Dynamic Hedging Managing Vanilla and Exotic Options

by Taleb, Nassim Nicholas

• ISBN13: 9780471152804
• ISBN10: 0471152803
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-01-14
• Publisher: Wiley

Summary

Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management.

Author Biography

Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.

Table of Contents

Introduction Dynamic Hedging	1	(8)
Principles of Real World Dynamic Hedging	1	(2)
General Risk Managements	3	(6)
PART I MARKETS, INSTRUMENTS, PEOPLE	9	(100)
1 Introduction to the Instruments	9	(29)
Derivatives	9	(3)
Synthetic Securities	12	(1)
Time-Dependent Linear Derivatives	13	(3)
Noncontingent Time-Dependent Nonlinear Derivatives	16	(1)
Options and Other Contingent Claims	16	(4)
Simple Options	18	(2)
Hard and Soft Optionality	20	(1)
Basic Rules of Options Equivalence	20	(4)
Mirror Image Rule	22	(2)
American Options, Early Exercise, and Other Headaches (Advanced Topic)	24	(5)
Soft American Options	24	(1)
Hard American Options	25	(2)
A Brief Warning about Early Exercise Tests	27	(2)
Forwards, Futures, and Forward-Forwards (Advanced Topic)	29	(3)
Credit	30	(1)
Marks-to-Market Differences	30	(1)
The Correlation between the Future and the Financing (Advanced Issue)	31	(1)
Core Risk Management: Distinction between Primary and Secondary Risks	32	(6)
Applying the Framework to Specific Instruments	35	(3)
2 The Generalized Option	38	(10)
Step 1. The Homogeneity of the Structure	38	(3)
Step 2. The Type of Payoff: Continuous and Discontinuous	41	(2)
Step 3. Barriers	43	(1)
Step 4. Dimension of the Structure and the Number of Assets	43	(2)
Step 5. Order of the Options	45	(1)
Step 6. Path Dependence	46	(2)
3 Market Making and Market Using	48	(20)
Book Runners versus Price Takers	48	(2)
Commoditized and Nonstandard Products	50	(4)
Trading Risks in Commoditized Products	51	(2)
Profitability	53	(1)
Proprietary Departments	54	(2)
Tacit Rules in Market Making	56	(1)
Market Making and the Price for Immediacy	57	(1)
Market Making and Autocorrelation of Price Changes	58	(1)
Market Making and the Illusion of Profitability	58	(2)
Adverse Selection, Signaling, and the Risk Management of Market Makers	60	(2)
Value Trading versus the Greater Fool Theory	62	(2)
Monkeys on a Typewriter	64	(4)
The Statistical Value of Track Records	64	(1)
More Modern Methods of Monitoring Traders	65	(1)
The Fair Dice and the Dubins-Savage Optimal Strategy	65	(1)
The ArcSine Law of the P/L	66	(2)
4 Liquidity and Liquidity Holes	68	(12)
Liquidity	68	(1)
Liquidity Holes	69	(1)
Liquidity and Risk Management	70	(1)
Stop Orders and the Path of Illiquidity	70	(2)
Barrier Options and the Liquidity Vacuum	72	(1)
One-Way Liquidity Traps	73	(1)
Holes, Black-Scholes, and the Ills of Memory	73	(1)
Limits and Market Failures	74	(1)
Reverse Slippage	74	(1)
Liquidity and Triple Witching Hour	75	(1)
Portfolio Insurance	75	(2)
Liquidity and Option Pricing	77	(3)
5 Arbitrage and the Arbitrageurs	80	(8)
A Trader's Definition	80	(1)
Mechanical versus Behavioral Stability	81	(1)
The Deterministic Relationships	82	(1)
Passive Arbitrage	83	(1)
An Absorbing Barrier Called the "Squeeze"	84	(1)
Duration of the Arbitrage	84	(1)
Arbitrage and the Accounting Systems	85	(1)
Other Nonmarket Forms of Arbitrage	86	(1)
Arbitrage and the Variance of Returns	87	(1)
6 Volatility and Correlation	88	(21)
Calculating Historical Volatility and Correlation	92	(3)
Centering around the Mean	92	(3)
Introducing Filtering	95	(2)
There Is No Such Thing as Constant Volatility and Correlation	97	(4)
The Parkinson Number and the Variance Ratio Method	101	(8)
PART II MEASURING OPTION RISKS The Real World and the Black-Scholes-Merton Assumptions Black-Scholes-Merton as an Almost Nonparametric Pricing System	109	(164)
7 Adapting Black-Scholes-Merton: The Delta	115	(17)
Characteristics of a Delta	116	(1)
The Continuous Time Delta Is Not Always a Headge Ratio	116	(5)
Delta as a Measure for Risk	121	(2)
Confusion: Delta by the Cash or by the Forward	123	(1)
Delta for Linear Instruments	123	(3)
Delta for a Forward	123	(2)
Delta for a Forward-Forward	125	(1)
Delta for a Future	125	(1)
Delta and the Barrier Options	126	(1)
Delta and the Bucketing	127	(1)
Delta in the Value at Risk	127	(1)
Delta, Volatility, and Extreme Volatility	127	(5)
8 Gamma and Shadow Gamma	132	(15)
Simple Gamma	132	(1)
Gamma Imperfections for a Book	133	(3)
Correction for the Gamma of the Back Month	136	(2)
First Adjustment	137	(1)
Second Adjustment	138	(1)
Shadow Gamma	138	(4)
Shadow Gamma and the Skew	142	(1)
GARCH Gamma	142	(1)
Advanced Shadow Gamma	142	(3)
Case Study in Shadow Gamma: The Syldavian Elections	145	(2)
9 Vega and the Volatility Surface	147	(20)
Vega and Modified Vega	147	(7)
Vega and the Gamma	149	(1)
The Modified Vega	150	(1)
How to Compute the Simple Weightings	151	(2)
Advanced Method: The Convariance Bucket Vega	153	(1)
Forward Implied Volatilities	154	(10)
Computing Forward Implied Volatility	154	(4)
Multifactor Vega	158	(6)
Volatility Surface	164	(1)
The Method of Squares for Risk Management	164	(3)
10 Theta and Minor Greeks	167	(24)
Theta and the Modified Theta	167	(4)
Modifying the Theta	167	(2)
Theta for a Bet	169	(1)
Theta, Interest Carry, and Self-Financing Strategies	169	(1)
Shadow Theta	170	(1)
Weakness of the Theta Measure	171	(1)
Minor Greeks	171	(10)
Rho, Modified Rho	171	(3)
Omega (Option Duration)	174	(4)
Alpha	178	(3)
Table of Greeks	181	(10)
Stealth and Health	182	(1)
Convexity, Modified Convexity	183	(7)
The "Double Bubble"	190	(1)
11 The Greeks and Their Behavior	191	(17)
The Bleed: Gamma and Delta Bleed (Holding Volatility Constant)	191	(9)
Bleed with Changes in Volatility	195	(1)
Going into the Expiration of a Vanilla Option	196	(4)
Ddeltadvol (Stability Ratio)	200	(2)
Test 1 of Stability	200	(1)
Test 2 of Stability: The Asymptotic Vega Test	201	(1)
Moments of an Option Position	202	(2)
Ignoring Higher Greeks: The Lock Delta	204	(4)
12 Fungibility, Convergence, and Stacking	208	(14)
Fungibility	208	(5)
Ranking of Fungibility	209	(1)
Fungibility and the Term Structure of Prices: The Cash-and-Carry Line	210	(2)
Fungibility and Option Arbitrage	212	(1)
Changes in the Rules of the Game	212	(1)
Convergence	213	(4)
Mapping Convergence	215	(1)
Convergence and Convexity	216	(1)
Levels of Convergence Trading	216	(1)
Volatility and Convergence	216	(1)
Convergence and Biased Assets	216	(1)
Stacking Techniques	217	(5)
Other Stacking Applications	220	(2)
13 Some Wrinkles of Option Markets	222	(7)
Expiration Pin Risks	222	(1)
Sticky Strikes	223	(1)
Market Barriers	224	(2)
A Currency Band: Is It a Barrier?	225	(1)
The Absent Barrier	226	(1)
What Flat Means	226	(3)
Primary and Secondary Exposures	228	(1)
14 Bucketing and Topography	229	(9)
Static Straight Bucketing	229	(3)
American and Path-Dependent Options	231	(1)
Advanced Topic: The Forward or "Forward-Forward" Bucket	231	(1)
Topography	232	(6)
Strike Topography (or Static Topography)	233	(2)
Dynamic Topography (Local Volatility Exposure)	235	(2)
Barrier Payoff Topography	237	(1)
15 Beware the Distribution	238	(18)
The Tails	238	(7)
Random Volatility	238	(4)
Histograms from the Markets	242	(3)
The Skew and Biased Assets	245	(7)
Biased Assets	248	(1)
Nonparallel Accounting	249	(1)
Value Linked to Price	250	(1)
Currencies as Assets	250	(1)
Reverse Assets	251	(1)
Volatility Regimes	251	(1)
Correlation between Interest Rates and Carry	252	(1)
More Advanced Put-Call Parity Rules	252	(4)
16 Option Trading Concepts	256	(17)
Initiation to Volatility Trading: Vega versus Gamma	260	(2)
Soft versus Hard Deltas	262	(1)
Volatility Betting	263	(2)
Higher Moment Bets	264	(1)
Case Study: Path Dependence of a Regular Option	265	(5)
Simple Case Study: The "Worst Case" Scenario	270	(3)
PART III TRADING AND HEDGING EXOTIC OPTIONS	273	(142)
17 Binary Options: European Style	273	(22)
European Binary Options	273	(6)
Hedging with a Vanilla	275	(3)
Definition of the Bet: Forward and Spot Bets	278	(1)
Pricing with the Skew	279	(10)
A Formal Pricing on the Skew	281	(1)
The Skew Paradox	282	(2)
Difference between the Binary and the Delta: The Delta Paradox Revisited	284	(2)
First Hedging Consequences	286	(1)
The Delta Is a Dirac Delta	286	(1)
Gamma for a Bet	287	(2)
Conclusion: Statistical Trading versus Dynamic Hedging	289	(1)
Case Study in Binary Packages--Contingent Premium Options	290	(2)
Recommended Use: Potential Devaluations	291	(1)
Case Study: The Betspreads	292	(3)
Avanced Case Study: Multiasset Bets	294	(1)
18 Binary Options: American Style	295	(17)
American Single Binary Options	295	(3)
Hedging an American Binary: Fooled by the Greeks	298	(1)
Case Study: National Vega Bank	298	(9)
The Ravages of Time	299	(4)
Understanding the Vega Convexity	303	(2)
Trading Methods	305	(1)
Case Study: At-Settlement American Binary Options	306	(1)
Other Greeks	307	(1)
American Double Binary Options	307	(5)
Vegas of the Double Binary	308	(1)
Other Applications of American Barriers	309	(2)
Credit Risk	311	(1)
19 Barrier Options (I)	312	(35)
Barrier Options (Regular)	312	(34)
Knock-Out Options	312	(5)
Knock-In Options	317	(2)
Effects of Volatility	319	(2)
Adding the Drift: Complexity of the Forward Line	321	(2)
Risk Reversals	323	(1)
Put/Call Symmetry and the Hedging of Barrier Options	323	(8)
Barrier Decomposition under Skew Environments	331	(4)
The Reflection Principle	335	(4)
Girsanov	339	(1)
Effect of Time on Knock-Out Options	339	(1)
First Exit Time and Its Risk-Neutral Expectation	340	(3)
Issues in Pricing Barrier Options	343	(1)
The Single Volatility Fudge	343	(1)
A More Accurate Method: The Dupire-Derman-Kani Technique	344	(1)
Additional Pricing Complexity: The Variance Ratios	345	(1)
Exercise: Adding the Puts	346	(1)
20 Barrier Options (II)	347	(29)
Reverse Barrier Options	347	(15)
Reverse Knock-Out Options	347	(1)
Case Study: The Konck-Out Box	348	(8)
Hedging Reverse Knock-Outs: A Graphical Case Study	356	(6)
Double Barrier Options	362	(6)
Rebate	363	(1)
Exercise: Adding the Knock-In	363	(1)
Alternative Barrier Options	363	(1)
The Exploding Option	364	(1)
Capped Index Option	365	(3)
Reading a Risk Management Report	368	(8)
Gaps and Gap Reports	374	(2)
21 Compound, Choosers, and Higher Order Options	376	(7)
Vege Convexity: The Costs of Dynamic Hedging	378	(1)
Uses of Compound Options: Hedging Barrier Vega	379	(1)
Chooser Options	380	(2)
A Few Applications of the Higher Order Options	382	(1)
22 Multiasset Options	383	(20)
Choice between Assets: Rainbow Options	384	(6)
Correlated and Uncorrelated Greeks	387	(3)
Linear Combinations	390	(5)
Basket Options	391	(1)
Lognormality	391	(1)
Correlation Issues	392	(3)
Composite Underlying Securities	395	(1)
Quantitative Case Study: Indexed Notes	395	(8)
Background	396	(1)
Terms of the Note	396	(1)
Where Is the Underlying?	397	(1)
Triangular Decomposition	398	(5)
23 Minor Exotics: Lookback and Asian Options	403	(12)
Lookback and Ladder Options	403	(5)
The Rollover Option	404	(4)
A Footnote on Basket Options: Asian Options	408	(7)
PART IV MODULES	415	(64)
Module A Brownian Motion on a Spreadsheet, A Tutorial	415	(11)
The Classical One-Asset Random Walk	415	(2)
Some Questions	417	(3)
A Two-Asset Random Walk: An Introduction to the Effects of Correlation	420	(4)
Extension: A Three-Asset Random Walk	424	(2)
Module B Risk Neutrality Explained	426	(5)
Step 1. Probabilistic Fairness, the "Fair Dice" and the Skew	426	(1)
Step 2. Adding the Real World: The Risk-Neutral Argument	427	(4)
The Drift	427	(4)
Module C Numeraire Relativity and the Two-Country Paradox	431	(7)
Extension: The Two-Country Paradox	433	(5)
Conclusion	435	(1)
Mathematical Note	436	(1)
Conclusion	437	(1)
Module D Correlation Triangles: A Graphical Case Study	438	(7)
Correlation Triangle Rule	441	(3)
Calculating an Implied Correlation Curve	444	(1)
Module E The Value-at-Risk	445	(8)
Simplified Examples	446	(7)
Example 1. No Diversification	447	(1)
Example 2. A Cross-Position	447	(1)
Example 3. Two Possible Trades	448	(5)
Module F Probabilistic Rankings in Arbitrage	453	(6)
Ranking of Securities	453	(4)
European Option Rules	453	(1)
Calendar Rules	454	(1)
Barrier and Digital Rules	454	(1)
Correlation Rules	455	(2)
Correlation Convexity Rules	457	(1)
General Convexity Rules	458	(1)
Module G Option Pricing	459	(20)
Ito's Lemma Explained	459	(4)
Black-Scholes Equation	463	(1)
The Risk-Neutral Argument	463	(1)
Stochastic Volatility Model	464	(2)
Multiasset Options	466	(1)
Rainbow Options	466	(1)
Outperformance Options	467	(1)
Spread Options	467	(1)
Compound and Chooser Order Options	467	(1)
Compound Options	468	(1)
Chooser Options	468	(1)
Barrier Options	468	(9)
The Reflection Principle	469	(1)
Girsanov's Theorem	469	(1)
Pricing Barriers	470	(7)
Numerical Stochastic Integration: A Sample	477	(2)
A Mathematica TM Program	477	(2)
Notes	479	(11)
Bibliography	490	(9)
Index	499