Chapter 28: Mathematical Applications 479
Theoretical synthetic Theoretical Strike Stock D" .d d = + - + 1vi en s put price call price price price
When the ranking analysis is performed, very few synthetic puts will appear as
attractive put buys. This is because, when the customer buys a synthetic put, he must
advance the full cost of the dividend, but receives no offsetting cost reduction for the
credit being earned by the short stock position. Consequently, synthetic puts are
always more expensive, on a relative basis, than are listed puts. However, if one is par
ticularly bearish on a stock that has no listed puts, a synthetic put may still prove to
be a worthwhile investment. The recommended analysis can give him a feeling for
the reward and risk potential of the investment.
CALENDAR SPREADS
The pricing nwdel can help in determining which neutral calendar spreads are nwst
attractive. Recall that in a neutral calendar spread, one is selling a near-term call and
buying a longer-term call, when the stock is relatively close to the striking price of the
calls. The object of the spread is to capture the time decay differential between the
two options. The neutral calendar spread is normally closed when the near-term
option expires. The pricing model can aid the spreader by estimating what the prof
it potential of the spread is, as well as helping in the determination of the break-even
points of the position at near-term expiration.
To determine the maximum profit potential of the spread, assume that the near
term call expires worthless and use the pricing model to estimate the value of the
longer-term call with the stock exactly at the striking price. Since commission costs
are relatively large in spread transactions, it would be best to have the computations
include commissions. Calculating a second profit potential is sometimes useful as
well the profit if unchanged. To determine how much profit would be made if the
stock were unchanged at near-term expiration, assume that the spread is closed with
the near-term call equal to its intrinsic value (zero if the stock is currently below the
strike, or the difference between the stock price and the strike if the stock is initial
ly above the strike). Then use the pricing model to estimate the value of the longer
term call, which will then have three or six months of life remaining, with the stock
unchanged. The resulting differential between the near-term call's intrinsic value and
the estimated value of the longer-term call is an estimate of the price at which the
spread could be liquidated. The profit, of course, is that differential minus the cur
rent (initial) differential, less commissions.
In the earlier discussion of calendar spreads, it was pointed out that there is
both an upside break-even point and a downside break-even point at near-term expi
ration. These break-even points can be estimated with the use of the pricing model.

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480 Part IV: Additional Considerations
One method of determination involves estimating the liquidating value of the spread
at successive stock prices. When the liquidating value is found to be equal to the ini
tial value, plus commissions, a break-even point has been located.
Example: If the spread in question is using options with a striking price of 30, one
would begin his break-even point calculations at a price of 30. Estimate the liquidat
ing value of the spread at 30, 297/s, 29¾, 29-5/s, and so forth until the break-even point
is found. Once the downside break-even point has been determined in this manner,
the iterations to locate the upside break-even point should begin again at the striking
price. Thus, one would evaluate the liquidating value at 30, 301/s, 30¼, and so on. This
is somewhat of a brute-force method, but with a computer it is fairly fast. The num
ber of calculations can be reduced by adopting a more complicated iteration process.
A final useful piece of information can be obtained with the aid of the pricing
model - the theoretical value of the spread. Recompute the estimated value of both
the near-term and longer-term calls at the current time and stock price, using the
implied volatility for the underlying stock. The resultant differential between the two
estimated call prices may differ substantially from the actual differential, perhaps
highlighting an attractive calendar spread situation. One would want to establish
spreads in which the theoretical differential is greater than the actual differential
(that is, he would want to buy a "cheap" calendar spread).
Once these pieces of information have been computed, the strategist can rank
the spread possibilities by whatever criterion he finds most workable. The logical
method of ranking the spreads is by their return if unchanged. The spreads with the
highest return if unchanged at near-term expiration are those in which the stock price
and striking price were close together initially, a basic requirement of the neutral cal
endar spread. More complicated ranking systems should tty to include the theoreti
cal value of the spread and possibly even the maximum potential of the spread. A
similar analysis can, of course, be worked out for put calendar spreads, using the
arbitrage pricing model for puts.
RATIO STRATEGIES
Ratio strategies involve selling naked options. Therefore, the strategist has potential
ly large risk, either to the upside or to the downside or both. He should attempt to
get a feeling for how probable this risk is. The formulae for determining the proba
bility of a stock being above or below a certain price at some time in the future can
give him these probabilities. For example, in a straddle writing situation, the strate
gist would want to compute such arithmetic quantities as maximum profit potential,
return if unchanged, collateral required at upside break-even point or at upside

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Chapter 29: Introduction to Index Option Products and Futures 513
At the present time, there are futures options on all of the various index futures
contracts.
EXPIRATION DATES
Futures options have specifics much the same as stock options do: expiration month
(agreeing with the expiration months of the underlying futures contract), striking
price, etc. If a trader buys a futures option, he must pay for it in full, just as with stock
options. Margin requirements vary for naked futures options, but are generally more
lenient than stock options. Often, the naked requirement is based on the futures
margin, which is much less than the 20% of the underlying stock price as is the case
with listed stock options.
When the futures option has a cash-based futures contract underlying it, the
option and the future generally expire on the same day. Thus, if one were to exercise
a '.ZYX option on expiration day, one would receive the future in his account, which
would in tum become cash because the future is cash-settled and expiring as well.
Example: Suppose that a trader owns a '.ZYX December 165 futures worth $500 per
point - call option and holds it through the last day of trading. On that last day, the
'.ZYX Index closes at 174.00. He gives instructions to exercise the call, so the follow
ing sequence occurs:
1. Buy one '.ZYX future at 165.00 via the call exercise.
2. Mark the future at 17 4.00, the closing price. This is a variation margin profit of
$4,500 (174.00-165.00) X $500.
3. The option is removed from the account because it was exercised, and the future
is removed as well because it expired.
Thus, the exercise of the option generates $4,500 in cash into the account and leaves
behind no futures or option contracts. We do not know if this represents a profit or
loss for this call holder, since we do not know if his original cost was greater than
$4,500 or not.
It should be noted that futures option expiration dates, in general, are fairly
complex. They are not normally the third Friday of the expiration month, as stock
options are. Index futures options generally do expire on the third Friday of the expi
ration month, but many physical commodity options do not. These differences will
be discussed in the later chapter on futures options.

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514 Part V: Index Options and Futures
OPTION PREMIUMS
The dollar amount of trading of a futures option contract is normally the same as that
of the underlying future. That is, since the S&P 500 future is worth $250 per point,
so are the S&P 500 futures options. The same holds true for the New York Stock
Exchange Index options.
Example: An investor buys an S&P 500 December 1410 call for 4.20 with the index
at 1409.50. The cost of the call is $1,050 (4.20 x 250). The call must be paid for in
full, as with equity options.
An interesting fact about futures options is that the longer-term options have a
"double premium" effect. The option itself has time value premium and its underly
ing security, the future, also has a premium over the physical commodity. This phe
nomenon can produce some rather startling prices when looking at calendar spreads.
Example: The ZYX Index is trading at 162.00 sometime during the month of
January. Suppose that the March ZYX futures contract is trading at 163.50 and the
June futures contract at 167.50. These prices are reasonable in that they represent a
premium over the index itself which is 162.00. These premiums are related to the
amount of time remaining until the expiration of the futures contract.
Now, however, let us look at two options - the March 165 put and the June 165
put. The March 165 put might be trading at 3 with its underlying security, the March
futures contract, trading at 163.50. The June 165 put option has as its underlying
security the June futures contract. Since the June option has more time remaining
until expiration, it will have more time value premium than a March option would.
However, the underlying June future is trading at 167.50, so the June 165 put option
is 2½ points out-of-the-money and therefore might be selling for 2½. This makes a
very strange-looking calendar spread with the longer-term option selling at 2½ and
the near-term option selling for 3. This is due to the fact, of course, that the two
options have different underlying securities. One is in-the-money and the other is
out-of-the-money. These two underlyings - the March and June futures - have a
price differential of their own. So the option calendar spread is inverted due to this
double premium effect.
FUTURES OPTION MARGIN
Most futures exchanges have gone to the form of option margin called SPAN, which
stands for Standard Portfolio Analysis of Risk. This form of margining is very fair and
attempts to base the margin requirement of an option position on the probability of

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Chapter 29: Introduction to Index Option Products and Futures 515
movement by the underlying futures contract, as well as on the potential change of
implied volatility of the options in question.
The older method of margining option positions is known as the "customer mar~
gin" method. The customer margin method generally results in higher margin
requirements. The reader is referred to the chapter on futures and futures options
for an in-depth discussion of SPAN and other option margin requirements.
OTHER TERMS
Just as futures on differing physical commodities have differing terms, so do options
on those futures. Some options have striking prices 5 points apart while others have
strikes only 1 point apart, reflecting the volatility of the commodity. Specifically, for
index futures options, the S&P 500 options have striking prices 5 points apart, and
the NYSE options have striking prices 2 points apart.
There is no standard method for quoting futures on options as there is with
stock options. In some cases, striking price symbols are similar to stock option sym
bols (A=5, B=lO, C=l5, etc.), while in others the letters are used incrementally (A=l,
B=2, C=3, etc.). Moreover, the method used may differ with each quote vendor. In
some cases, quote systems use the numeric value of the strike instead of letters. This
makes quoting options much simpler, and perhaps the entire industry (including
stock option vendors) will adopt this method someday. Since there is no standard
method for quoting, one must obtain the symbols individually for futures options, a
fact that makes quoting them extremely inconvenient.
There are position limits for some futures options, hut they allow for very large
positions. Check with your broker for exact limits in the various futures options.
QUOTES
Most futures option quotes (bids and offers) are not displayed on quote-vending
machines, as is also the case with futures. Options traded on the Chicago Mercantile
Exchange are the exception. This can he somewhat distressing to the trader used to
dealing in stock options, since options are normally far less liquid than the underly
ing security. It might be acceptable to trade off of last sales in a liquid futures con
tract, but not so with the options. As a result, futures options have not attracted many
stock option traders into their fold. Of course, where electronic markets exist, the
bids and offers of options would be shown publicly.
The consequence of the inconsistencies in terms as well as the general unavail
ability of quotes has been that index futures options are generally traded by profes
sionals, with the public largely ignoring them. This does not mean, however, that

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584 Part V: Index Options and Futures
The S&P 500 has more stocks, and while both indices are capitalization-weight
ed, 500 stocks include many smaller stocks than the 100-stock index. Also, the OEX
is more heavily weighted by technology issues and is therefore slightly more volatile.
Finally, the OEX does not contain several stocks that are heavily weighted in the S&P
500 because those stocks do not have options listed on the CBOE: Procter and
Gamble, Philip Morris, and Royal Dutch, to name a few. There are two ways to
approach this spread - either from the perspective of the derivative products differ
ential or by attempting to predict the cash spread.
In actual practice, most market-makers in the OEX use the S&P 500 futures to
hedge with. Therefore, if the futures have a larger premium - are overpriced - then
the OEX calls will be expensive and the puts will be cheap. Thus, there is not as much
of an opportunity to establish an inter-index spread in which the derivative products
(futures and options in this case) spread differs significantly from the cash spread.
That is, the derivative products spread will generally follow the cash spread very
closely, because of the number of people trading the spread for hedging purposes.
Nevertheless, the application does arise, albeit infrequently, to spread the
premium of the derivative products in two indices on strictly a hedged basis with
out trying to predict the direction of movement of the cash indices. In order to
establish such a spread, one would take a position in futures and an opposite posi
tion in both the puts and calls on OEX. Due to the way that options must be exe
cuted, one cannot expect the same speed of execution that he can with the futures,
unless he is trading from the OEX pit itself. Therefore, there is more of an execu
tion risk with this spread. Consequently, most of this type of inter-index spreading
is done by the market-makers themselves. It is much more difficult for upstairs
traders and customers.
USING OPTIONS IN INDEX SPREADS
Whenever both indices have options, as most do, the strategist may find that he can
use the options to his advantage. This does not mean merely that he can use a syn
thetic option position as a substitute for the futures position (long call, short put at
the same strike instead of long futures, for example). There are at least two other
alternatives with options. First, he could use an in-the-money option as a substitute
for the future. Second, he could use the options' delta to construct a more leveraged
spread. These alternatives are best used when one is interested in trading the spread
between the cash indices - they are not really amenable to the short-term strategy of
spreading the premiums between the futures.
Using in-the-money options as a substitute for futures gives one an additional
advantage: If the cash indices move far enough in either direction, the spreader could

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O,apter 31: Index Spreading 585
still make money, even if he was wrong in his prediction of the relationship of the
cash indices.
Example: The following prices exist:
ZYX: 175.00
UVX: 150.00
ZYX Dec 185 put: 10½
UVX Dec 140 call: 11
Suppose that one wants to buy the UVX index and sell the ZYX index. He
expects the spread between the two - currently at 25 points - to narrow. He could
buy the UVX futures and sell the ZYX futures. However, suppose that instead he buys
the ZYX put and buys the UVX call.
The time value of the Dec 185 put is 1/2 point and that of the Dec 140 call is 1
point. This is a relatively small amount of time value premium. Therefore, the com
bination would have results very nearly the same as the futures spread, as long as
both options remain in-the-money; the only difference would be that the futures
spread would outperform by the amount of the time premium paid.
Even though he pays some time value premium for this long option combina
tion, the investor has the opportunity to make larger profits than he would with the
futures spread. In fact, he could even make a profit if the cash spread widens, if the
indices are volatile. To see this, suppose that after a large upward move by the over
all market, the following prices exist:
ZYX: 200.00
UVX: 170.00
ZYX Dec 185 put: 0 ( virtually worthless)
UVX Dec 140 call: 30
The combination that was originally purchased for 21 ½ points is now worth 30,
so the spread has made money. But observe what has happened to the cash spread:
It has widened to 30 points, from the original price of 25. This is a movement in the
opposite direction from what was desired, yet the option position still made money.
The reason that the option combination in the example was able to make
money, even though the cash spread moved unfavorably, is because both indices rose
so much in price. The puts that were owned eventually became worthless, but the
long call continued to make money as the market rose. This is a situation that is very
similar to owning a long strangle (long put and call with different strikes), except that

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586 Part V: Index Options and Futures
the put and call are based on different underlying indices. This concept is discussed
in more detail in Chapter 35 on futures spreads.
The second way to use options in index spreading is to use options that are less
deeply in-the-money. In such a case, one must use the deltas of the options in order
to accurately compute the proper hedge. He would calculate the number of options
to buy and sell by using the formula given previously for the ratio of the indices,
which incorporates both price and volatility, and then multiplying by a factor to
include delta.
where
vi is the volatility of index i
Pi is the price of index i
ui is the unit of trading
and di is the delta of the selected option on index i
Example: The following data is known:
ZYX: 175.00, volatility= 20%
UVX: 150.00, volatility = 15%
ZYX Dec 175 put: 7, delta= - .45, worth $500/pt.
UVX Dec 150 call: 5, delta= .52, worth $100/pt
Suppose one decides that he wants to set up a position that will profit if the
spread between the two cash indices shrinks. Rather than use the deeply in-the
money options, he now decides to use the at-the-money options. He would use the
option ratio formula to determine how many puts and calls to buy. (Ignore the put's
negative delta for the purposes of this formula.)
.20 175.00 500 .45 Option Ratio= -x ---x - x - = 6 731 .15 150.00 100 .52 .
He would buy nearly 7 UVX calls for every ZYX put purchased.
In the previous example, using in-the-money options, one had a very small
expense for time value premium and could profit if the indices were volatile, even if
the cash spread did not shrink. This position has a great deal of time value premium
e:x--pense, but could make profits on smaller moves by the indices. Of course, either
one could profit if the cash indices moved favorably.

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594 Part V: Index Options and Futures
Cash Surrender Value = $10 x Final Value/ 1,245.27
This shortened version of the formula only works, though, when the participa
tion rate is 100% of the increase in the Final Index Value above the striking price.
Otherwise, the longer formula should be used.
Not all structured products of this type offer the holder 100% of the appreci
ation of the index over the initial striking price. In some cases, the percentage is
smaller ( although in the early days of issuance, some products offered a percentage
appreciation that was actually greater than 100%). After 1996, options in general
became more expensive as the volatility of the stock market increased tremendous
ly. Thus, structured products issued after 1997 or 1998 tend to include an "annual
adjustment factor." Adjustment factors are discussed later in the chapter.
Therefore, a more general formula for Cash Surrender Value - one that applies
when the participation rate is a fixed percentage of the striking price - is:
Cash Surrender Value =
Guarantee + Guarantee x Participation Rate x (Final Index Value/ Striking Price - I)
THE COST OF THE IMBEDDED CALL OPTION
Few structured products pay dividends. 1 Thus, the "cost" of owning one of these
products is the interest lost by not having your money in the bank ( or money market
fund), but rather having it tied up in holding the structured product.
Continuing with the preceding example, suppose that you had put the $10 in
the bank instead of buying a structured product with it. Let's further assume that the
money in the bank earns 5% interest, compounded continuously. At the end of seven
years, compounded continuously, the $10 would be worth:
Money in the bank = Guarantee Price x ert
= $10 x e 0-05 x 7 = 14.191, in this case
This calculation usually raises some eyebrows. Even compounded annually, the
amount is 14.07. You would make roughly 40% (without considering taxes) just by
1Some do pay dividends, though. A structured product existed on a contrived index, called the Dow-Jones
Top 10 Yield index (symbol: $XMT). This is a sort of "dogs of the Dow" index. Since part of the reason for owning a
"dogs of the Dow" product is that dividends are part of the performance, the creators of the structured product
(Merrill Lynch) stated that the minimum price one would receive at maturity would be 12.40, not the 10 that was
the initial offering price. Thus, this particular structured product had a "dividend" built into it in the form of an ele
vated minimum price at maturity.

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Chapter 32: Structured Products 595
having your money in the bank. Forgetting structured products for a moment, this
means that stocks in general would have to increase in value by over 40% during the
seven-year period just for your performance to beat that of a bank account.
In this sense, the cost of the imbedded call option in the structured product is
this lost interest - 4.19 or so. That seems like a fairly expensive option, but if you con
sider that it's a seven-year option, it doesn't seem quite so expensive. In fact, one
could calculate the implied volatility of such a call and compare it to the current
options on the index in question.
In this case, with the stock at 10, the strike at 10, no dividends, a 5% interest
rate, and seven years until expiration, the implied volatility of a call that costs $4.19
is 28.1 %. Call options on the S&P 500 index are rarely that expensive. So you can see
that you are paying "something" for this call option, even if it is in the form of lost
interest rather than an up-front cost.
As an aside, it is also unlikely that the underwriter of the structured product
actually paid that high an implied volatility for the call that was purchased; but he is
asking you to pay that amount. This is where his underwriting profit comes from.
The above example assumed that the holder of the structured product is par
ticipating in 100% of the upside gain of the underlying index over its striking price.
If that is not the case, then an adjustment has to be made when computing the price
of the imbedded option. In fact, one must compute what value of the index, at matu
rity, would result in the cash value being equal to the "money in the bank" calcula
tion above. Then calculate the imbedded call price, using that value of the index. In
that way, the true value of the imbedded call can be found.
You might ask, "Why not just divide the 'money in the bank' formula by the par
ticipation rate?" That would be okay if the participation were always stated as a per
centage of the striking price, but sometimes it is not, as we will see when we look at
the more complicated examples. Further examples of structured products in this
chapter demonstrate this method of computing the cost of the imbedded call.
PRICE BEHAVIOR PRIOR TO MATURITY
The structured product cannot normally be "exercised" by the holder until it
matures. That is, the cash surrender value is only applicable at maturity. At any other
time during the life of the product, one can compute the cash surrender value, but
he cannot actually attain it. What you can attain, prior to maturity, is the market price,
since structured products trade freely on the exchange where they are listed. In actu
al fact, the products generally trade at a slight discount to their theoretical cash sur
render value. This is akin to a closed-end mutual fund selling at a discount to net

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596 Part V: Index Options and Futures
asset value. Eventually, upon maturity, the actual price will be the cash surrender
value price; so if you bought the product at a discount, you would benefit, providing
you held all the way to maturity.
Example: Assume that two years ago, a structured product was issued with an initial
offering price of $10 and a strike price of 1,245.27, based upon the S&P 500 index.
Since issuance, the S&P 500 index has risen to 1,522.00. That is an increase of
22.22% for the S&P 500, so the structured product has a theoretical cash surrender
value of 12.22. I say "theoretical" because that value cannot actually be realized, since
the structured product is not exercisable at the current time - five years prior to
maturity.
In the real marketplace, this particular structured product might be trading at
a price of 11. 75 or so. That is, it is trading at a discount to its theoretical cash sur
render value. This is a fairly common occurrence, both for structured products and
for closed-end mutual funds. If the discount were large enough, it should serve to
attract buyers, for if they were to hold to maturity, they would make an extra 4 7 cents
(the amount of this discount) from their purchase. That's 4% (0.47 divided by 11.75
= 4%) over five years, which is nothing great, but it's something.
Why does the product trade at a discount? Because of supply and demand. It is
free to trade at any price - premium or discount - because there is nothing to keep
it fixed at the theoretical cash surrender value. If there is excess demand or supply in
the open market, then the price of the structured product will fluctuate to reflect that
excess. Eventually, of course, the discount will disappear, but five years prior to
maturity, one will often find that the product differs from its theoretical value by
somewhat significant amounts. If the discount is large enough, it will attract buyers;
alternatively, if there should be a large premium, that should attract sellers.
SIS
One of the first structured products of this type that came to my attention was one
that traded on the AMEX, entitled "Stock Index return Security" or SIS. It also trad
ed under the symbol SIS. The product was issued in 1993 and matured in 2000, so
we have a complete history of its movements. The terms were as follows: The under
lying index was the S&P Midcap 400 index (symbol: $MID). Issued in June 1993, the
original issue price was $10, and $MID was trading at 166.10 on the day of issuance,
so that was the striking price. Moreover, buyers were entitled to 115% of the appre
ciation of $MID above the strike price. Thus, the cash value formula was:

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621
This lowering of the call price continues as more dividends are paid, until it finally
reaches the final call price at maturity. The PERCS holder should not be confused
this sliding scale of call prices. The sliding call feature is designed to ensure that
PERC S holder is compensated for not receiving all his "promised" dividends if the
PERCS should be called prior to maturity.
Example: As before, XYZ issues a PERCS when the common is at 35. The PERCS
pays an annual dividend of $2.50 per share as compared to $1 per share on the com
mon stock. The PERCS has a final call price of 39 dollars per share in three years.
If XYZ stock should undergo a sudden price advance and rise dramatically in a
very short period of time, it is possible that the PERCS could be called before any
dividends are paid at all. In order to compensate the PERCS holder for such an
c>ecurrence, the initial call price would be set at 43.50 per share. That is, the PERCS
can't be called unless XYZ trades to a price over 43.50 dollars per share. Notice that
the difference between the eventual call price of 39 and the initial call price of 43.50
is 4.50 points, which is also the amount of additional dividends that the PERCS
would pay over the three-year period. The PER CS pays $2.50 per year and the com
mon $1 per year, so the difference is $1.50 per year, or $4.50 over three years.
Once the PERCS dividends begin to be paid, the call price will be reduced to
reflect that fact. For example, after one year, the call price would be 42, reflecting
the fact that if the PERCS were not called until a year had passed, the PERCS hold
er would be losing $3 of additional dividends as compared to the common stock
($1.50 per year for the remaining two years). Thus, the call price after one year is set
at the eventual call price, 39, plus the $3 of potential dividend loss, for a total call
price of 42.
This example shows how the company uses the sliding call price to compensate
the PERCS holder for potential dividend loss if the PERCS is called before the
three-year time to maturity has elapsed. Thus, the PER CS holder will make the same
dollars of profit - dividends and price appreciation combined - no matter when the
PERCS is called. In the case of the XYZ PERCS in the example, that total dollar
profit is $11.50 (see the prior example). Notice that the investor's annualized rate of
return would be much higher if he were called prior to the eventual maturity date.
One final point: The call price §lides on a scale as set forth in the prospectus for
the PERCS. It may be every time a dividend is paid, but more likely it will be daily!
That is, the present worth of the remaining dividends is added to the final call price
to calculate the sliding call price daily. Do not be overwhelmed by this feature.
Remember that it is just a means of giving the PERCS holder his entire "dividend
premium" if the PERCS is called before maturity.

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622 Part V: Index Options and Futures
For the remainder of this chapter, the call price of the PERCS will be referrea
to as the redemption price. Since much of the rest of this chapter will be concemec
with discussing the fact that a PERCS is related to a call option, there could be somE
confusion when the word call is used. In some cases, call could refer to the price at
which the PER CS can be called; in other cases, it could refer to a call option - either
a listed one or one that is imbedded within the PERCS. Hence, the word redemp
tion will be used to refer to the action and price at which the issuing compa:J)ly may
call the PERCS.
A PERCS IS A COVERED CALL WRITE
It was stated earlier that a PER CS is like a covered write. However, that has not yet
been proven. It is known that any two strategies are equivalent if they have the same
profit potential. Thus, if one can show that the profitability of owning a PER CS is the
same as that of having established a covered call write, then one can conclude that
they are equivalent.
Example: For the purposes of this example, suppose that there is a three-year listed
call option with striking price 39 available to be sold on XYZ common stock. Also,
assume that there is a PERCS on XYZ that has a redemption price of 39 in three
years. The following prices exist:
XYZ common: 35
XYZ PERCS: 35
3-year call on XYZ common with striking price of 39: 4.50
First, examine the XYZ covered call write's profitability from buying 100 XY2 and
selling one call. It was initially established at a debit of 30.50 (35 less the 4.50
received from the call sale). The common pays $1 per year in dividends, for a total of
$3 over the life of the position.
XYZ Price Price of a Profit/loss on Total Profit/loss
in 3 Years 3-Year Call Securities Incl. Dividend
25 0 -$550 -$250
30 0 -50 +250
35 0 +450 +750
39 0 +850 + 1,150
45 6 +850 + 1,150
50 11 +850 + 1,150

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O.,,ter 32: Structured Products 623
TI1is is the typical picture of the total return from a covered write - potential losses on
the downside with profit potential limited above the striking price of the written call.
Now look at the profitability of buying the PER CS at 35 and holding it for three
(Assume that it is not called prior to maturity.) The PER CS holder will earn a
total of $750 in dividends over that time period.
XYZ Price Profit/Loss on Total Profit/Loss
in 3 Years PERCS Incl. Dividend
25 -$1,000 -$250
30 -500 +250
35 0 +750
>=39 +400 + 1, 150
This is exactly the same profitability as the covered call write. Therefore, it can be
concluded with certainty that a PERCS is equivalent to a covered call write. Note
that the PER CS potential early redemption feature does not change the truth of this
statement. The early redemption possibility merely allows the PERCS holder to
receive the same total dollars at an earlier point in time if the PERCS is demanded
prior to maturity. The covered call writer could theoretically be facing a similar situ
ation if the written call option were assigned before expiration: He would make the
same total profit, but he would realize it in a shorter period of time.
The PERCS is like a covered write of a call option with striking price equal to
the redemption price of the PERCS, except that the holder does not receive a call
option premium, but rather receives additional dividends. In essence, the PERCS
has a call option imbedded within it. The value of the imbedded call is really the
value of the additional dividends to be paid between the current date and maturity.
The buyer of a PERCS is, in effect, selling a call option and buying common
stock. He should have some idea of whether or not he is selling the option at a rea
sonably fair price. The next section of this chapter addresses the problem of valuing
the call option that is imbedded in the PERCS.
PRICE BEHAVIOR
The way that a PERCS price is often discussed is in relationship to the common
stock. One may hear that the PERCS is trading at the same price as the common or
at a premium or discount to the common. As an option strategist who understands
covered call writing, it should be a simple matter to picture how the PERCS price
will relate to the common price.

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624 Part V: Index Options and Futures
FIGURE 32-6.
PERCS price estimate versus common stock.
44
(I)
iii 39 6 Months
E
~ w
(I)
u
ct 34
Cf)
(.)
a: w a.
29
0 1-.J. ____ ,__ ___ ...._ ___ _._ ___ __._ ___ _.__
25 30 35 40
Stock Price
45 50
First, consider the out-of-the-money situation. If the underlying common
declines in price, the PERCS will not decline as fast because the additional dividends
will provide yield support. The PER CS will therefore trade at a higher price than the
common. Howeve1~ as the maturity date nears and the remaining number of addi
tional dividends dwindles to a small amount, then the PER CS price and the common
price will converge.
The opposite effect occurs if the underlying common moves higher. The
PERCS will trade at a lower price than the common when the common trades above
the issue price. In fact, since there is a redemption price on the PERCS, it will not
trade higher than the redemption price. The common, however, has no such restric
tion, so it could continue to trade at prices significantly higher than the PERCS does.
These points are illustrated in Figure 32-6, which contains the price curves of two
PER CS: one at issuance, thus having three years remaining, and the other with just six
months remaining until the maturity of the PERCS. For purposes of comparison, it
was assumed that there is no sliding redemption feature involved. Several significant
points can be made from the figure. First, notice that the PERCS and the common._
tend to sell at approximately the same price at the point labeled "I." This would be the
price at which the PER CS are issued. This issue price must be below the redemption
price of the PERCS. More will be said later about how this price is determined.

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642 Part V: Index Options and Futures
exercise it; or is there too great a chance that OEX will rally and wipe out his dis
count?
If he buys this put when there is very little time left in the trading day, it might
be enough of a discount. Recall that a one-point move in OEX is roughly equivalent
to 15 points on the Dow (while a one-point move in SPX is about 7.5 Dow points).
Thus, this O EX discount of 0.4 7 is about equal to 7 Dow points. Obviously, this is not
a lot of cushion, because the Dow can easily move that far in a short period of time,
so it would be sufficient only if there are just a few minutes of trading left and there
were not previous indications oflarge orders to buy "market on close."
However, if this situation were presented to the discounter at an earlier time in
the trading day, he might defer because he would have to hedge his position and that
might not be worth the trouble. If there were several hours left in the trading day,
even a discount of a full point would not be enough to allow him to remain unhedged
(one full OEX point is about 15 Dow points). Rather, he would, for example, buy
futures, buy OEX calls, or sell puts on another index. At the end of the day, he could
exercise the puts he bought at a discount and reverse the hedge in the open market.
CONVERSIONS AND REVERSALS
Conversions and reversals in cash-based options are really the market basket hedges
(index arbitrage) described in Chapter 30. That is, the underlying security is actually
all the stocks in the index. However, the more standard conversions and reversals can
be executed with futures and futures options.
Since there is no credit to one's account for selling a future and no debit for buy
ing one, most futures conversions and reversals trade very nearly at a net price equal
to the strike. That is, the value of the out-of-the-money futures option is equal to the
time premium of the in-the-money option that is its counterpart in the conversion or
reversal.
Example: An index future is trading at 179.00. If the December 180 call is trading
for 5.00, then the December 180 put should be priced near 6.00. The time value pre
mium of the in-the-money put is 5.00 (6.00 + 179.00 - 180.00), which is equal to the
price of the out-of-the-money call at the same strike.
If one were to attempt to do a conversion or reversal with these options, he
would have a position with no risk of loss but no possibility of gain: A reversal would
be established, for example, at a "net price" of 180. Sell the future at 179, add the
premium of the put, 6.00, and subtract the cost of the call, 5.00: 179 + 6.00 - 5.00 =
180.00. As we know from Chapter 27 on arbitrage, one unwinds a conversion or
reversal for a "net price" equal to the strike. Hence, there would be no gain or loss
from this futures reversal.

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Chapter 33: Mathematical Considerations for Index Products 643
For index futures options, there is no risk when the underlying closes near the
strike, since they settle for cash. One is not forced to make a choice as to whether to
exercise his calls. (See Chapter 27 on arbitrage for a description of risks at expiration
when trading reversals or conversions.)
In actual practice, floor traders may attempt to establish conversions in futures
options for small increments - perhaps 5 or 10 cents in S&P futures, for example.
The arbitrageur should note that futures options do actually create a credit or debit
in the account. That is, they are like stock options in that respect, even though the
underlying instrument is not. This means that if one is using a deep in-the-money
option in the conversion, there will actually be some carrying cost involved.
Example: An index future is trading at 179.00 and one is going to price the
December 190 conversion, assuming that December expiration is 50 days away.
Assume that the current carrying cost of money is 10% annually. Finally, assume that
the December 190 call is selling for 1.00, and the December 190 put is selling for
11.85. Note that the put has a time value premium of only 85 cents, less than the pre
mium of the call. The reason for this is that one would have to pay a carrying cost to
do the December 190 conversion.
If one established the 190 conversion, he would buy the futures (no credit or
debit to the account), buy the put (a debit of 11.85), and sell the call (a credit of 1.00).
Thus, the account actually incurs a debit of 10.85 from the options. The carrying cost
for 10.85 at 10% for 50 days is 10.85 x 10% x 50/365 = 0.15. This indicates that the
converter is willing to pay 15 cents less time premium for the put (or conversely that
the reversal trader is willing to sell the put for 15 cents less time premium). Instead
of the put trading with a time value premium equal to the call price, the put will trade
with a premium of 15 cents less. Thus, the time premium of the put is 85 cents,
rather than being equal to the price of the call, 1.00.
BOX SPREADS
Recall that a "box" consists of a bullish vertical spread involving two striking prices,
and a bearish vertical spread using the same two strikes. One spread is constructed
with puts and the other with calls. The profitability of the box is the same regardless
of the price of the underlying security at expiration.
Box arbitrage with equity options involves trying to buy the box for less than the
difference in the striking prices, for ~ple, trying to buy a box in which the strikes
are 5 points apart for 4. 75. Selling the box for more than 5 points would represent
arbitrage as well. In fact, even selling the box at exactly 5 points would produce a
profit for the arbitrageur, since he earns interest on the credit from the sale.

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644 Part V: Index Options and Futures
These same strategies apply to options on futures. However, boxes on cash
based options involve another consideration. It is often the case with cash-based
options that the box sells for more than the difference in the strikes. For example, a
box in which the strikes are 10 points apart might sell for 10.50, a substantial premi
um over the striking price differential. The reason that this happens is because of the
possibility of early assignment. The seller of the box assumes that risk and, as a result,
demands a higher price for the box.
If he sells the box for half a point more than the striking price differential, then
he has a built-in cushion of .50 point of index movement if he were to be assigned
early. In general, box strategies are not particularly attractive. However, if the pre
mium being paid for the box is excessively high, then one should consider selling the
box. Since there are four commissions involved, this is not normally a retail strategy.
MATHEMATICAL APPLICATIONS
The following material is intended to be a companion to Chapter 28 on mathemati
cal applications. Index options have a few unique properties that must be taken into
account when trying to predict their value via a model.
The Black-Scholes model is still the model of choice for options, even for index
options. Other models have been designed, but the Black-Scholes model seems to
give accurate results without the extreme complications of most of the other models.
FUTURES
Modeling the fair value of most futures contracts is a difficult task. The
Black-Scholes model is not usable for that task. Recall that we saw earlier that the
fair value of a future contract on an index could be calculated by computing the pres
ent value of the dividend and also knowing the savings in carrying cost of the futures
contract versus buying the actual stocks in the index.
CASH-BASED INDEX OPTIONS
The futures fair value model for a capitalization-weighted index requires knowing the
exact dividend, dividend payment date, and capitalization of each stock in the index
(for price-weighted indices, the capitalization is unnecessary). This is the only way of
getting the accurate dividend for use in the model. The same dividend calculation
must be done for any other index before the Black-Scholes formula can be applied.
In the actual model, the dividend for cash-based index options is used in much
the same way that dividends are used for stock options: The present value of the div-

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Chapter 34: Futures and Futures Options
FIGURE 34-2.
January soybean, ratio spread.
90
80
70
60
50
:!::
40 0 ... a.. 30
0 20 .le
C 10
~ 0
-10
-20
-30
575 625 650
At Expiration
Futures Price
Points of maximum profit = Maximum downside loss
+ Difference in strikes
x Number of calls owned
=-4½ + 50 X 2
=95½
Upside break-even price = Higher striking price
700
+ Maximum profit/Net number of naked calls
= 650 + 95½/3
= 681.8
689
These are the significant points of profitability at expiration. One does not care
what the unit of trading is (for example, cents for soybeans) or how many dollars are
involved in one unit of trading ($50 for soybeans and soybean options). He can con
duct his analysis strictly in terms of points, and he should do so.
Before proceeding into the comparisons beleen the backspread and the ratio
spread as they apply to mispriced futures options, it should be pointed out that the seri
ous strategist should analyze how his position will perform over the short term as well
as at expiration. These analyses are presented in Chapter 36 on advanced concepts.

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690 Part V: Index Options and Futures
WHICH STRATEGY TO USE
The profit potential of the put backspread is obviously far different from that of the
call ratio spread. They are similar in that they both offer the strategist the opportu
nity to benefit from spreading mispriced options. Choosing which one to implement
(assuming liquidity in both the puts and calls) may be helped by examining the tech
nical picture ( chart) of the futures contract. Recall that futures traders are often more
technically oriented than stock traders, so it pays to be aware of basic chart patterns,
because others are watching them as well. If enough people see the same thing and
act on it, the chart pattern will be correct, if only from a "self-fulfilling prophecy"
viewpoint if nothing else.
Consequently, if the futures are locked in a (smooth) downtrend, the put strat
egy is the strategy of choice because it offers the best downside profit. Conversely, if
the futures are in a smooth uptrend, the call strategy is best.
The worst result will be achieved if the strategist has established the call ratio
spread, and the futures have an explosive rally. In certain cases, very bullish rumors
- weather predictions such as drought or El Nifio, foreign labor unrest in the fields
or mines, Russian buying of grain - will produce this mispricing phenomenon. The
strategist should be leery of using the call ratio spread strategy in such situations,
even though the out-of-the-money calls look and are ridiculously expensive. If the
rumors prove true, or if there are too many shorts being squeezed, the futures can
move too far, too fast and seriously hurt the spreader who has the ratio call spread in
place. His margin requirements will escalate quickly as tl1e futures price moves high
er. The option premiums will remain high or possibly even expand if the futures rally
quickly, thereby overriding the potential benefit of time decay. Moreover, if the fun
damentals change immediately - it rains; the strike is settled; no grain credits are
offered to the Russians - or rumors prove false, the futures can come crashing back
down in a hurry.
Consequently, if rumors of fundamentals have introduced volatility in the
futures rnarket, implement the strategy with the put backspread. The put backspread
is geared to taking advantage of volatility, and this fundamental situation as described
is certainly volatile. It may seem that because the market is exploding to the upside,
it is a waste of time to establish the put spread. Still, it is the wisest choice in a volatile
market, and there is always the chance that an explosive advance can turn into a quick
decline, especially when the advance is based on rumors or fundamentals that could
change overnight.
There are a few "don'ts" associated with the ratio call spread. Do not be tempt
ed to use the ratio spread strategy in volatile situations such as those just described;
it works best in a slowly rising market. Also, do not implement the ratio spread with

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Chapter 34: Futures and Futures Options 691
ridiculously far out-of-the-money options, as one is wasting his theoretical advantage
if the futures do not have a realistic chance to climb to the striking price of the writ
ten options. Finally, do not attempt to use overly large ratios in order to gain the most
theoretical advantage. This is an important concept, and the next example illustrates
it well.
Example: Assume the same pricing pattern for January soybean options that has
been the basis for this discussion. January beans are trading at 583. The (novice)
strategist sees that the slightly in-the-money January 575 call is the cheapest and the
deeply out-of-the-money January 675 call is the most expensive. This can be verified
from either of two previous tables: the one showing the actual price as compared to
the "theoretical" price, or Table 34-2 showing the implied volatilities.
Again, one would use the deltas (see Table 34-2) to create a neutral spread. A
neutral ratio of these two would involve selling approximately six calls for each one
purchased.
Buy 1 January bean 575 call at 191/z
Sell 6 January bean 675 calls at 21/4
Net position:
191/z DB
131/z CR
6 Debit
Figure 34-3 shows the possible detrimental effects of using this large ratio.
While one could make 94 points of profit if beans were at 675 at January expiration,
he could lose that profit quickly if beans shot on through the upside break-even
point, which is only 693.8. The previous formulae can be used to verify these maxi
mum profit and upside break-even point calculations. The upside break-even point
is too close to the striking price to allow for reasonable follow-up action. Therefore,
this would not be an attractive position from a practical viewpoint, even though at
first glance it looks attractive theoretically.
It would seem that neutral spreading could get one into trouble if it "recom
mends" positions like the 6-to-l ratio spread. In reality, it is the strategist who is get
ting into trouble if he doesn't look at the whole picture. The statistics are just an aid
- a tool. The strategist must use the tools to his advantage. It should be pointed out
as well that there is a tool missing from the toolkit at this point. There are statistics
that will clearly show the risk of this type of high-rati<,Yspread. In this case, that tool
is the gamma of the option. Chapter 40 covers the -Lise of gamma and other more
advanced statistical tools. This same example is expanded in that chapter to include
the gamma concept.

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692 Part V: Index Options and Futures
FIGURE 34-3.
January soybean, heavily ratioed spread.
90
60
30
- 0
e 575 625 650 675 725 a. -30 0
.1!l -60 C
~
-90
-120 At Expiration
-150
-180
Futures Price
FOLLOW-UP ACTION
The same follow-up strategies apply to these futures options as did for stock options.
They will not be rehashed in detail here; refer to earlier chapters for broader expla
nations. This is a summary of the normal follow-up strategies:
Ratio call spread:
Follow-up action in strategies with naked options, such as this, generally involves
taking or limiting losses. A rising market will produce a negative EFP.
Neutralize a negative EFP by:
Buying futures
Buying some calls
Limit upside losses by placing buy stop orders for futures at or near the upside
break-even point.
Put backspread:
Follow-up action in strategies with an excess of long options generally involves
taking or protecting profits. A falling market will produce a negative EFP.
Neutralize a negative EFP by:
Buying futures
Selling some puts

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Chapter 34: Futures and Futures Options 693
The reader has seen these follow-up strategies earlier in the book. However,
there is one new concept that is important: The mispricing continues to propagate
itself no matter what the price of the underlying futures contract. The at-the-money
options will always be about fairly priced; they will have the average implied volatility.
Example: In the previous examples, January soybeans were trading at 583 and the
implied volatility of the options with striking price 575 was 15%, while those with a
600 strike were 17%. One could, therefore, conclude that the at-the-money January
soybean options would exhibit an implied volatility of about 16%.
This would still be true if beans were at 525 or 675. The mispricing of the other
options would extend out from what is now the at-the-money strike. Table 34-3 shows
what one might expect to see if January soybeans rose 75 cents in price, from 583 to
658.
Nate that the same mispricing properties exist in both the old and new situa
tions: The puts that are 58 points out-of-the-money have an implied volatility of only
12%, while the calls that are 92 points out-of-the-money have an implied volatility of
23%.
TABLE 34-3.
Propagation of volatility skewing.
Original Situation
January beans: 583
Implied
Strike Volatility
525 12%
550 13%
575 15%
600 17%
625 19%
650 21%
675 23%
New Situation
January beans: 658
Strike
600
625
650
675
700
725
750
This example is not meant to infer that the volatility of an at-the-money soybean
futures option will always be 16%. It could be anything, depending on the historical
and implied volatility of the futures contract itself. However, the volatility skewing
will still persist even if the futures rally or decline.
This fact will affect how these strategies behave as the(linderlying futures con
tract moves. It is a benefit to both strategies. First, look at the put backspread when
the stock falls to the striking price of the purchased puts.

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694 Part V: Index Options and Futures
Example: The put backspread was established under the following conditions:
Strike
550
600
Put
Price
Theoretical
Put Price
5.4
27.6
Implied
Volatility
13%
17%
If January soybean futures should fall to 550, one would expect the implied
volatility of the January 550 puts that are owned to be about 16% or 17%, since they
would be at-the-money at that time. This makes the assumption that the at-the
money puts will have about a 17% implied volatility, which is what they had when the
position was established.
Since the strategy involves being long a large quantity of January 550 puts, this
increase in implied volatility as the futures drop in price will be of benefit to the
spread.
Note that the implied volatility of the January 600 puts would increase as well,
which would be a small negative aspect for the spread. However, since there is only
one put short and it is quite deeply in the money with the futures at 550, this nega
tive cannot outweigh the positive effect of the expansion of volatility on the long
January 550 puts.
In a similar manner, the call spread would benefit. The implied volatility of the
written options would actually drop as the futures rallied, since they would be less far
out-of-the-money than they originally were when the spread was established. While
the same can be said of the long options in the spread, the fact that there are extra,
naked, options means the spread will benefit overall.
In summary, the futures option strategist should be alert to mispricing situations
like those described above. They occur frequently in a few commodities and occa
sionally in others. The put backspread strategy has limited risk and might therefore
be attractive to more individuals; it is best used in downtrending and/or volatile mar
kets. However, if the futures are in a smooth uptrend, not a volatile one, a ratio call
spread would be better. In either case, the strategist has established a spread that is
statistically attractive because he has sold options that are expensive in relation to the
ones that he has bought.

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Chapter 34: Futures and Futures Options 695
SUMMARY
This chapter presented the basics of futures and futures options trading. The basic
differences between futures options and stock or index options were laid out. In a
certain sense, a futures option is easier to utilize than is a stock option because the
effects of dividends, interest rates, stock splits, and so forth do not apply to futures
options. However, the fact that each underlying physical commodity is completely
different from most other ones means that the strategist is forced to familiarize him
self with a vast array of details involving striking prices, trading units, expiration
dates, first notice days, etc.
More details mean there could be more opportunities for mistakes, most of
which can be avoided by visualizing and analyzing all positions in terms of points and
not in dollars.
Futures options do not create new option strategies. However, they may afford
one the opportunity to trade when the futures are locked limit up. Moreover, the
volatility skewing that is present in futures options will offer opportunities for put
backspreads and call ratio spreads that are not normally present in stock options.
Chapter 35 discusses futures spreads and how one can use futures options with
those spreads. Calendar spreads are discussed as well. Calendar spreads with futures
options are different from calendar spreads using stock or index options. These are
important concepts in the futures markets - distinctly different from an option
spread - and are therefore significant for the futures option trader.

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Chapter 35: Futures Option Strategies for Futures Spreads
TABLE 35-2.
Terms of oil production contract.
Contract
Crude Oil
Unleaded Gasoline
Heating Oil
Initial
Price
18.00
.6000
.5500
Subsequent
Price
19.00
.6100
.5600
The following formula is generally used for the oil crack spread:
Crack= (Unleaded gasoline + Heating oil) x 42 - 2 x Crude
2
(.6000 + .5500) X 42 - 2 X 18.00 =
2
= (48.3 - 36)/2
= 6.15
703
Gain in
Dollars
$1,000
$ 420
$ 420
Some traders don't use the divisor of 2 and, therefore, would arrive at a value
of 12.30 with the above data.
In either case, the spreader can track the history of this spread and will attempt
to buy oil and sell the other two, or vice versa, in order to attempt to make an over
all profit as the three products move. Suppose a spreader felt that the products were
too expensive with respect to crude oil prices. He would then implement the spread
in the following manner:
Buy 2 March crude oil futures @ 18.00
Sell 1 March heating oil future @ 0.5500
Sell l March unleaded gasoline future @ 0.6000
Thus, the crack spread was at 6.15 when he entered the position. Suppose that
he was right, and the futures prices subsequently changed to the following:
March crude oil futures: 18.50
March unleaded gas futures: .6075
March heating oil futures: .5575
The profit is shown in Table 35-3.

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704
TABLE 35-3.
Profit and loss of crack spread.
Contract
2 March Crude
1 March Unleaded
1 March Heating Oil
Net Profit (before commissions)
Initial
Price
18.00
.6000
.5500
Part V: Index Options and Futures
Subsequent
Price
18.50
.6075
.5575
Gain in
Dollars
+ $1,000
- $ 315
- $ 315
+ $ 370
One can calculate that the crack spread at the new prices has shrunk to 5.965.
Thus, the spreader was correct in predicting that the spread would narrow, and he
profited.
Margin requirements are also favorable for this type of spread, generally being
slightly less than the speculative requirement for two contracts of crude oil.
The above examples demonstrate some of the various intermarket spreads that
are heavily watched and traded by futures spreaders. They often provide some of the
most reliable profit situations without requiring one to predict the actual direction of
the market itself. Only the differential of the spread is important.
One should not assume that all intermarket spreads receive favorable margin
treatment. Only those that have traditional relationships do.
USING FUTURES OPTIONS IN FUTURES SPREADS
After viewing the above examples, one can see that futures spreads are not the same
as what we typically know as option spreads. However, option contracts may be use
ful in futures spreading strategies. They can often provide an additional measure of
profit potential for very little additional risk. This is true for both intramarket and
intermarket spreads.
The futures option calendar spread is discussed first. The calendar spread with
futures options is not the same as the calendar spread with stock or index options. In
fact, it may best be viewed as an alternative to the intramarket futures spread rather
than as an option spread strategy.
CALENDAR SPREADS
A calendar spread with futures options would still be constructed in the familiar
manner - buy the May call, sell the March call with the same striking price. However,

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Chapter 35: Futures Option Strategies for Futures Spreads 705
there is a major difference between the futures option calendar spread and the stock
option calendar spread. That difference is that a calendar spread using futures
options involves two separate underlying instruments, while a calendar spread using
stock options does not. When one buys the May soybean 600 call and sells the March
soybean 600 call, he is buying a call on the May soybean futures contract and selling
a call on the March soybean futures contract. Thus, the futures option calendar
spread involves two separate, but related, underlying futures contracts. However, if
one buys the IBM May 100 call and sells the IBM March 100 call, both calls are on
the same underlying instrument, IBM. This is a major difference between the two
strategies, although both are called "calendar spreads."
To the stock option trader who is used to visualizing calendar spreads, the
futures option variety may confound him at first. For example, a stock option trader
may conclude that if he can buy a four-month call for 5 points and sell a two-month
call for 2 points, he has a good calendar spread possibility. Such an analysis is mean
ingless with futures options. If one can buy the May soybean 600 call for 5 and sell
the March soybean 600 call for 3, is that a good spread or not? It's impossible to tell,
unless you know the relationship between May and March soybean futures contracts.
Thus, in order to analyze the futures option calendar spread, one must not only ana
lyze the options' relationship, but the two futures contracts' relationship as well.
Simply stated, when one establishes a futures option calendar spread, he is not only
spreading time, as he does with stock options, he is also spreading the relationship
between the underlying futures.
Example: A trader notices that near-term options in soybeans are relatively more
expensive than longer-term options. He thinks a calendar spread might make sense,
as he can sell the overpriced near-term calls and buy the relatively cheaper longer
term calls. This is a good situation, considering the theoretical value of the options
involved. He establishes the spread at the following prices:
Soybean Trading
Contract Initial Price Position
March 600 call 14 Sell 1
May 600 call 21 Buy 1
March future 594 none
May future 598 none
The May/March 600 call calendar spread is established for 7 points debit.
March expiration is two months away. At the current time, the May futures are trad
ing at a 4-point premium to March futures. The spreader figures that if March

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706 Part V: Index Options and Futures
futures are approximately unchanged at expiration of the March options, he should
profit handsomely, because the March calls are slightly overpriced at the current
time, plus they will decay at a faster rate than the May calls over the next two months.
Suppose that he is correct and March futures are unchanged at expiration of the
March options. This is still no guarantee of profit, because one must also determine
where May futures are trading. If the spread between May and March futures
behaves poorly (May declines with respect to March), then he might still lose money.
Look at the following table to see how the futures spread between March and May
futures affects the profitability of the calendar spread. The calendar spread cost 7
debit when the futures spread was +4 initially.
Futures Calendar
Futures Prices Spread May 600 Call Spread
March/May Price Price Profit/Loss
594/570 -24 4 -3 cents
594/580 -14 61/2 _1/2
594/590 -4 10 +3
594/600 +6 141/2 +71/2
Thus, the calendar spread could lose money even with March futures
unchanged, as in the top two lines of the table. It also could do better than expected
if the futures spread widens, as in the bottom line of the table.
The profitability of the calendar spread is heavily linked to the futures spread
price. In the above example, it was possible to lose money even though the March
futures contract was unchanged in price from the time the calendar spread was
initially established. This would never happen with stock options. If one placed a
calendar spread on IBM and the stock were unchanged at the expiration of the near
term option, the spread would make money virtually all of the time ( unless implied
volatility had shrunk dramatically).
The futures option calendar spreader is therefore trading two spreads at once.
The first one has to do with the relative pricing differentials (implied volatilities, for
example) of the two options in question, as well as the passage of time. The second
one is the relationship between the two underlying futures contracts. As a result, it is
difficult to draw the ordinary profit picture. Rather, one must approach the problem
in this manner:
1. Use the horizontal axis to represent the futures spread price at the expiration of
the near-term option.

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Chapter 35: Futures Option Strategies for Futures Spreads 707
2. Draw several profit curves, one for each price of the near-term future at near
term expiration.
Example: Expanding on the above example, this method is demonstrated here.
Figure 35-1 shows how to approach the problem. The horizontal axis depicts
the spread between March and May soybean futures at the expiration of the March
futures options. The vertical axis represents the profit and loss to be expected from
the calendar spread, as it always does.
The major difference between this profit graph and standard ones is that there
are now several sets of profit curves. A separate one is drawn for each price of the
March futures that one wants to consider in his analysis. The previous example
showed the profitability for only one price of the March futures - unchanged at 594.
However, one cannot rely on the March futures to remain unchanged, so he must
view the profitability of the calendar spread at various March futures prices.
The data that is plotted in the figure is summarized in Table 35-4. Several things
are readily apparent. First, if the futures spread improves in price, the calendar
spread will generally make money. These are the points on the far right of the figure
and on the bottom line of Table 35-4. Second, if the futures spread behaves miser-
FIGURE 35-1.
Soybean futures calendar spreads, at March expiration.
gj
20
16
12
.3 8
::.:
0
ct 4
0
-8
March/May Spread
March =604
March =594
March= 614
March =584
March= 574

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708 Part V: Index Options and Futures
ably, the calendar spread will almost certainly lose money (points on the left-hand
side of the figure, or top line of the table).
Third, if March futures rise in price too far, the calendar spread could do poor
ly. In fact, if March futures rally and the futures spread worsens, one could lose more
than his initial debit (bottom left-hand point on figure). This is partly due to the fact
that one is buying the March options back at a loss if March futures rally, and may
also be forced to sell his May options out at a loss if May futures have fallen at the
same time.
Fourth, as might be expected, the best results are obtained if March futures
rally slightly or remain unchanged and the futures spread also remains relatively
unchanged (points in the upper right-hand quadrant of the figure).
In Table 35-4, the far right-hand column shows how a futures spreader would
have fared if he had bought May and sold March at 4 points May over March, not
using any options at all.
TABLE 35-4.
Profit and loss from soybean call calendar.
All Prices at March Option Expiration
Futures Future
Spread Calendar Spread Profit Spread
(May-March) March Future Price: 574 584 594 604 614 Profit
-24 -5.5 - 4.5 -3 -4.5 -11.5 -28
-14 -4.5 3 -0.5 -1 -7 -18
-4 -2.5 0 +3 +3.5 -1 - 8
6 0 + 3 +7.5 +9 +5.5 + 2
16 +7 + 11 +17 +19 +13 +12
This example demonstrates just how powerful the influence of the futures
spread is. The calendar spread profit is predominantly a function of the futures
spread price. Thus, even though the calendar spread was attractive from the theo
retical viewpoint of the option's prices, its result does not seem to reflect that theo
retical advantage, due to the influence of the futures spread. Another important
point for the calendar spreader used to dealing with stock options to remember is
that one can lose more than his initial debit in a futures calendar spread if the spread
between the underlying futures inverts.
There is another way to view a calendar spread in futures options, however, and
that is as a substitute or alternative to an intramarket spread in the futures contracts
themselves. Look at Table 35-4 again and notice the far right-hand column. This is

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Chapter 35: Futures Option Strategies for Futures Spreads 709
the profit or loss that would be made by an intramarket soybean spreader who bought
May and sold March at the initial prices of 598 and 594, respectively. The calendar
spread generally outperforms the intramarket spread for the prices shown in this
example. This is where the true theoretical advantage of the calendar spread comes
in. So, if one is thinking of establishing an intrarnarket spread, he should check out
the calendar spread in the futures options first. If the options have a theoretical pric
ing advantage, the calendar spread may clearly outperform the standard intramarket
spread.
Study Table 35-4 for a moment. Note that the intramarket spread is only better
when prices drop but the spread widens (lower left comer of table). In all other
cases, the calendar spread strategy is better. One could not always expect this to be
true, of course; the results in the example are partly due to the fact that the March
options that were sold were relatively expensive when compared with the May
options that were bought.
In summary, the futures option calendar spread is more complicated when
compared to the simpler stock or index option calendar spread. As a result, calendar
spreading with futures options is a less popular strategy than its stock option coun
terpart. However, this does not mean that the strategist should overlook this strate
gy. As the strategist knows, he can often find the best opportunities in seemingly
complex situations, because there may be pricing inefficiencies present. This strate
gy's main application may be for the intramarket spreader who also understands the
usage of options.
LONG COMBINATIONS
Another attractive use of options is as a substitute for two instruments that are being
traded one against the other. Since intermarket and intramarket futures spreads
involve two instruments being traded against each other, futures options may be able
to work well in these types of spreads. You may recall that a similar idea was pre
sented with respect to pairs trading, as well as certain risk arbitrage strategies and
index futures spreading.
In any type of futures spread, one might be able to substitute options for the
actual futures. He might buy calls for the long side of the spread instead of actually
buying futures. Likewise, he could sell calls or buy puts instead of selling futures for
the other side of the spread. In using options, however, he wants to avoid two prob
lems. First, he does not want to increase his risk. Second, he does not want to pay a
lot of time value premium that could waste away, costing him the profits from his
spread.

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710 Part V: Index Options and Futures
Let's spend a short time discussing these two points. First, he does not want to
increase his risk. In general, selling options instead of utilizing futures increases one's
risk. If he sells calls instead of selling futures, and sells puts instead of buying futures,
he could be increasing his risk tremendously if the futures prices moved a lot. If the
futures rose tremendously, the short calls would lose money, but the short puts would
cease to make money once the futures rose through the striking price of the puts.
Therefore, it is not a recommended strategy to sell options in place of the futures in
an intramarket or intennarket spread. The next example will show why not.
Example: A spreader wants to trade an intramarket spread in live cattle. The con
tract is for 40,000 pounds, so a one-cent move is worth $400. He is going to sell April
and buy June futures, hoping for the spread to narrow between the two contracts.
The following prices exist for live cattle futures and options:
April future: 78.00
June future: 74.00
April 78 call: 1.25
June 74 put: 2.00
He decides to use the options instead of futures to implement this spread. He
sells the April 78 call as an alternative to selling the April future; he also sells the June
74 put as an alternative to buying the June future.
Sometime later, the following prices exist:
April future: 68.00
June future: 66.00
April 78 call: 0.00
June 74 put: 8.05
The futures spread has indeed narrowed as expected - from 4.00 points to 2.00.
However, this spreader has no profit to show for it; in fact he has a loss. The call that
he sold is now virtually worthless and has therefore earned a profit of 1.25 points;
however, the put that was sold for 2.00 is now worth 8.05 - a loss of 6.05 points.
Overall, the spreader has a net loss of 4.80 points since he used short options, instead
of the 2.00-point gain he could have had if he had used futures instead.
The second thing that the futures spreader wants to ensure is that he does not
pay for a lot of time value premium that is wasted, costing him his potential profits.
If he buys at- or out-of-the-money calls instead of buying futures, and if he buys at-

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Chapter 35: Futures Option Strategies for Futures Spreads 711
or out-of-the-money puts instead of selling futures, he could be exposing his spread
profits to the ravages of time decay. Do not substitute at- or out-of-the-rrwney options
for the futures in intramarket or intennarket spreads. The next example will show
why not.
Example: A futures spreader notices that a favorable situation exists in wheat. He
wants to buy July and sell May. The following prices exist for the futures and options:
May futures: 410
July futures: 390
May 410 put: 20
July 390 call: 25
This trader decides to buy the May 410 put instead of selling May futures; he
also buys the July 390 call instead of buying July futures.
Later, the following prices exist:
May futures: 400
July futures: 400
May 410 put: 25
July 390 call: 30
The futures spread would have made 20 points, since they are now the same
price. At least this time, he has made money in the option spread. He has made 5
points on each option for a total of 10 points overall - only half the money that could
have been made with the futures themselves. Nate that these sample option prices
still show a good deal of time value premium remaining. If more time had passed and
these options were trading closer to parity, the result of the option spread would be
worse.
It might be pointed out that the option strategy in the above example would
work better if futures prices were volatile and rallied or declined substantially. This
is true to a certain extent. If the market had moved a lot, one option would be very
deeply in-the-money and the other deeply out-of-the-money. Neither one would
have much time value premium, and the trader would therefore have wasted all the
money spent for the initial time premium. So, unless the futures moved so far as to
outdistance that loss of time value premium, the futures strategy would still outrank
the option strategy.
However, this last point of volatile futures movement helping an option position
is a valid one. It leads to the reason for the only favorable option strategy that is a sub-

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712 Part V: Index Options and Futures
stitute for futures spreads - that is, using in-the-money options. If one buys in-the
rnoney calls instead of buying futures, and buys in-the-money puts instead of selling
futures, he can often create a position that has an advantage over the intramarket or
intermarket futures spread. In-the-money options avoid most of the problems
described in the two previous examples. There is no increase of risk, since the options
are being bought, not sold. In addition, the amount of money spent on time value
premium is small, since both options are in-the-money. In fact, one could buy them
so far in the money as to virtually eliminate any expense for time value premium.
However, that is not recommended, for it would negate the possible advantage of
using moderately in-the-money options: If the underlyingfutures behave in a volatile
manner, it might be possible for the option spread to make money, even if the futures
spread does not behave as expected.
In order to illustrate these points, the TED spread, an intermarket spread, will
be used. Recall that in order to buy the TED spread, one would buy T-bill futures
and sell an equal quantity of Eurodollar futures.
Options exist on both T-bill futures and Eurodollar futures. If T-bill calls were
bought instead of T-bill futures, and if Eurodollar puts were bought instead of sell
ing Eurodollar futures, a similar position could be created that might have some
advantages over buying the TED spread using futures. The advantage is that if T-bills
and/or Eurodollars change in price by a large enough amount, the option strategist
can make money, even if the TED spread itself does not cooperate.
One might not think that short-term rates could be volatile enough to make this
a worthwhile strategy. However, they can move substantially in a short period of time,
especially if the Federal Reserve is active in lowering or raising rates. For example,
suppose the Fed continues to lower rates and both T-bills and Eurodollars substan
tially rise in price. Eventually, the puts that were purchased on the Eurodollars will
become worthless, but the T-bill calls that are owned will continue to grow in value.
Thus, one could make money, even if the TED spread was unchanged or shrunk, as
long as short-term rates dropped far enough.
Similarly, if rates were to rise instead, the option spread could make money as
the puts gained in value (rising rates mean T-bills and Eurodollars will fall in price)
and the calls eventually became worthless.
Example: The following prices for June T-bill and Eurodollar futures and options
exist in January. All of these products trade in units of 0.01, which is worth $25. So a
whole point is worth $2,500.
June T-bill futures: 94.75
June Euro$ futures: 94.15

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Chapter 35: Futures Option Strategies for Futures Spreads
June T-bill 9450 calls: 0.32
June Euro$ 9450 puts: 0.40
713
The TED spread, basis June, is currently at 0.60 (the difference in price of the
two futures). Both futures have in-the-money options with only a small amount of
time value premium in them.
The June T-bill calls with a striking price of 94.50 are 0.25 in the money and are
selling for 0.32. Their time value premium is only 0.07 points. Similarly, the June
Eurodollar puts with a striking price of 94.50 are 0.35 in the money and are selling
for 0.40. Hence, their time value premium is 0.05.
Since the total time value premium - 0.12 ($300) - is small, the strategist
decides that the option spread may have an advantage over the futures intermarket
spread, so he establishes the following position:
Buy one June T-bill call @ 0.40
Buy one June Euro$ put @ 0.32
Total cost:
Cost
$1,000
$ 800
$1,800
Later, financial conditions in the world are very stable and the TED spread
begins to shrink. However, at the same time, rates are being lowered in the United
States, and T-bill and Eurodollar prices begin to rally substantially. In May, when the
June T-bill options expire, the following prices exist:
June T-bill futures: 95.50
June Euro$ futures: 95.10
June T-bill 9450 calls: 1.00
June Euro$ 9450 puts: 0.01
The TED spread has shrunk from 0.60 to only 0.40. Thus, any trader attempt
ing to buy the TED spread using only futures would have lost $500 as the spread
moved against him by 0.20.
However, look at the option position. The options are now worth a combined
value of 1.01 points ($2,525), and they were bought for 0.72 points ($1,800). Thus,
the option strategy has turned a profit of $725, while the futures strategy would have
lost money.
Any traders who used this option strategy instead of using futures would have
enjoyed profits, because as the Federal Reserve lowered rates time after time, the
prices of both T-bills and Eurodollars rose far enough to make the option strategist's

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714 Part V: Index Options and Futures
calls more profitable than the loss in his puts. This is the advantage of using in-the
money options instead of futures in futures spreading strategies.
In fairness, it should be pointed out that if the futures prices had remained rel
atively unchanged, the 0.12 points of time value premium ($300) could have been
lost, while the futures spread may have been relatively unchanged. However, this
does not alter the reasoning behind wanting to use this option strategy.
Another consideration that might come into play is the margin required. Recall
that the initial margin for implementing the TED spread was $400. However, if one
uses the option strategy, he must pay for the options in full - $1,800 in the above
example. This could conceivably be a deterrent to using the option strategy. Of
course, if by investing $1,800, one can make money instead of losing money with the
smaller investment, then the initial margin requirement is irrelevant. Therefore, the
profit potential must be considered the more important factor.
FOLLOW-UP CONSIDERATIONS
When one uses long option combinations to implement a futures spread strategy, he
may find that his position changes from a spread to more of an outright position. This
would occur if the markets were volatile and one option became deeply in-the
money, while the other one was nearly worthless. The TED spread example above
showed how this could occur as the call wound up being worth 1.00, while the put
was virtually worthless.
As one side of the option spread goes out-of-the-money, the spread nature
begins to disappear and a more outright position takes its place. One can use the
deltas of the options in order to calculate just how much exposure he has at any one
time. The following examples go through a series of analyses and trades that a strate
gist might have to face. The first example concerns establishing an intermarket
spread in oil products.
Example: In late summer, a spreader decides to implement an intermarket spread.
He projects that the coming winter may be severely cold; furthermore, he believes
that gasoline prices are too high, being artificially buoyed by the summer tourist sea
son, and the high prices are being carried into the future months by inefficient mar
ket pricing.
Therefore, he wants to buy heating oil futures or options and sell unleaded
gasoline futures or options. He plans to be out of the trade, if possible, by early
December, when the market should have discounted the facts about the winter.
Therefore, he decides to look at January futures and options. The following prices
exist:

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CHAPTER 36
The Basics of
Volatility Trading
Volatility trading first attracted mathematically oriented traders who noticed that the
market's prediction of forthcoming volatility - for example, implied volatility - was
substantially out of line with what one might reasonably expect should happen.
Moreover, many of these traders (market-makers, arbitrageurs, and others) had
found great difficulties with keeping a "delta neutral" position neutral. Seeking a bet
ter way to trade without having a market opinion on the underlying security, they
turned to volatility trading. This is not to suggest that volatility trading eliminates all
market risk, turning it all into volatility risk, for example. But it does suggest that a
certain segment of the option trading population can handle the risk of volatility with
more deference and aplomb than they can handle price risk
Simply stated, it seems like a much easier task to predict volatility than to pre
dict prices. That is said notwithstanding the great bull market of the 1990s, in which
every investor who strongly participated certainly feels that he understands how to
predict prices. Remember not to confuse brains with a bull market. Consider the chart
in Figure 36-1. This seems as if it might be a good stock to trade: Buy it near the lows
and sell it near the highs, perhaps even selling it short near the highs and covering
when it later declines. It appears to have been in a trading range for a long time, so
that after each purchase or sale, it returns at least to the midpoint of its trading range
and sometimes even continues on to the other side of the range. There is no scale on
the chart, but that doesn't change the fact that it appears to be a tradable entity. In
fact, this is a chart of implied volatility of the options on a major U.S. corporation. It
really doesn't matter which one (it's IBM), because the implied volatility chart of near
ly every stock, index, or futures contract has a similar pattern - a trading range. The
only time that implied volatility will totally break out of its "normal" range is if some
thing material happens to change the fundamentals of the way the stock moves - a
takeover bid, for example, or perhaps a major acquisition or other dilution of the stock
727

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728 Part VI: Measuring and Trading Volatility
FIGURE 36-1.
A sample chart.
Buy at these points.
So, many traders observed this pattern and have become adherents of trying to
predict volatility. Notice that if one is able to isolate volatility, he doesn't care where
the stock price goes he is just concerned with buying volatility near the bottom of
the range and selling it when it gets back to the middle or high end of the range, or
vice versa. In real life, it is nearly impossible for a public customer to be able to iso
late volatility so specifically. He will have to pay some attention to the stock price, but
he still is able to establish positions in which the direction of the stock price is irrel
evant to the outcome of the position. This quality is appealing to many investors, who
have repeatedly found it difficult to predict stock prices. Moreover, an approach such
as this should work in both bull and bear markets. Thus, volatility trading appeals to
a great number of individuals. Just remember that, for you personally to operate a
strategy properly, you must find that it appeals to your own philosophy of trading.
Trying to use a strategy that you find uncomfortable will only lead to losses and frus
tration. So, if this somewhat neutral approach to option trading sounds interesting to
you, then read on.
DEFINITIONS OF VOLATILITY
Volatility is merely the term that is used to describe how fast a stock, future, or index
changes in price. When one speaks of volatility in connection with options, there are
two types of volatility that are important. The first is historical volatility, which is a
measure of how fast the underlying instrument has been changing in price. The other
is implied volatility, which is the option market's prediction of the volatility of the

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