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Chukchi
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 22nd, 2006, 9:47 pm

The Complete Guide to Option Pricing Formulas + CD-ROMby Espen Gaarder HaugHardcover Publisher: McGraw-Hill; 2 edition (October 1, 2006) ISBN: 0071389970 FinMath.com
 
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WilmottBookshop
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 8:15 am

The Complete Guide to Option Pricing Formulas can be pre-ordered from the Wilmott Bookshop.
Last edited by WilmottBookshop on November 22nd, 2006, 11:00 pm, edited 1 time in total.
 
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ppauper
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 1:28 pm

so collector, how's it different from the 1st edition (which I own) ?
 
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player
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 1:44 pm

there is a CD rom??
 
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 1:56 pm

publisher told me it will go in print Dec 20. What is new: Old version is about 220 pages, 2nd edtion is about 530 pagesNew version has CD (with lots of 3D graphics of all types of things), no longer floppy disk. In particular I am happy with the CD. very user friendly and in many cases have more than described in book Below is preliminary table of content that can give you a little idea: page numbers no longer fit as the book got a bit longer and various adjustments just took place: (more than twice as long as first edition, CD instead of floppy, much more of everything and price is same, or actually has gone down, this is a no brainier, excellent Christmas present! If you dont like it you can always use the pages to wrap your other Christmas presents. Presents wrapped in option formulas, what a original idea in these days when people have everything! Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix What is New in the Second Edition? . . . . . . . . . . . . . . . . . . xi Options Pricing Formulas Overview . . . . . . . . . . . . . . . . . . xiii Glossary of Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv 1Plain European . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Black-Scholes-Merton . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 The Black-Scholes Option Pricing Formula . . . . 1.1.2 Options on Stock Indexes . . . . . . . . . . . . . . . . . 1.1.3 Options on Futures . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Margined Options on Futures . . . . . . . . . . . . . . 1.1.5 Currency Options . . . . . . . . . . . . . . . . . . . . . . . 1.1.6 The Generalized Black-Scholes-Merton Option Pricing Formula . . . . . . . . . . . . . . . . . . . 1.2 Parities and Symmetries . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Put-Call Parity for European Options . . . . . . . . 1.2.2 At-the-Money Forward Value Symmetry . . . . . . 1.2.3 Put-Call Symmetry . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Put-Call Supersymmetry . . . . . . . . . . . . . . . . . . 1.2.5 Black-Scholes-Merton on Variance Form . . . . . . 1.3 Before Black-Scholes-Merton . . . . . . . . . . . . . . . . . . . . 1.3.1 The Bachelier Model . . . . . . . . . . . . . . . . . . . . . 1.3.2 The Sprenkle Model . . . . . . . . . . . . . . . . . . . . . 1.3.3 The Boness Model . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 The Samuelson Model . . . . . . . . . . . . . . . . . . . . 1.4 Appendix A: The Black-Scholes-Merton PDE . . . . . . . . 1.4.1 Ito’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Dynamic HedgingGreeks . . . . . . . . . . . . . . . . . . . . 17 2.1 Delta Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.2 Delta Mirror Strikes and Assets . . . . . . . . . . . . 25 2.1.3 Strike from Delta . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.4 Futures Delta from Spot Delta . . . . . . . . . . . . . 27 2.1.5 DdeltaDvol and DvegaDspot . . . . . . . . . . . . . . . 28 2.1.6 DvannaDvol . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.7 DdeltaDtime, Charm . . . . . . . . . . . . . . . . . . . . . 31 2.1.8 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Gamma Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.1 Gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.2 Maximal Gamma and the Illusions of Risk . . . . . 35 2.2.3 GammaP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.4 Gamma Symmetry . . . . . . . . . . . . . . . . . . . . . . 41 2.2.5 DgammaDvol, Zomma . . . . . . . . . . . . . . . . . . . . 41 2.2.6 DgammaDspot, Speed . . . . . . . . . . . . . . . . . . . . 43 2.2.7 DgammaDtime, Color . . . . . . . . . . . . . . . . . . . . 45 2.3 Vega Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.1 Vega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.2 Vega Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.3.3 Vega-Gamma Relationship . . . . . . . . . . . . . . . . 51 2.3.4 Vega from Delta . . . . . . . . . . . . . . . . . . . . . . . . 52 2.3.5 VegaP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.3.6 Vega Leverage, Vega Elasticity . . . . . . . . . . . . . 53 2.3.7 DvegaDvol, Vomma . . . . . . . . . . . . . . . . . . . . . . 53 2.3.8 DvommaDvol, Ultima . . . . . . . . . . . . . . . . . . . . 56 2.3.9 DvegaDtime . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4 Variance Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.1 Variance Vega . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.2 DdeltaDvar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.4.3 Variance Vomma . . . . . . . . . . . . . . . . . . . . . . . . 59 2.4.4 Variance Ultima . . . . . . . . . . . . . . . . . . . . . . . . 59 2.5 Volatility-Time Greeks . . . . . . . . . . . . . . . . . . . . . . . . 60 2.6 Theta Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.6.1 Theta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.6.2 Theta Symmetry . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7 Rho Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7.1 Rho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7.2 Phi/Rho-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.7.3 Carry Rho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.8 Probability Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.8.1 In-the-Money Probability . . . . . . . . . . . . . . . . . 72 2.8.2 DzetaDvol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.8.3 DzetaDtime . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.8.4 Risk-Neutral Probability Density . . . . . . . . . . . 76 2.8.5 From in-the-Money Probability to Density . . . . . 76 2.8.6 Probability of Ever Getting in-the-Money . . . . . . 76 2.9 Greeks Aggregations . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.9.1 Net Weighted Vega Exposure . . . . . . . . . . . . . . . 78 2.10 At-the-Money Forward Approximations . . . . . . . . . . . . 80 2.10.1 Approximation of the Black-Scholes-Merton Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.10.2 Delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.10.3 Gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.10.4 Vega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.10.5 Theta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.10.6 Rho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.10.7 Cost of Carry . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.11 Numerical Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.11.1 First-Order Greeks . . . . . . . . . . . . . . . . . . . . . . 81 2.11.2 Second-Order Greeks . . . . . . . . . . . . . . . . . . . . 82 2.11.3 Third-Order Greeks . . . . . . . . . . . . . . . . . . . . . . 82 2.11.4 Mixed Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.11.5 Third-Order Mixed Greeks . . . . . . . . . . . . . . . . 83 2.12 Greeks from Closed-Form Approximations . . . . . . . . . . 86 2.13 Appendix B Taking Partial Derivatives . . . . . . . . . . . . 86 Analytical Formulas for American Options . . . . . . . . . . 93 3.1 The Barone-Adesi & Whaley Approximation . . . . . . . . . 93 3.2 The Bjerksund & Stensland 1993 Approximation . . . . . 97 3.3 The Bjerksund & Stensland 2002 Approximation . . . . . 100 3.4 Put-Call Transformation American Options . . . . . . . . . 104 3.5 American Perpetual Options . . . . . . . . . . . . . . . . . . . . 105 Exotic Options—Single Asset . . . . . . . . . . . . . . . . . . . . . 107 4.1 Variable Purchase Options . . . . . . . . . . . . . . . . . . . . . . 107 4.2 Executive Stock Options . . . . . . . . . . . . . . . . . . . . . . . 110 4.3 Moneyness Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.4 Power Contracts and Power Options . . . . . . . . . . . . . . 111 4.4.1 Power Contracts . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.2 Standard Power Option . . . . . . . . . . . . . . . . . . . 112 4.4.3 Capped Power Option . . . . . . . . . . . . . . . . . . . . 113 4.4.4 Powered Option . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.5 Log Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.5.1 Log(S) Contract . . . . . . . . . . . . . . . . . . . . . . . . . 1164.5.2 Log Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.6 Forward Start Options . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.7 Fade-in Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.8 Ratchet Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.9 Reset Strike Options—Type 1 . . . . . . . . . . . . . . . . . . . 120 4.10 Reset Strike Options—Type 2 . . . . . . . . . . . . . . . . . . . 121 4.11 Time-Switch Options . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.12 Chooser Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.12.1 Simple Chooser Options . . . . . . . . . . . . . . . . . . 124 4.12.2 Complex Chooser Options . . . . . . . . . . . . . . . . . 125 4.13 Options on Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.13.1 Put–Call Parity Compound Options . . . . . . . . . . 131 4.13.2 Compound Option Approximation . . . . . . . . . . . 131 4.14 Options with Extendible Maturities . . . . . . . . . . . . . . . 133 4.14.1 Options That Can Be Extended by the Holder . . 133 4.14.2 Writer-Extendible Options . . . . . . . . . . . . . . . . . 136 4.15 Lookback Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.15.1 Floating-Strike Lookback Options . . . . . . . . . . . 137 4.15.2 Fixed-Strike Lookback Options . . . . . . . . . . . . . 139 4.15.3 Partial-Time Floating-Strike Lookback Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.15.4 Partial-Time Fixed-Strike Lookback Options . . . 143 4.15.5 Extreme-Spread Options . . . . . . . . . . . . . . . . . . 144 4.16 Mirror Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.17 Barrier Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.17.1 Standard Barrier Options . . . . . . . . . . . . . . . . . 148 4.17.2 Standard American Barrier Options . . . . . . . . . 150 4.17.3 Double-Barrier Options . . . . . . . . . . . . . . . . . . . 152 4.17.4 Partial-Time Single-Asset Barrier Options . . . . . 156 4.17.5 Look-Barrier Options . . . . . . . . . . . . . . . . . . . . 158 4.17.6 Discrete-Barrier Options . . . . . . . . . . . . . . . . . . 160 4.17.7 Soft-Barrier Options . . . . . . . . . . . . . . . . . . . . . 161 4.17.8 Use of Put-Call Symmetry for Barrier Options . . 162 4.18 Barrier Option Symmetries . . . . . . . . . . . . . . . . . . . . . 163 4.18.1 First-Then-Barrier Options . . . . . . . . . . . . . . . . 165 4.18.2 Double-Barrier Option Using Barrier Symmetry . . . . . . . . . . . . . . . . . . . . . . . 166 4.18.3 Dual Double-Barrier Options . . . . . . . . . . . . . . . 168 4.19 Binary Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4.19.1 Gap Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.19.2 Cash-or-Nothing Options . . . . . . . . . . . . . . . . . . 170 4.19.3 Asset-or-Nothing Options . . . . . . . . . . . . . . . . . 171 4.19.4 Supershare Options . . . . . . . . . . . . . . . . . . . . . 171 4.19.5 Binary Barrier Options . . . . . . . . . . . . . . . . . . . 172 4.19.6 Double-Barrier Binary Options . . . . . . . . . . . . . 1764.19.7 Double-Barrier Binary Asymmetrical . . . . . . . . 177 4.20 Asian Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 4.20.1 Geometric Average-Rate Options . . . . . . . . . . . . 178 4.20.2 Arithmetic Average-Rate Options . . . . . . . . . . . 181 4.20.3 Discrete Arithmetic Average-Rate Options . . . . . 187 4.20.4 Equivalence of Floating-Strike and Fixed-Strike Asian Options . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4.20.5 Asian Options with Volatility Term-Structure . . 194 Exotic Options on Two Assets . . . . . . . . . . . . . . . . . . . . 199 5.1 Relative Outperformance Options . . . . . . . . . . . . . . . . 199 5.2 Product Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 5.3 Two-Asset Correlation Options . . . . . . . . . . . . . . . . . . 201 5.4 Exchange-One-Asset-for-Another Options . . . . . . . . . . 202 5.5 American Exchange-One-Asset-for-Another Option . . . 204 5.6 Exchange Options on Exchange Options . . . . . . . . . . . 205 5.7 Options on the Maximum or the Minimum of Two Risky Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 5.8 Spread-Option Approximation . . . . . . . . . . . . . . . . . . . 209 5.9 Two-Asset Barrier Options . . . . . . . . . . . . . . . . . . . . . 211 5.10 Partial-Time Two-Asset Barrier Options . . . . . . . . . . . 213 5.11 Margrabe Barrier Options . . . . . . . . . . . . . . . . . . . . . . 215 5.12 Discrete-Barrier Options . . . . . . . . . . . . . . . . . . . . . . . 217 5.13 Two-Asset Cash-or-Nothing Options . . . . . . . . . . . . . . 217 5.14 Best or Worst Cash-or-Nothing Options . . . . . . . . . . . . 219 5.15 Options on the Minimum or Maximum of Two Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 5.16 Currency-Translated Options . . . . . . . . . . . . . . . . . . . 222 5.16.1 Foreign Equity Options Struck in Domestic Currency . . . . . . . . . . . . . . . . . . . . . . 222 5.16.2 Fixed Exchange Rate Foreign Equity Options . . 224 5.16.3 Equity Linked Foreign Exchange Options . . . . . 226 5.16.4 Takeover Foreign Exchange Options . . . . . . . . . 228 5.17 Greeks for Two-Asset Options . . . . . . . . . . . . . . . . . . . 228 Black-Scholes-Merton Adjustments and Alternatives . 229 6.1 The Black-Scholes-Merton Model with Delayed Settlement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 6.2 The Black-Scholes-Merton Model Adjusted for Trading Day Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 6.3 Discrete Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 6.3.1 Hedging Error . . . . . . . . . . . . . . . . . . . . . . . . . . 232 6.3.2 Discrete-Time Option Valuation and Delta Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . 233 6.3.3 Discrete-Time Hedging with Transaction Cost . . 2346.4 Option Pricing in Trending Markets . . . . . . . . . . . . . . 236 6.5 Alternative Stochastic Processes . . . . . . . . . . . . . . . . . 238 6.6 Constant Elasticity of Variance . . . . . . . . . . . . . . . . . . 238 6.7 Skewness Kurtosis Models . . . . . . . . . . . . . . . . . . . . . 240 6.7.1 Definition of Skewness and Kurtosis . . . . . . . . . 240 6.7.2 The Skewness and Kurtosis for a Lognormal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 6.7.3 Jarrow and Rudd Skewness and Kurtosis Model 242 6.7.4 The Corrado and Su Skewness and Kurtosis Model . . . . . . . . . . . . . . . . . . . . . . . . . 243 6.7.5 Modified Corrado-Su Skewness Kurtosis Model . 245 6.7.6 Skewness-Kurtosis Put-Call Supersymmetry . . . 247 6.7.7 Skewness Kurtosis Equivalent Black-Scholes-Merton Volatility . . . . . . . . . . . . . 248 6.7.8 Gram Charlier Density . . . . . . . . . . . . . . . . . . . 248 6.7.9 Skewness-Kurtosis Trees . . . . . . . . . . . . . . . . . . 248 6.8 Pascal Distribution and Option Pricing . . . . . . . . . . . . 248 6.9 Jump-Diffusion Models . . . . . . . . . . . . . . . . . . . . . . . . 249 6.9.1 The Merton Jump-Diffusion Model . . . . . . . . . . 249 6.9.2 Bates Generalized Jump-Diffusion Model . . . . . 250 6.10 Stochastic Volatility Models . . . . . . . . . . . . . . . . . . . . . 254 6.10.1 Hull-White Uncorrelated Stochastic Volatility Model . . . . . . . . . . . . . . . . . . . . . . . . . 254 6.10.2 Hull-White Correlated Stochastic Volatility Model . . . . . . . . . . . . . . . . . . . . . . . . . 257 6.10.3 The SABR Model . . . . . . . . . . . . . . . . . . . . . . . . 261 6.11 Variance and Volatility Swaps . . . . . . . . . . . . . . . . . . . 266 6.11.1 Variance Swaps . . . . . . . . . . . . . . . . . . . . . . . . . 266 6.11.2 Volatility Swaps . . . . . . . . . . . . . . . . . . . . . . . . 269 6.12 More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Trees and Finite Difference Methods . . . . . . . . . . . . . . 275 7.1 Binomial Option Pricing . . . . . . . . . . . . . . . . . . . . . . . 275 7.1.1 Cox-Ross-Rubinstein American Binomial Tree . . 280 7.1.2 Greeks in CRR Binomial Tree . . . . . . . . . . . . . . 283 7.1.3 Rendleman Bartter Binomial Tree . . . . . . . . . . . 285 7.1.4 Leisen-Reimer Binomial Tree . . . . . . . . . . . . . . 286 7.1.5 Convertible Bonds in Binomial Trees . . . . . . . . . 288 7.2 Binomial Model with Skewness and Kurtosis . . . . . . . . 293 7.3 Trinomial Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 7.4 Exotic Options in Tree Models . . . . . . . . . . . . . . . . . . . 299 7.4.1 Options on Options . . . . . . . . . . . . . . . . . . . . . . 299 7.4.2 Barrier Options Using Brownian Bridge Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 3017.4.3 American Barrier Options in CRR Binomial Tree . . . . . . . . . . . . . . . . . . . . . . . . . . 302 7.4.4 European Reset Options Binomial . . . . . . . . . . . 303 7.4.5 American Asian Options in a Tree . . . . . . . . . . . 309 7.5 Three-Dimensional Binomial Trees . . . . . . . . . . . . . . . 310 7.6 Implied Tree Models . . . . . . . . . . . . . . . . . . . . . . . . . . 315 7.6.1 Implied Binomial Trees . . . . . . . . . . . . . . . . . . . 316 7.6.2 Implied Trinomial Trees . . . . . . . . . . . . . . . . . . 321 7.7 Finite Difference Methods . . . . . . . . . . . . . . . . . . . . . . 329 7.7.1 Explicit Finite Difference . . . . . . . . . . . . . . . . . 330 7.7.2 Implicit Finite Difference . . . . . . . . . . . . . . . . . 333 7.7.3 Finite Difference in ln(S ) . . . . . . . . . . . . . . . . . . 334 7.7.4 The Crank-Nicolson Method . . . . . . . . . . . . . . . 336 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 339 8.1 Standard Monte Carlo Simulation . . . . . . . . . . . . . . . . 339 8.1.1 Greeks in Monte Carlo . . . . . . . . . . . . . . . . . . . 341 8.1.2 Monte Carlo for Callable Options . . . . . . . . . . . . 343 8.1.3 Two Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 8.1.4 Three Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 8.1.5 N Assets, Cholesky Decomposition . . . . . . . . . . 347 8.2 Monte Carlo of Mean Reversion . . . . . . . . . . . . . . . . . . 349 8.3 Generating Pseudo-Random Numbers . . . . . . . . . . . . . 349 8.4 Variance Reduction Techniques . . . . . . . . . . . . . . . . . . 351 8.4.1 Antithetic Variance Reduction . . . . . . . . . . . . . . 352 8.4.2 IQ-MC/Importance Sampling . . . . . . . . . . . . . . 352 8.4.3 IQ-MC Two Correlated Assets . . . . . . . . . . . . . . 355 8.4.4 Quasi-Random Monte Carlo . . . . . . . . . . . . . . . 356 8.5 American Option Monte Carlo . . . . . . . . . . . . . . . . . . . 358 Options on Stocks That Pay Discrete Dividends . . . . . 361 9.1 European Options on Stock with Discrete Cash Dividend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 9.1.1 The Escrowed Dividend Model . . . . . . . . . . . . . . 362 9.1.2 Simple Volatility Adjustment . . . . . . . . . . . . . . . 363 9.1.3 Haug-Haug Volatility Adjustment . . . . . . . . . . . 363 9.1.4 Bos-Gairat-Shepeleva Volatility Adjustment . . . 364 9.1.5 Bos-Vandermark . . . . . . . . . . . . . . . . . . . . . . . . 365 9.2 Non-Recombining Tree . . . . . . . . . . . . . . . . . . . . . . . . 366 9.3 Black’s Method for Calls on Stocks with Known Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 9.4 The Roll, Geske, and Whaley model . . . . . . . . . . . . . . . 369 9.5 Benchmark Model for Discrete Cash Dividend . . . . . . . 372 9.5.1 A Single Dividend . . . . . . . . . . . . . . . . . . . . . . . 372 9.5.2 Multiple Dividends . . . . . . . . . . . . . . . . . . . . . . 3769.5.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 9.6 Options on Stocks with Discrete Dividend Yield . . . . . . 383 9.6.1 European with Discrete Dividend Yield . . . . . . . 384 9.6.2 Closed-Form American Call . . . . . . . . . . . . . . . . 384 9.6.3 Recombining Tree Model . . . . . . . . . . . . . . . . . . 386 Commodity and Energy Options . . . . . . . . . . . . . . . . . . 391 10.1 Energy Swaps/Forwards . . . . . . . . . . . . . . . . . . . . . . . 391 10.2 Energy Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 10.2.1 Options on Forwards, Black-76F . . . . . . . . . . . . 394 10.2.2 Energy Swaptions . . . . . . . . . . . . . . . . . . . . . . . 395 10.2.3 Hybrid Payoff Energy Swaptions . . . . . . . . . . . . 399 10.3 The Miltersen-Schwartz Model . . . . . . . . . . . . . . . . . . 400 10.4 Mean Reversion Model . . . . . . . . . . . . . . . . . . . . . . . . 404 10.5 Seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Interest Rate Derivatives . . . . . . . . . . . . . . . . . . . . . . . . 407 11.1 FRAs and Money Market Instruments . . . . . . . . . . . . . 407 11.1.1 FRAs From Cash Deposits . . . . . . . . . . . . . . . . . 407 11.1.2 The Relationship between FRAs and Currency Forwards . . . . . . . . . . . . . . . . . . . . . . 407 11.1.3 Convexity Adjustment Money Market Futures . . 409 11.2 Simple Bond Mathematics . . . . . . . . . . . . . . . . . . . . . . 411 11.2.1 Dirty and Clean Bond Price . . . . . . . . . . . . . . . . 411 11.2.2 Current Yield . . . . . . . . . . . . . . . . . . . . . . . . . . 411 11.2.3 Modified Duration and BPV . . . . . . . . . . . . . . . 411 11.2.4 Bond Price and Yield Relationship . . . . . . . . . . . 412 11.2.5 Price and Yield Relationship for a Bond . . . . . . . 412 11.2.6 From Bond Price to Yield . . . . . . . . . . . . . . . . . . 413 11.3 Pricing Interest Rate Options Using Black-76 . . . . . . . 413 11.3.1 Options on Money Market Futures . . . . . . . . . . 414 11.3.2 Price and Yield Volatility in Money Market Futures . . . . . . . . . . . . . . . . . . . . . . . . . 415 11.3.3 Caps and Floors . . . . . . . . . . . . . . . . . . . . . . . . 415 11.3.4 Swaptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 11.3.5 Swaption Volatilities from Caps or FRA Volatilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 11.3.6 Swaptions with Stochastic Volatility . . . . . . . . . 419 11.3.7 Convexity Adjustments . . . . . . . . . . . . . . . . . . . 419 11.3.8 European Short-Term Bond Options . . . . . . . . . 421 11.3.9 From Price to Yield Volatility in Bonds . . . . . . . 422 11.3.10 The Schaefer and Schwartz Model . . . . . . . . . . 422 11.4 One-Factor Term Structure Models . . . . . . . . . . . . . . . 423 11.4.1 The Rendleman and Bartter Model . . . . . . . . . . 423 11.4.2 The Vasicek Model . . . . . . . . . . . . . . . . . . . . . . . 42411.4.3 The Ho and Lee Model . . . . . . . . . . . . . . . . . . . . 426 11.4.4 The Hull and White Model . . . . . . . . . . . . . . . . . 427 11.4.5 The Black-Derman-Toy Model . . . . . . . . . . . . . . 428 Volatility and Correlation . . . . . . . . . . . . . . . . . . . . . . . . 437 12.1 Historical Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 12.1.1 Historical Volatility from Close Prices . . . . . . . . 437 12.1.2 High-Low Volatility . . . . . . . . . . . . . . . . . . . . . . 439 12.1.3 High-Low-Close Volatility . . . . . . . . . . . . . . . . . 440 12.1.4 Exponential Weighted Historical Volatility . . . . . 441 12.1.5 From Annual Volatility to Daily Volatility . . . . . 442 12.1.6 Confidence Intervals for the Volatility Estimate . 443 12.1.7 Volatility Cones . . . . . . . . . . . . . . . . . . . . . . . . . 444 12.2 Implied Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 12.2.1 The Newton-Raphson Method . . . . . . . . . . . . . . 445 12.2.2 The Bisection Method . . . . . . . . . . . . . . . . . . . . 446 12.2.3 Implied Volatility Approximations . . . . . . . . . . . 448 12.2.4 Implied Forward Volatility . . . . . . . . . . . . . . . . . 449 12.2.5 From Implied Volatility Surface to Local Volatility Surface . . . . . . . . . . . . . . . . . . . . . . . 450 12.3 Confidence Interval for the Asset Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 12.4 Basket Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 12.5 Historical Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 452 12.5.1 Distribution of Historical Correlation Coefficient 452 12.6 Implied Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . 454 12.6.1 Implied Correlation from Currency Options . . . . 454 12.6.2 Average Implied Index Correlation . . . . . . . . . . 454 12.7 Various Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 12.7.1 Probability of High or Low, the Arctangent Rule . . . . . . . . . . . . . . . . . . . . . 455 12.7.2 Siegel’s Paradox and Volatility Ratio Effect . . . . 455 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 13.1 The Cumulative Normal Distribution Function . . . . . . 457 13.1.1 The Hart Algorithm . . . . . . . . . . . . . . . . . . . . . . 457 13.1.2 Polynomial Approximations . . . . . . . . . . . . . . . . 459 13.2 The Inverse Cumulative Normal Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 13.3 The Bivariate Normal Density Function . . . . . . . . . . . 466 13.3.1 The Cumulative Bivariate Normal Distribution Function . . . . . . . . . . . . . . . . . . . . 466 13.4 The Trivariate Cumulative Normal Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472Some Useful Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 14.1 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 14.1.1 Linear Interpolation . . . . . . . . . . . . . . . . . . . . . 479 14.1.2 Log-Linear Interpolation . . . . . . . . . . . . . . . . . . 479 14.1.3 Exponential Interpolation . . . . . . . . . . . . . . . . . 479 14.1.4 Cubic Interpolation: Lagrange’s Formula . . . . . . 480 14.1.5 Cubic-Spline Interpolation . . . . . . . . . . . . . . . . 480 14.1.6 Two-Dimensional Interpolation . . . . . . . . . . . . . 482 14.2 Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 14.2.1 Future Value of Annuity . . . . . . . . . . . . . . . . . . 483 14.2.2 Net Present Value of Annuity . . . . . . . . . . . . . . 483 14.2.3 Continuous Compounding . . . . . . . . . . . . . . . . . 483 14.2.4 Compounding Frequency . . . . . . . . . . . . . . . . . . 483 14.2.5 Zero-Coupon Rates from Par Bonds/Par Swaps . . . . . . . . . . . . . . . . . . . . 484 14.3 Risk-Reward Measures . . . . . . . . . . . . . . . . . . . . . . . . 485 14.3.1 Treynor’s Measure . . . . . . . . . . . . . . . . . . . . . . . 485 14.3.2 Sharpe Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 14.3.3 Confidence Ratio . . . . . . . . . . . . . . . . . . . . . . . . 486 14.3.4 Sortino Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 14.3.5 Burke Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 14.3.6 Return on VaR . . . . . . . . . . . . . . . . . . . . . . . . . 487 14.3.7 Jensen’s Measure . . . . . . . . . . . . . . . . . . . . . . . 488 14.4 Appendix C Basic Useful Information . . . . . . . . . . . . . 488
Last edited by Collector on November 22nd, 2006, 11:00 pm, edited 1 time in total.
 
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Cuchulainn
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 2:15 pm

Congratulations! It looks very comprehensive.
 
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Collector
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Joined: August 21st, 2001, 12:37 pm

New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 2:37 pm

CD Example Bates Jump-Diffusion CD Example two asset barrier CD Example Modified Corrado-Su Skewness Kurtosis model If you can dream it you can price it and graph it in 3D
Last edited by Collector on November 25th, 2006, 11:00 pm, edited 1 time in total.
 
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QuantOption
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 23rd, 2006, 9:26 pm

I'm going to buy this book, but can someone tell me why is it that it costs almost the same amount in dollars and pounds?
 
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DominicConnor
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 24th, 2006, 8:59 am

I'm sure those nice people at the Wilmott bookshop will make it cheaper.For whatever reason The Collector hasn't sent me a copy of the new book, but I would point out that the old version was one of the books we recommend in our Guide to Getting a Quant job.
 
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Cuchulainn
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 24th, 2006, 9:25 am

QuoteOriginally posted by: DCFCI'm sure those nice people at the Wilmott bookshop will make it cheaper.For whatever reason The Collector hasn't sent me a copy of the new book, but I would point out that the old version was one of the books we recommend in our Guide to Getting a Quant job.yes, he has not sent me - a fellow author - a copy either
 
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cemil
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 24th, 2006, 12:42 pm

me 2 :-)
 
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Collector
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 26th, 2006, 12:04 am

Besides what mentioned in table of contents the CD also show how to value a series of exotic options not mention in book: like square root options and for example options on tangens and cosinus options.... window barrier (using MC) etc. I did last proof reading just now, would like to do more, but at some point I had to let the manuscript go....next is get it to the printing press....they told me Dec 20, so not sure if it will be ready for Christmas....so unfortunately looks like Cuchulainn wife not will get the present she wish for this year, she will have to get another copy of "Introduction to C++ For Financial Engineers "
Last edited by Collector on November 25th, 2006, 11:00 pm, edited 1 time in total.
 
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Cuchulainn
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 29th, 2006, 3:19 am

QuoteOriginally posted by: CollectorBesides what mentioned in table of contents the CD also show how to value a series of exotic options not mention in book: like square root options and for example options on tangens and cosinus options.... window barrier (using MC) etc. I did last proof reading just now, would like to do more, but at some point I had to let the manuscript go....next is get it to the printing press....they told me Dec 20, so not sure if it will be ready for Christmas....so unfortunately looks like Cuchulainn wife not will get the present she wish for this year, she will have to get another copy of "Introduction to C++ For Financial Engineers "Mrs. Cuch is very good at makiing the books. All those formulae are her work.Greeting from Vancouver (unexpected climate change last weekend: lots of snow and fallen power lines). On Whistler it was minus 20 degree Celsius.
Last edited by Cuchulainn on November 28th, 2006, 11:00 pm, edited 1 time in total.
 
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mj
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 29th, 2006, 3:45 am

is the source code available, and in what language and licence?
 
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Collector
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New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

November 29th, 2006, 3:53 am

Source code included in VBA for almost any modelIt goes to the press this week!
Last edited by Collector on November 28th, 2006, 11:00 pm, edited 1 time in total.
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