Index
Active management,
117
,
125
–126,
150
capital allocation, relationship,
79
–81
volatility trading concept,
58
Active traders,
125
Active trading,
2
–3,
123
,
149
Advanced portfolio management,
3
,
133
,
149
advanced diversification,
149
–153
capital (balancing), POP (usage),
153
–156
market/underlying IV, consideration (absence),
156
portfolio construction,
156
–160
positions, POP‐weighting,
156
straddle, price,
181
strategy diversification,
151
American options, exercise,
7
Assets
combination,
38
correlation history,
138t
illiquid asset,
94
management, Kelly Criterion (application),
185
portfolio, trading,
137
rates, experience,
52t
realized moves, IV overstatement,
46t
trading,
94
,
173
–174
universe, selection,
94
–95
volatility,
31
weighting, POP (usage),
149
At‐the‐money (ATM)
contract description,
9
positions,
33
straddle,
181
strikes,
32
closeness,
99
–100,
146
Autocorrelation,
26
Backtest period, usage,
158
Beta (
β
)
beta‐weighted delta,
38
,
144
–145,
148
,
174
index, assumption,
145
metric,
38
Bid‐ask spread,
94
,
95t
Binary events,
3
EMH, relationship,
164
examples,
163
option strategies,
166
–167
outcomes, predictability (absence),
164
premium, buying/selling result (evidence),
164
stock‐specific binary events,
156
trades,
166
–167,
175
volatility expansion, impact,
164
Black‐Scholes assumptions, usage,
44
–45
Black‐Scholes equation,
29
European‐style option price evolution, relationship,
23
Black‐Scholes model,
22
–31,
35
,
42
,
179
,
181t
assumptions,
23
,
27
,
35
,
44
,
45
Brownian motion (Wiener process), relationship,
23
–26
geometric Brownian motion, relationship,
27
–28
mathematical definition, derivation,
111
mechanics,
30
options fair price, estimate,
30
,
42
price dynamics approximation,
24
Black‐Scholes option pricing formalism, impact,
22
–23
Black‐Scholes options pricing model,
44
–45
Black‐Scholes theoretical price range,
179
Brownian motion
Black‐Scholes model, relationship,
23
–26
cumulative horizontal displacements,
24
–25,
25f
particle, 2D position,
25f
price dynamics, comparison,
25
–26
stock log‐returns, evolution,
179
Bullish directional exposure,
90t
Buying power, allocation percentages,
154t
Buying Power Reduction (BPR),
3
,
66
,
83
,
153
average BPR comparison,
110t
,
113t
calculation,
84
capital
coverage,
89
requirement, correspondence,
85
–86
definition, variation,
84
historical effectiveness,
84
IV
comparison,
66
inverse relationship,
87
loss percentage,
85f
margin, contrast,
84
maximum per‐trade BPR, limitation,
134
option price, inverse correlation,
87
options, capital efficiency (relationship),
90
portfolio capital amount,
171
reduction, impact,
89
result,
87t
short call/put BPR,
86
short strangle BPR,
86
stock margin, option counterpart,
84
undefined risk strategies, relationship,
84
underlying IV function/underlying price function,
88f
understanding, importance,
90
usage,
83
,
89
variables, dependence,
85
–86
Call option,
7
,
9
strike prices, comparison,
114t
trading level (determination), Black‐Scholes model (usage),
31
Call skew,
112
Call strikes, comparison,
111
–112
Capital
balancing, POP (usage),
153
–156
requirement, BPR (correspondence),
85
–86
Capital allocation
amounts, differences,
78f
control,
81
efficiency, active management (relationship),
79
–81
estimate, risk‐free rate value (usage),
154
–155
guidelines,
133
,
152
,
155
,
156
maintenance,
149
,
173
market IV, impact,
76t
violation, avoidance,
155
position sizing, relationship,
134
–136
positional capital allocation, quantitative approach,
153
preferences,
129
,
131
,
172
proportions, estimation,
155
risk management techniques, incorporation (impact),
158
scaling,
79
,
134
short premium capital allocation, scaling up,
76
undefined risk capital allocation, sharing,
110
undefined risk strategy, usage,
110
volatility trading concept,
58
Capital at risk (comparison), BPR (usage),
89
Casinos
long‐run statistical advantage,
58
,
72
–73
options trading,
1
–2
CBOE volatility index.
See
Volatility index
Central limit theorem,
20
,
72
,
166
,
170
,
178
Company exposure,
98
Company‐specific risk,
96
Company‐specific uncertainty,
43
Conditional probability,
183
–184
calculation,
184
usage,
142
Conditional value at risk (CVaR),
63
inclusion,
40f
metric,
38
usage,
39
–40,
65
–66,
123
VaR, contrast,
40
Contract delta,
33
–35,
79
,
111
,
114
implied volatility (IV), equivalence,
87
risk,
172
Contract duration
middle ground contract duration,
101
selection,
94
,
99
–102
trading, importance,
151
Contracts
average daily P/L and average duration,
121t
extrinsic value, decrease,
34
prices, differences,
42t
Core positions,
134
P/L standard deviations, presence,
156
–157
Covariance
correlation, relationship,
35
–38
measures,
37
negative covariance,
36
positive covariance,
35
Cumulative horizontal displacement,
25f
Cumulative horizontal displacements,
24
Daily P/Ls, standard deviation,
150f
Daily returns, distribution,
39f
,
40f
Days to expiration (DTE), management usage,
118
–120
Defined risk, selection,
102
–104
Defined risk strategies,
152
maximum loss,
102
BPR, usage,
84
limitation,
59
P/L targets, attainment,
153
POP, usage,
110
portfolio allocation,
103t
risk, comparison,
89
selection,
94
short premium allocation,
173
stop losses, unsuitability,
173
undefined risk strategies, comparison,
102t
,
109
avoidance,
110
Delta (Δ),
31
–32,
106t
basis,
112
beta‐weighted delta,
38
,
144
–145,
148
,
174
contract delta,
33
–35,
79
,
111
,
114
implied volatility (IV), equivalence,
87
contract risk,
172
contract usage,
32
directional exposure measurement,
111
drift,
145
level,
114
magnitude,
32
,
114
negative delta/positive delta,
33
neutral position,
33
,
61
,
146
,
156
neutral positions
profit,
111
normalization,
145
perceived risk measure,
112
–113
raw delta, comparisons (impossibility),
146
–147
re‐centering,
114
scaling up,
114
selection,
94
,
111
–115
optimum, factors,
114
sensitivity,
146
sign,
32
value, range,
32
Derivatives, gamma comparison (impossibility),
146
–147
Deterministic price trends,
28
–29
Dice rolls, histogram,
13
,
14f
,
17f
,
19f
,
21f
Directional assumption, selection,
94
,
104
–110
Directional exposure (measurement), delta (usage),
111
Directional risk, degree (measure),
32
Distributions
asymmetry (measure), skew (usage),
65
mean (histogram),
17e
normal distribution,
22f
,
44
–45,
180f
skew,
16
–18,
20
,
39
statistics, understanding,
21
–22
Diversification,
136
–144,
158
effectiveness, understanding,
137
–138
time diversification,
151
tools,
173
Dividends payment, avoidance,
23
Downside risk
amount, preference,
104
limitation, absence,
102
Downside skew,
112
Early‐managed contracts,
126
,
129
occurrences allowance,
80
Early‐managed portfolio, losses,
129
Early‐management strategies,
80
Earnings dates, marking,
54f
Earnings report,
115
dates,
53
,
96
,
102
impact,
43
inclusion,
163
quarterly earnings report (single‐company factors),
52
,
166
,
175
Efficient market hypothesis (EMH),
11
–13,
177
–178,
183
binary events, relationship,
164
forms,
11
–12,
104
–105
interpretation,
104
,
116
Equities
implied volatility indexes,
54f
pricing/bid‐ask spread/volume data,
95t
trading,
137
,
140
European call options,
29
European options, expiration (payoff),
29
European‐style option (price evolution), Black‐Scholes equation (relationship),
23
Events
outcomes,
44
–45
sampling, probability distribution (usage),
72
Exchange‐traded funds (ETFs),
5
–7,
36
,
157
BPR, historical effectiveness,
84
correlations,
157t
diversification,
53
–54,
134
historical risk, approximation,
63
IV overstatement rates,
46
market ETFs,
139
–142,
145
,
157
volatility assets, correlation,
139
skewed returns distribution,
22
stability,
98
underlyings,
95
,
135
,
137
,
172
advantages/disadvantages,
96t
losses,
84
,
171
strangles, usage,
156
usage,
97
volatility profiles, differences,
96
Expected move cones,
44
,
45f
,
60f
Expected move range,
179
Expected price range,
45f
Expected range,
58
,
179
–183
adjustment,
68
–69
calculation,
43
–45,
47
,
179
,
181
estimates,
44
increase,
115
short strike prices, relationship,
111
tightness,
51
underlying price expected range,
60
–61
External events, outlier underlying moves/IV expansions (relationship),
58
Financial derivative, options (comparison),
7
Financial insurance, risk‐reward trade‐off,
47
Gamma (
Γ
),
31
,
33
comparison, impossibility,
146
–147
increase,
79
magnitude,
33
risk,
146
–147
Gaussian distribution (bell curve),
20
Geometric Brownian motion, Black‐Scholes model (relationship),
27
–28
GLD returns, SPY returns (contrast),
36f
Greeks,
31
–35.
See also
Delta
;
Gamma
;
Sigma
;
Theta
assumptions,
35
balance,
148
option Greeks,
38
portfolio Greeks,
160
maintenance,
133
,
144
–147
risk measures,
174
Heteroscedasticity,
26
High implied volatility (high IV)
short premium trading,
75
trading,
66
–72,
75
Histogram
daily returns/prices,
27f
dice rolls,
14f
,
17f
,
19f
,
21f
Historical distribution,
73f
Historical P/L distribution,
62f
,
64f
,
71f
Historical returns, standard deviation,
28
,
30
Historical tail risk, estimation,
65
Historical volatility,
21
–22,
38
increase,
42
market historical volatility,
69
representation,
43
stock historical volatility,
30
underlying historical volatility,
31
usage,
30
,
63
Historic risk, estimation,
21
–22
Horizontal displacements, distribution,
26f
Hurricane insurance
price, proportion,
47
sellers, strategic room,
47
–48
Idiosyncratic risk,
137
Illiquid asset, example,
94
Illiquidity risk, minimization,
171
Implied volatility (IV),
3
,
38
,
41
,
83
,
169
–170,
181
basis,
48
BPR
comparison,
66
inverse volatility,
87
contract delta, equivalence,
87
contraction,
50
conversion,
66
correlation,
42
–43
decrease/increase,
42
–43,
87
,
89
derivation,
44
–45
differences,
42t
environments, short option strategies (trading),
76
expansion,
58
,
122
–123,
163
indexes,
53f
,
54f
,
165f
indication,
30
IV‐derived price range,
44
–45
long‐term baseline reversion,
52
metric, importance,
30
–31
overstatement,
46
,
46t
,
164
profits,
58
rates,
47
peak, increase,
49
price range forecast,
47
ranges,
76t
realized risk measurement,
46
reversion,
51
–54
signals, capacity,
51
source,
23
SPY annualized implied volatility (tracking),
48
SPY implied volatility,
69f
standard deviation range,
43
tracking,
48
trading (volatility trading concept),
58
underlying IV,
60
,
86
,
88f
usage,
41
,
134
Implied volatility percentile (IVP),
66
–68
Implied volatility rank (IVR),
68
Increments, distribution,
26f
Insider trading,
12
,
105
In‐the‐money (ITM),
99
contract description,
9
ITM put, price,
10
long calls ITM,
33
movement,
34
–35
options, directional risk,
114
positions,
34
relationship,
32
Iron condors,
105
,
110t
,
151
cap, long wings,
106
,
108
drawdowns, experience,
151
narrow wings, POP (presence),
109
neutral SPY strategies,
151
profit potential,
109
representation,
107f
risk,
110
short iron condor BPR,
108
short iron condors, range,
134
,
173
statistical comparison,
109t
underlying strangle, contrast,
171
wide iron condors,
116
,
172
wide wings, inclusion (trading),
109
wings, inclusion,
106
Kelly Criterion
application,
185
buying power percentage,
153
derivation,
184
–186
formula,
186
heuristic derivation,
160
uncorrelated bets,
154
Law of large numbers,
72
,
170
,
185
Liquidity
importance, understanding,
94
net liquidity,
89t
options liquidity,
94
–95
portfolio net liquidity,
104
,
145
theta ratio/net portfolio liquidity,
145
Log‐normal distribution,
177
comparison,
180f
skew,
179
stock prices, relationship,
179
Log returns
equation,
7
standard deviation,
23
Long call,
32
,
34
addition,
106
directional assumption,
8t
option, price,
32
,
111
P/L,
10
–11
position,
33
profit potential,
90
Long premium
contracts, impact,
84
positions, profit yield (comparison),
12
strategies,
58
,
170
trade,
8
Long put,
32
,
34
addition,
106
directional assumption,
8t
option, price,
111
P/L,
10
–11
position,
33
Long stock,
32
Long strikes,
207f
Loss
incurring, probability,
113t
targets,
122t
,
123
Low‐loss targets, attainment,
122
Management
P/L target, usage,
120
–124
techniques,
123
–126,
152
timeline, usage,
118
–119
Management strategies,
121t
,
122t
,
158
average daily P/L and average duration,
121t
impact/comparison,
79
–80,
80t
,
102
long‐term risks,
126
,
129
performance, scenarios (impact),
126
qualitative comparison,
125t
selection,
172
usage,
117
–118
Management time, selection,
119
,
129
Margin, BPR (contrast),
84
Market
conditions, risk/return expectations,
35
exposure,
98
frictionlessness,
23
historical volatility,
69
implied volatility (IV),
76t
,
152
perceived uncertainty,
46
trader beliefs,
171
–172
uncertainty sentiment, IV tracking,
48
volatility amounts, differences,
89t
Market ETFs,
139
–142,
145
,
157
historic correlations,
141t
,
143t
percentage,
138t
volatility assets, correlation,
139
Market risk
sentiment, IV proxy,
42
sentiment, IV proxy (usage),
169
–170
Maximum per‐trade BPR, limitation,
134
Mean (moment),
14
–15
Middle ground contract duration,
101
Mid‐range stop loss,
123
,
130
,
173
Moments,
14
–22
Near‐the‐money options, gamma (increase),
79
Negative covariance,
36
Non‐dividend‐paying stock, trading,
30
–31
Non‐fungible tokens (NFTs),
5
Normal distribution
comparison,
180f
mean/standard deviation,
180f
plot,
22f
standard deviation range,
44
–45
Occurrences,
62f
,
71f
,
101
compound occurrences, loss potential,
142
concentration,
20
consistency,
117
density,
64
early‐managed contract allowance,
80
final P/L, correspondence,
61
goal,
125
–126,
151
increase,
117
P/L distribution,
39
reduction/increase,
72
,
89
,
124
standard deviation range,
64
VIX level, contrast,
67
Occurrences, number,
58
,
72
–76,
99
attainment,
99
compromise, absence,
151
increase,
81
,
101
–102,
118
presence,
15
,
126
,
129
trade‐off,
119
volatility trading concept,
58
Off‐diagonal entries,
141t
Options,
5
–6
buying, profit,
57
–58
capital efficiency, BPR (relationship),
90
demand,
42
–43
fair price (estimation), Black‐Scholes model (usage),
30
,
42
financial derivative, comparison,
7
Greeks,
38
illiquidity, risk,
94
leverage, effects (clarity),
90
liquidity,
94
–95
market, liquidity,
98
P/L standard deviation, usage,
73
P/L statistics,
97t
price, BPR (inverse correlation),
87
profitability,
10
risk, visualization,
59
–63
traders, assumptions,
11
types,
7
underlyings, sample,
98t
Options trading,
84
,
97
,
102
,
169
,
175
casinos, usage,
1
–2
diversification, importance,
136
ETF underlyings, usage,
97
gamma, awareness (importance),
33
implied volatility
metric,
30
–31
reversion,
51
learning curve/math knowledge,
3
option theory, transition,
90
profitability, option pricing (impact),
11
quantitative options trading,
3
retail options trading, assets (suitability),
94
risk management, relationship,
2
usage, market performance,
12
Outlier losses,
142
capital exposure, limitation,
134
probability,
141t
Outlier risk
carrying, avoidance,
103
reduction,
76
Out‐of‐the‐money (OTM)
contract description,
9
positions,
34
volatility curve,
182f
Over‐the‐counter (OTC) options,
7
Passive investment, daily performance statistics,
146t
Passive traders,
125
Perceived risk (measurement), delta (usage),
112
–113
Personal profit goals,
171
–172
Per‐trade allocation percentage,
158t
Per‐trade standard deviation,
158
,
166
Per‐trade statistics, differences,
166
Per‐trade variance,
167
P/L targets, attainment,
153
Portfolio
averages, variance,
74f
backtest performance statistics,
159t
concentration excess, avoidance,
77
construction,
12
,
156
–160
cumulative P/L,
152f
delta skew,
145
expected loss, CVaR estimate,
40
Greeks,
149
,
160
maintenance,
133
,
144
–147
net liquidity,
89t
,
104
,
146
passive investment, daily performance statistics,
146t
performance,
159f
comparison,
139f
P/L averages,
74f
POP‐weighted portfolio,
157
–158
risk management, diversification tools,
173
statistical analysis,
153t
Portfolio allocation,
109
defined/undefined risk strategies,
103t
guidelines, usage,
89
,
104
,
134
percentages,
137
–138,
138t
,
154
,
154t
position sizing, relationship,
75
–79
scaling,
77
,
156
strategies, comparison,
77
usage,
103
volatility trading concept,
58
Portfolio buying power,
83
,
89
,
134
allotment/allocation,
134
–135,
154
–155,
157
defined risk position occupation,
118
expected profit,
146
undefined risk strategy occupation,
110
usage,
99
,
109
,
117
Portfolio capital
allocation
control,
81
guidelines, market IV (impact),
76t
amount, BPR (relationship),
171
diversification,
152
investment,
127f
,
128f
Portfolio management,
3
,
93
,
149
back‐of‐the‐envelope tactics,
133
beta (
β
) metric, importance,
38
capital allocation,
134
–136
capital balancing, POP (usage),
153
–156
concepts,
133
construction,
156
–160
diversification, usage,
136
–144,
149
–153
portfolio Greeks, maintenance,
144
–147
position sizing,
134
–136
simplification,
101
Positional capital allocation, quantitative approach,
153
Positions
core position statistics,
158t
delta drift,
145
delta level,
114
expected loss, CVaR estimate,
40
intrinsic value,
9
ITM, relationship,
32
long side/short side, adoption,
8
management,
118
P/L correlation, reduction,
150
POP‐weighting,
156
profiting, likelihood,
104
sizing
capital allocation, relationship,
134
–136
portfolio allocation, relationship,
75
–79
volatility trading concept,
58
Positive covariance,
35
Premium sellers, profit,
50
Premium, trading,
172
Price dynamics
Black‐Scholes model approximation,
24
Brownian motion, comparison,
25
–26
Price predictability (limitation), EMH implications,
105
Probabilistic system, probability distribution,
14
Probability distribution,
13
–22
asymmetry,
16
events sampling,
72
Gaussian distribution (bell curve),
20
mean (moment),
14
–15
normal distribution,
20
skew (moment),
16
–22
variance (moment),
15
–16
Probability of profit (POP),
89
,
164
,
185
asset weighting,
149
buying power, allocation percentages,
154t
capital, balancing,
153
–156
decrease,
114
dependence,
77
heuristic,
160
IV ranges,
76t
level, elevation,
61
,
90
,
105
,
108
–109,
120
,
123
–124,
151
percentage,
62
,
73
,
109
POP‐weighted allocation,
158
POP‐weighted portfolio,
157
–158,
159t
POP‐weight scaling method,
156
positions, POP‐weighting,
156
profit potential, differences,
103
selection,
2
statistics,
80t
,
97t
,
153t
trade‐off,
63
trades, level (elevation),
134
usage,
110
,
149
,
153
,
185
–186
weights, usage,
155
yield,
121
Product indifference,
97
–98
Profitability, considerations,
8t
Profit and loss (P/L)
average daily P/L,
121t
average P/L,
76t
,
164
averages,
74f
cumulative P/L,
152f
daily P/Ls, standard deviation,
150f
distribution skew,
62
–63
expectations,
135
frequency,
124
historical distribution,
73f
historical P/L distribution,
62f
,
64f
,
71f
IV ranges,
76t
per‐day standard deviation,
150
standard deviation,
134
,
153t
,
157
carrying,
120
–121
core position usage,
156
–157
reduction,
118
–119,
122
,
126
trade‐offs,
124
usage,
63
–65,
74
–75,
80t
,
99
,
100t
,
123
swings,
79
,
97
magnitude,
98
tolerance,
97
–98
Profit potential, POP
differences,
103
level, elevation,
151
Profit targets,
104
,
120t
,
123
Put options,
9
Put prices, differences,
98t
Put skew,
112
Puts (option type),
7
QQQ
returns, SPY returns (contrast),
36f
,
37
strangles, outlier losses,
142
Quantitative options trading,
3
Quarterly earnings report (single‐company factors),
52
,
166
,
175
Random variable, probability distribution,
13
Realized moves, IV overstatement,
46t
Realized risk (measurement), IV (usage),
46
Realized volatility, IV overstatement,
46
Reference index, usage,
144
Relative volatility, metrics,
66
–68
Retail options trading, assets (suitability),
94
Returns
distributions skews,
22
past volatility/future volatility,
43
standard deviation,
21
–22
usage,
63
Risk
approximation,
30
categories,
137
measures,
38
–40
minimization, liquidity (impact),
95
reduction, trade‐by‐trade basis,
117
sentiment, measure,
30
–31
tolerances,
171
–172
trade‐off,
12
Risk‐free rate,
29
approximation,
154
value, usage,
154
–155
Risk management,
2
–3,
37
,
140
,
156
importance,
51
strategy/technique,
136
,
151
,
158
,
174
Risk‐reward trade‐off,
59
Sector exposure,
98
Sector‐specific risk,
96
Sell‐offs
2020 sell‐off, performances (2017‐2021),
78f
volatility conditions,
164
Semi‐strong EMH,
12
,
104
–105
Short call,
32
,
34
addition,
147
,
175
BPR,
86
directional assumption,
8t
P/L,
10
–11
position,
33
removal,
175
short put, pairing,
33
strike,
60
undefined risk,
59
Short‐call/put BPR,
86
Short iron condors, range,
134
,
173
Short options
P/L distribution skew,
63
trading, capital requirements,
90
Short option strategies,
106t
profitability, factors,
170
trading,
76
,
170
Short premium
allocation,
173
capital allocation, scaling up,
76
positions, losses (unlikelihood),
170
risk (evaluation), BPR (usage),
83
strategies, POP trade‐off,
63
traders, profit,
51
Short premium trading,
48
,
114
benefits,
68
implied volatility
elevation, impact,
71
importance,
59
mechanics,
57
risk‐reward trade‐off,
59
Short put,
34
addition,
147
,
174
–175
BPR,
86
bullish strategy,
32
directional assumption,
8t
position,
33
removal,
175
strike,
60
Short strangles, POP level (elevation),
61
Short strike prices, expected range (relationship),
111
Short volatility trading,
83
Sigma (
σ
),
15
Single‐company factors,
52
–53
Single company risk factors, impact,
46
Skew,
68
amount, consideration,
71
contextualization,
65
distribution skew,
16
–18,
20
,
39
log‐normal distribution skew,
179
magnitude, decrease,
72
moment,
16
–22
P/L distribution skew,
62
–63
portfolio delta skew,
145
pure number,
17
reduction,
71
–72
returns distribution skews,
22
strike skew,
111
–112,
179
–183
tail skew, usage,
39
usage,
65
–66
volatility skew (volatility smirk),
181
SPDR S&P 500 (SPY)
annualized implied volatility, tracking,
48
daily returns distribution,
39f
,
40f
expected move cone,
45f
expected price ranges,
44
histogram, daily returns/prices,
27f
implied volatility (IV),
69f
,
70f
iron condors, wings (inclusion),
107t
–110t
neutral SPY strategies,
151
price,
112f
change,
60f
,
78f
trends,
24
returns, QQQ/TLT/GLD returns (contrast),
36f
,
37
trading level,
183
SPDR S&P 500 (SPY) strangles,
64f
,
73f
BPR loss,
85f
data (2005‐2021),
88f
,
89t
deltas (differences), statistical comparison,
113t
durations, differences,
183t
example,
107t
initial credits,
108t
management
statistics,
119t
,
120t
,
122t
,
124t
,
125t
strategies, comparison,
80t
outlier losses,
142
P/L per‐day standard deviation,
150
stability,
63
VIX level labeling,
69f
Standard deviation,
20
–21
daily P/Ls, standard deviation,
150
estimates,
16
expected move range,
179
expected range,
60
strikes, correspondence,
183
histogram,
17f
historical returns, standard deviation,
28
,
30
indication,
16
interpretation,
18
–19,
64
–65
log returns, standard deviation,
23
normal distribution usage,
180f
per‐trade standard deviation,
158
,
166
P/L per‐day standard deviation,
150
P/L standard deviation,
63
–65,
74
–75,
80t
,
99
,
100t
,
134
,
153t
,
157
carrying,
120
–121
reduction,
118
–119,
122
,
126
trade‐offs,
124
usage,
123
probabilities,
22f
range, sigma (
σ
),
37
,
43
–45,
64
–65
representation,
15
returns, standard deviation,
21
–22
sigma (
σ
),
15
usage,
63
–65
Steady‐state value,
48
Stocks,
5
–6
historical risk, approximation,
63
historical volatility,
30
IV overstatement rates,
46
liquidity,
94
–95
log returns,
23
options, trading,
96
–97
prices
differences,
98t
log‐normal distribution, relationship,
179
skewed returns distributions,
22
stock‐specific binary events,
156
trading,
90
,
179
margin, usage,
84
underlyings
advantages/disadvantages,
96t
trading,
135
volatility profiles, differences,
96
Stop loss,
122
application,
129
implementation,
122
,
130
,
173
mid‐range stop loss,
123
,
130
,
173
threshold, usage,
122
–123
usage,
123
–125
Straddles
ATM straddle, price,
181
trades, BPR result,
87t
Strangles,
105
buyer assumption,
61
drawdowns, experience,
151
durations, differences,
101t
magnitude,
65
management strategies,
123
neutral SPY strategies,
151
P/L distributions, skew/tail losses,
71
–72
sale, BPR requirement,
86
seller, profit,
61
short strangle BPR,
86
statistics,
167t
management,
122t
,
136t
trades, examples,
87t
trading, effects,
142
usage,
156
Strategy‐specific factors,
152
–153
Strike skew,
111
–112,
179
–183
Strikes
long strikes,
107f
prices, comparison,
114t
range,
104
standard deviation, expected range (correspondence),
183
Strong EMH,
12
,
104
–105
Supplemental positions,
134
Swaptions,
5
Systemic risk,
137
Tail exposure
limitation, capital allocation guidelines (maintenance),
173
magnitude,
98
Tail losses
CVaR sensitivity,
40
reduction,
71
–72
Tail risk,
83
,
103
,
121
,
145
acceptance,
57
carrying,
58
,
62
,
120
elimination,
122
–123
exposure,
102
,
135
historical tail risk, estimation,
65
increase,
97
,
108
–109,
119
inherent tail risk, justification,
121
mitigation,
135
–136
negative tail risk,
65
,
72
,
80
Tail skew, usage,
39
Theta (
Θ
),
31
,
34
,
144
,
174
additivity,
145
–147
ratio, size (reaction),
147
theta ratio/net liquidity,
174
theta ratio/net portfolio liquidity,
145
Time diversification,
151
TLT returns, SPY returns (contrast),
36f
Trade‐by‐trade basis,
79
–80,
117
,
125
–126
Trade‐by‐trade performance, comparison,
118
Trade‐by‐trade risk tolerances,
119
–120
Trades
BPR,
98
bullish directional exposure,
90t
management,
3
,
80
–81,
117
–118
strategies, usage,
101
maximum loss, reduction,
108
Trades, construction,
93
asset universe, selection,
94
–95
contract duration, selection,
99
–102
defined risk, selection,
102
–104
delta, selection,
111
–115
directional assumption, selection,
104
–110
procedure,
94
undefined risk, selection,
102
–104
underlying, selection,
96
–98
Trading
engagement, preferences,
124
mechanics,
48
platforms, usage,
179
,
181
strategies,
129
,
166
Uncertainty sentiment, IV tracking,
48
Undefined risk
capital allocation, sharing,
110
selection,
102
–104
Undefined risk strategies,
59
,
152
BPR, relationship,
84
,
103
defined risk strategies, comparison,
102t
,
109
avoidance,
110
downside risk, limitation (absence),
102
gain, limitation,
84
loss, limitation (absence),
59
,
84
management, focus,
118
P/L targets, attainment,
153
portfolio allocation,
103t
risk, comparison,
89
selection,
94
short premium allocation,
173
trader compensation,
103
Underlying
historical volatility,
31
increase,
42
implied volatility (IV),
98
option underlyings, sample,
98t
selection,
94
,
96
–98
strangle, iron condor (contrast),
171
Underlying price
BPR function,
88f
expected range,
60
–61,
181t
Upside skew,
112
Value at risk (VaR).
See
Conditional value at risk
CVaR, contrast,
40
distribution statistic,
39
inclusion,
39f
,
40f
Variance
moment,
15
–16
per‐trade variance,
166
–167
Volatility
curve,
182
expansions,
50
–51
forecast,
43
realized volatility, IV overstatement,
46
reversion,
105
smile,
179
–183
smirk (volatility skew),
181
trading,
41
,
44
–48,
58
Volatility assets, market ETFs (correlation),
139
Volatility index (VIX) (CBOE volatility index),
51
,
60
,
78f
2008 sell‐off,
50
,
63
2020 sell‐off,
50
,
63
,
77
,
78f
comparison,
89
contraction,
50
contracts, acceleration,
49
correlations,
141t
expansion,
48
increase,
54
IVP labeling,
67f
levels,
127f
,
128f
differences,
103t
SPY strangles, labeling,
69f
long‐term average,
67
,
69
long‐term behavior,
66
lull/expansion/contraction,
49
occurrences, relationship,
71f
phases,
49f
range,
48
,
66
,
72
,
171
reduction/increase,
69
,
134
frequency,
75t
spikes, causes,
50
states,
48
–51
valuation,
135
VXAZN
IVP values labeling,
67f
level,
66
Weak EMH,
11
,
29
,
31
,
104
–105
Wide iron condors,
116
,
172
Wide wings, usage,
109
Wiener process,
29
Black‐Scholes model, relationship,
23
–26
increments, distribution,
26f
Wings,
105