving a put and a call at different strikes with the same
expiration date.
Strategy: with respect to option investments, a preconceived, logical plan of position
selection and follow-up action.
Striking Price: see Exercise Price.
Striking Price Interval: the distance between striking prices on a particular under
lying security. For stocks, the interval is normally 2.5 points for lower-priced stocks
and 5 points for higher-priced stocks. For indices, the interval is either 5 or 10
points. For futures, the interval is often as low as one or two points.
Str


ection and follow-up action.
Striking Price: see Exercise Price.
Striking Price Interval: the distance between striking prices on a particular under
lying security. For stocks, the interval is normally 2.5 points for lower-priced stocks
and 5 points for higher-priced stocks. For indices, the interval is either 5 or 10
points. For futures, the interval is often as low as one or two points.
Structured Product: a combination of securities and possibly options into a single
security that behaves like stock and trades on a listed stock exchange. Structured
products are created by many of the largest financial institutions (banks and bro
kerage firms). Many of the more popular ones are known by their acronyms, cre
ated by the institutions that issued them: MITTS, TARGETS, BRIDGES, LINKS,
DINKS, ELKS, and PERCS. See also PERCS.
Subindex: see Narrow-Based.
Suitable: describing a strategy or trading philosophy in which the investor is operat
ing in accordance with his financial means and investment objectives.
Support: a term in technical analysis indicating a price area lower than the current
price of the stock, where demand is thought to exist. Thus, a stock would stop
declining when it reached a support area. See also Resistance.
Synthetic Put: a strategy constructed by shorting the underlying instrument and
buying a call. The resulting position has the same profit and loss characteristics as
a long put option.
Synthetic Stock: an option strategy that is equivalent to the underlying stock. A long
call and a short put is synthetic long stock. A long put and a short call is synthetic
short stock.
Technical Analysis: the method of predicting future stock price movements based
on observation of historical stock price movements.
Glossary 981
Terms: the collective name denoting the expiration date, striking price, and under
lying stock of an option contract.
Theoretical Value: the price of an option, or a spread, as computed by a mathe
matical model.
Theta: the measure of how much an option's price decays for each day of time that
passes.
Time Spread: see Calendar Spread.
Time Value Premium: the amount by which an option's total premium exceeds its
intrinsic value.
Total Return Concept: a covered call writing strategy in which one views the
potential profit of the strategy as the sum of capital gains, dividends, and option
premium.income, rather than viewing each one of the three separately.
Tracking Error: the amount of difference between the performance of a specific
portfolio of stocks and a broad-based index with which they are being compared.
See Market Basket.
Trader: a speculative investor or professional who makes frequent purchases and
sales.
Trading Limit: the exchange-imposed maximum daily price change that a futures
contract or futures option contract can undergo.
Treasury BilVOption Strategy: a method of investment in which one places
approximately 90% of his funds in risk-free, interest-bearing assets such as
Treasury bills, and buys options with the remainder of his assets.
Type: the designation to distinguish between a put or call option.
Uncovered Option: a written option is considered to be uncovered if the investor
does not have a corresponding position in the underlying security. See also
Covered.
Underlying Security: the security that one has the right to buy or sell via the terms
of a listed option contract.
Undervalued: describing a security that is trading at a lower price than it logically
should. Usually determined by the use of a mathematical model. See also Fair
Value, Overvalued.
Variable Ratio Write: an option strategy in which the investor owns 100 shares of
the underlying security and writes two call options against it, each option having a
different striking price.
982 Glossary
Vega: the measure of how much an option's price changes for an incremental
change-usually one percentage point-in volatility.
Vertical Spread: any option spread strategy in which the options have different
striking prices but the same expiration dates.
Volatility: a measure of the amount by which an underlying security is expected to
fluctuate in a given period of time. Generally measured by the annual standard
deviation of the daily price changes in the security, volatility is not equal to the beta
of the stock. Also called historical volatility, statistical volatility, or actual volatility.
See also Implied Volatility.
Volatility Skew: the term used to describe a phenomenon in which individual
options on a single underlying instrument have different implied volatilities. I 11
general, not only are the individual options' implied volatilities different, but they
form a pattern. If the lower striking prices have the lowest implied volatilities, and
then implied volatility progresses higher as one moves up through the striking
prices, that is called a forward or positive skew. A reverse or negative skew works
in the opposite way: The higher strikes have the lowest implied volatilities.
Warrant: a long-term, nonstandardized security that is much like an option.
Warrants on stocks allow one to buy (usually one share of) the common at a ("(•r
tain price until a certain date. Index warrants are generally warrants on the pri<·<·
of foreign indices. Warrants have also been listed on other things such as cross-('m
rency spreads and the future price of a barrel of oil.
Write: to sell an option. The investor who sells is called the writer.
Index
Adjusted volatility, 539
Advanced concepts, 846-907
"greeks," 848-866, 902-905
delta, 848-853, 866
gamma, 853-859, 867, 882
gamma of the gamma, 865-866, 902-905
rho, 864-865
"six measures of risk," 865
strategy considerations using, 866-901 (see also
Advanced concepts, strategy considerations,
using greeks)
summary, 866
theta, 862-864, 866
vega/tau, 859-862, 866
mathematical concepts, advanced, 901-907
difference of implied volatilities, measuring, 905-907
gamma of the


48-853, 866
gamma, 853-859, 867, 882
gamma of the gamma, 865-866, 902-905
rho, 864-865
"six measures of risk," 865
strategy considerations using, 866-901 (see also
Advanced concepts, strategy considerations,
using greeks)
summary, 866
theta, 862-864, 866
vega/tau, 859-862, 866
mathematical concepts, advanced, 901-907
difference of implied volatilities, measuring, 905-907
gamma of the gamma, 902-905
"greeks," calculating, 901-902
neutrality, 846-847
strategy considerations, using "greeks," 866-901
delta neutral, 868-879
evaluating position using risk measures, 885-892
mathematical approach, 883-885
multifaceted neutrality, creating, 879-883
risk exposure, general, of common, 866-868
trading gamma from long side, 893-901
summary, 907
tau, 859-862
American exercise, 501-504
American Stock Exchange, 22
Index,497,500
structured products listed, 618
Arbitrage, 251-252, 253-255, 422-455, 641-644
block positioning, 455
boxspreads,439-443,643-644
risks, 443
call arbitrage, 444
carrying costs, 430-431
conversions and reversals, 428-430, 431-438,
642-643
borrowing stock to sell short, 432-433
risksin,fou½433-437
summary, 437-438
"using box stock," 432
discounting, 423-425, 641-642
dividend, 425-428
effects, 444-445
equivalence, variations on, 443-444
facilitation (block positioning), 455
"interest play" strategy, 438-439
pairs trading, 454-455
as hedged strategy, 454
put arbitrage, 445
put and call, basic (discounting), 423-425
risk arbitrage, 21, 426-427
definition, 445
risk arbitrage using options, 445-454
"hooks," 449-450
limits on merger, 448-450
mergers, 445-448
profitability, 454
short tendering, 453
tender offers, 451-454 (see also Tender offers)
synthetic put, 439-440
Arbitrageurs, 19-21 (see also Arbitrage)
definition, 422
role of in butterfly spread, 338
box spread, 338
983
984
Assignment of options, 7, 16-22
anticipating, 18-22
automatic, 18-19
call options, 7
of cash-based options, 501
commissions, 17-18
margin requirements, 16-17
put options, 7
Backspreads, 232-235 (see also Reverse spreads)
diagonal, 240-241
effect on of implied volatility changes, 781-782
and LEAPS, 407-408
Bear spreads using call options, 186-190
call bear spread, 186-188
as credit spread, 186
follow-up action, 190
assignment of short call, impending, 190
selecting, 189-190
an aggressive position usually, 189
summary, 190
Bear spread, put, 329-332 (see also Put spreads, basic)
Beta, 533-539
Black, Fisher, 459
Black-Scholes model, 456-466, 538, 610, 611, 635, 640,
644-645,646,647-648,651,677,678, 731,734,
758, 767-768, 798,902 (see also Mathematical
applications)
Black model, 647-648, 651, 677
characteristics, 459-461
dividends paid by common stock not included, 459
formula, 456-457
hedge ratio, 457
historical volatility, lognormal, computing, 461-466
lognormal distribution of stock prices, 460
vega, 750
volatility, computation of, 460-466
weighting factor, 459-460, 463-465
Block positioning, 455, 482-485 (see also Mathematical
applications)
Board broker system, 22
Box spread, 338, 439-44,3, 643-644
risks, 443
"Box" stock, 432
Broad-based indices, 500
Brownian motion, 806
Bull spread, structured product as, 608-612
valuing, 610-612
Bull spreads, 110-111, 113-116, 117, 172-185
aggressiveness, degrees of, 175-176
call bull spread, 172-173
effect on of implied volatility changes, 767-775
follow-up action, 178-180
credit spread, 179
"legging" out of spread, 180
and outright purchase, comparison of, 179
and LEAPS, 403-404
ranking, 176-178
diagonal bull spread, 177
summary, 185
uses, other, 180-184
Index
break-even price on common stock, lowering, 182,
183
simple form of spreading, 180, 185
as "substitute" for covered writing, 182-184
vertical, 172
when options are expensive, 177
Bull spread, put, 332-333 (see also Put spreads, basic)
Bullish calendar spread, 196-198 (see also Calendar
spread)
Butterfly spread, 200-209, 336-338 (see also Put
spreads, basic)
combination of bull and bear spreads, 200, 209
commissions costly, 200, 203
example, 201
follow-up action, 206-209
assignment, 206
"legging out," 207
neutral position, 200
results of at expiration, 201-203
selecting, 203-206
striking prices, three, 200-203
summary, 209
Calendar combination of calls and puts, 345-348
Calendar spread, 116-117, 191-199
as antivolatility strategy, 194
bullish, 196-198, 199
follow-up action, 197-198
definition, 191
expiration series, using all three, 198-199
horizontal spread, 191
in volatility trading, 825-826
and LEAPS, 408-409
mathematical calculations of volatility, applying lo.
478-480
neutral, 192-194, 199
follow-up action, 194-196
volatility, effect of, 194
summary, 199
time spread another name, 191
volatility changes, effect of on, 778-780
with futures options, 704-709 (see also Futtm's
options and strategies)
Index
Calendar spread, put, 333-335 (see also Put spreads,
basic) 333-335
Calendar and ratio spreads, combining, 222-229
choosing spread, 225-226
pricing model, using, 225
delta-neutral calendar spreads, 227-228
in-the-money, 228
follow-up action, 226-227, 229
probabilities, good, 226-227
out-of-the-money call spread, 222-225 (see also
Calendar and ratio spreads, combining, ratio
calendar spread)
ratio calendar spread, 222-225
collateral requirements possibly large, 223-224
profitability of, 227
Calendar straddle, 348-350 (see also Spreads combining
calls and puts)
Call arbitrage, 444 (see also Arbitrage)
Call bull spread, effect on of implied volatility changes,
767-775
Call buying, 95-117
advanced selection criteria, 103-107
overpriced/underpriced calls, 106-107
time value premium and volatility trading, 106-107
volatilities of underlying stock, 103-106
follow-up actions, 107-117
bull spread, 110-111, 113-116, 117
calendar spread, creating, 116-117
commissions, 108
defensive action, two strategies for, 112-117
locking in profits