Description of The Complete Guide to Option Pricing Formulas
This title offers instant access to formulas used daily by the best talent on Wall Street. Since its publication in 1997, "The Complete Guide to Option Pricing Formulas" has become the bible of option formulas for everyone from professional traders to money managers and investors. When pricing options in today's fast-action markets, experience and intuition are not enough - financial professionals need precise facts and tested information that has been proven time and again. This authoritative reference contains a complete listing of virtually every option pricing formula, all presented in an easy-to-use dictionary format; author commentary that explains key points in the most important formulas; and, ready-to-use programming code that enhances your understanding of option pricing models and their practical implementation.
Contents of The Complete Guide to Option Pricing Formulas
Introduction
Acknowledgments
What is New in the Second Edition?
Options Pricing Formulas Overview
Glossary of Notations
Plain 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 Hedging
Greeks
2.1 Delta Greeks
2.1.1 Delta
2.1.2 Delta Mirror Strikes and Assets
2.1.3 Strike from Delta
2.1.4 Futures Delta from Spot Delta
2.1.5 DdeltaDvol and DvegaDspot
2.1.6 DvannaDvol
2.1.7 DdeltaDtime, Charm
2.1.8 Elasticity
2.2 Gamma Greeks
2.2.1 Gamma
2.2.2 Maximal Gamma and the Illusions of Risk
2.2.3 GammaP
2.2.4 Gamma Symmetry
2.2.5 DgammaDvol, Zomma
2.2.6 DgammaDspot, Speed
2.2.7 DgammaDtime, Color
2.3 Vega Greeks
2.3.1 Vega
2.3.2 Vega Symmetry
2.3.3 Vega-Gamma Relationship
2.3.4 Vega from Delta
2.3.5 VegaP
2.3.6 Vega Leverage, Vega Elasticity
2.3.7 DvegaDvol, Vomma
2.3.8 DvommaDvol, Ultima
2.3.9 DvegaDtime
2.4 Variance Greeks
2.4.1 Variance Vega
2.4.2 DdeltaDvar
2.4.3 Variance Vomma
2.4.4 Variance Ultima
2.5 Volatility-Time Greeks
2.6 Theta Greeks
2.6.1 Theta
2.6.2 Theta Symmetry
2.7 Rho Greeks
2.7.1 Rho
2.7.2 Phi/Rho-2
2.7.3 Carry Rho
2.8 Probability Greeks
2.8.1 In-the-Money Probability
2.8.2 DzetaDvol
2.8.3 DzetaDtime
2.8.4 Risk-Neutral Probability Density
2.8.5 From in-the-Money Probability to Density
2.8.6 Probability of Ever Getting in-the-Money
2.9 Greeks Aggregations
2.9.1 Net Weighted Vega Exposure
2.10 At-the-Money Forward Approximations
2.10.1 Approximation of the Black-Scholes-Merton Formula
2.10.2 Delta
2.10.3 Gamma
2.10.4 Vega
2.10.5 Theta
2.10.6 Rho
2.10.7 Cost of Carry
2.11 Numerical Greeks
2.11.1 First-Order Greeks
2.11.2 Second-Order Greeks
2.11.3 Third-Order Greeks
2.11.4 Mixed Greeks
2.11.5 Third-Order Mixed Greeks
2.12 Greeks from Closed-Form Approximations
2.13 Appendix B Taking Partial Derivatives
Analytical Formulas for American Options
3.1 The Barone-Adesi & Whaley Approximation
3.2 The Bjerksund & Stensland 1993 Approximation
3.3 The Bjerksund & Stensland 2002 Approximation
3.4 Put-Call Transformation American Options
3.5 American Perpetual Options
Exotic Options, Single Asset
4.1 Variable Purchase Options
4.2 Executive Stock Options
4.3 Moneyness Options
4.4 Power Contracts and Power Options
4.4.1 Power Contracts
4.4.2 Standard Power Option
4.4.3 Capped Power Option
4.4.4 Powered Option
4.5 Log Contracts
4.5.1 Log(S) Contract
4.5.2 Log Option
4.6 Forward Start Options
4.7 Fade-in Option
4.8 Ratchet Options
4.9 Reset Strike Options - Type 1
4.10 Reset Strike Options -Type 2
4.11 Time-Switch Options
4.12 Chooser Options
4.12.1 Simple Chooser Options
4.12.2 Complex Chooser Options
4.13 Options on Options
4.13.1 Put�Call Parity Compound Options
4.13.2 Compound Option Approximation
4.14 Options with Extendible Maturities
4.14.1 Options That Can Be Extended by the Holder
4.14.2 Writer-Extendible Options
4.15 Lookback Options
4.15.1 Floating-Strike Lookback Options
4.15.2 Fixed-Strike Lookback Options
4.15.3 Partial-Time Floating-Strike Lookback Options
4.15.4 Partial-Time Fixed-Strike Lookback Options
4.15.5 Extreme-Spread Options
4.16 Mirror Options
4.17 Barrier Options
4.17.1 Standard Barrier Options
4.17.2 Standard American Barrier Options
4.17.3 Double-Barrier Options
4.17.4 Partial-Time Single-Asset Barrier Options
4.17.5 Look-Barrier Options
4.17.6 Discrete-Barrier Options
4.17.7 Soft-Barrier Options
4.17.8 Use of Put-Call Symmetry for Barrier Options
4.18 Barrier Option Symmetries
4.18.1 First-Then-Barrier Options
4.18.2 Double-Barrier Option Using Barrier Symmetry
4.18.3 Dual Double-Barrier Options
4.19 Binary Options
4.19.1 Gap Options
4.19.2 Cash-or-Nothing Options
4.19.3 Asset-or-Nothing Options
4.19.4 Supershare Options
4.19.5 Binary Barrier Options
4.19.6 Double-Barrier Binary Options
4.19.7 Double-Barrier Binary Asymmetrical
4.20 Asian Options
4.20.1 Geometric Average-Rate Options
4.20.2 Arithmetic Average-Rate Options
4.20.3 Discrete Arithmetic Average-Rate Options
4.20.4 Equivalence of Floating-Strike and Fixed-Strike Asian Options
4.20.5 Asian Options with Volatility Term-Structure
Exotic Options on Two Assets
5.1 Relative Outperformance Options
5.2 Product Options
5.3 Two-Asset Correlation Options
5.4 Exchange-One-Asset-for-Another Options
5.5 American Exchange-One-Asset-for-Another Option
5.6 Exchange Options on Exchange Options
5.7 Options on the Maximum or the Minimum of Two Risky Assets
5.8 Spread-Option Approximation
5.9 Two-Asset Barrier Options
5.10 Partial-Time Two-Asset Barrier Options
5.11 Margrabe Barrier Options
5.12 Discrete-Barrier Options
5.13 Two-Asset Cash-or-Nothing Options
5.14 Best or Worst Cash-or-Nothing Options
5.15 Options on the Minimum or Maximum of Two Averages
5.16 Currency-Translated Options
5.16.1 Foreign Equity Options Struck in Domestic Currency
5.16.2 Fixed Exchange Rate Foreign Equity Options
5.16.3 Equity Linked Foreign Exchange Options
5.16.4 Takeover Foreign Exchange Options
5.17 Greeks for Two-Asset Options
Black-Scholes-Merton Adjustments and Alternatives
6.1 The Black-Scholes-Merton Model with Delayed Settlement
6.2 The Black-Scholes-Merton Model Adjusted for Trading Day Volatility
6.3 Discrete Hedging
6.3.1 Hedging Error
6.3.2 Discrete-Time Option Valuation and Delta Hedging
6.3.3 Discrete-Time Hedging with Transaction Cost
6.4 Option Pricing in Trending Markets
6.5 Alternative Stochastic Processes
6.6 Constant Elasticity of Variance
6.7 Skewness Kurtosis Models
6.7.1 Definition of Skewness and Kurtosis
6.7.2 The Skewness and Kurtosis for a Lognormal Distribution
6.7.3 Jarrow and Rudd Skewness and Kurtosis Model
6.7.4 The Corrado and Su Skewness and Kurtosis Model
6.7.5 Modified Corrado-Su Skewness Kurtosis Model
6.7.6 Skewness-Kurtosis Put-Call Supersymmetry
6.7.7 Skewness Kurtosis Equivalent Black-Scholes-Merton Volatility
6.7.8 Gram Charlier Density
6.7.9 Skewness-Kurtosis Trees
6.8 Pascal Distribution and Option Pricing
6.9 Jump-Diffusion Models
6.9.1 The Merton Jump-Diffusion Model
6.9.2 Bates Generalized Jump-Diffusion Model
6.10 Stochastic Volatility Models
6.10.1 Hull-White Uncorrelated Stochastic Volatility Model
6.10.2 Hull-White Correlated Stochastic Volatility Model
6.10.3 The SABR Model
6.11 Variance and Volatility Swaps
6.11.1 Variance Swaps
6.11.2 Volatility Swaps
6.12 More Information
Trees and Finite Difference Methods
7.1 Binomial Option Pricing
7.1.1 Cox-Ross-Rubinstein American Binomial Tree
7.1.2 Greeks in CRR Binomial Tree
7.1.3 Rendleman Bartter Binomial Tree
7.1.4 Leisen-Reimer Binomial Tree
7.1.5 Convertible Bonds in Binomial Trees
7.2 Binomial Model with Skewness and Kurtosis
7.3 Trinomial Trees
7.4 Exotic Options in Tree Models
7.4.1 Options on Options
7.4.2 Barrier Options Using Brownian Bridge Probabilities
7.4.3 American Barrier Options in CRR Binomial Tree
7.4.4 European Reset Options Binomial
7.4.5 American Asian Options in a Tree
7.5 Three-Dimensional Binomial Trees
7.6 Implied Tree Models
7.6.1 Implied Binomial Trees
7.6.2 Implied Trinomial Trees
7.7 Finite Difference Methods
7.7.1 Explicit Finite Difference
7.7.2 Implicit Finite Difference
7.7.3 Finite Difference in ln(S )
7.7.4 The Crank-Nicolson Method
Monte Carlo Simulation
8.1 Standard Monte Carlo Simulation
8.1.1 Greeks in Monte Carlo
8.1.2 Monte Carlo for Callable Options
8.1.3 Two Assets
8.1.4 Three Assets
8.1.5 N Assets, Cholesky Decompositio
8.2 Monte Carlo of Mean Reversion
8.3 Generating Pseudo-Random Numbers
8.4 Variance Reduction Techniques
8.4.1 Antithetic Variance Reduction
8.4.2 IQ-MC/Importance Sampling
8.4.3 IQ-MC Two Correlated Assets
8.4.4 Quasi-Random Monte Carlo
8.5 American Option Monte Carlo
Options on Stocks That Pay Discrete Dividends
9.1 European Options on Stock with Discrete Cash Dividend
9.1.1 The Escrowed Dividend Model
9.1.2 Simple Volatility Adjustment
9.1.3 Haug-Haug Volatility Adjustment
9.1.4 Bos-Gairat-Shepeleva Volatility Adjustment
9.1.5 Bos-Vandermark
9.2 Non-Recombining Tree
9.3 Black's Method for Calls on Stocks with Known Dividends
9.4 The Roll, Geske, and Whaley model
9.5 Benchmark Model for Discrete Cash Dividend
9.5.1 A Single Dividend
9.5.2 Multiple Dividends
9.5.3 Applications
9.6 Options on Stocks with Discrete Dividend Yield
9.6.1 European with Discrete Dividend Yield
9.6.2 Closed-Form American Call
9.6.3 Recombining Tree Model
Commodity and Energy Options
10.1 Energy Swaps Forwards
10.2 Energy Options
10.2.1 Options on Forwards, Black-76F
10.2.2 Energy Swaptions
10.2.3 Hybrid Payoff Energy Swaptions
10.3 The Miltersen-Schwartz Model
10.4 Mean Reversion Model
10.5 Seasonality
Interest Rate Derivatives
11.1 FRAs and Money Market Instruments
11.1.1 FRAs From Cash Deposits
11.1.2 The Relationship between FRAs and Currency Forwards
11.1.3 Convexity Adjustment Money Market Futures
11.2 Simple Bond Mathematics
11.2.1 Dirty and Clean Bond Price
11.2.2 Current Yield
11.2.3 Modified Duration and BPV
11.2.4 Bond Price and Yield Relationship
11.2.5 Price and Yield Relationship for a Bond
11.2.6 From Bond Price to Yield
11.3 Pricing Interest Rate Options Using Black-76
11.3.1 Options on Money Market Futures
11.3.2 Price and Yield Volatility in Money Market Futures
11.3.3 Caps and Floors
11.3.4 Swaptions
11.3.5 Swaption Volatilities from Caps or FRA Volatilities
11.3.6 Swaptions with Stochastic Volatility
11.3.7 Convexity Adjustments
11.3.8 European Short-Term Bond Options
11.3.9 From Price to Yield Volatility in Bonds
11.3.10 The Schaefer and Schwartz Model
11.4 One-Factor Term Structure Models
11.4.1 The Rendleman and Bartter Model
11.4.2 The Vasicek Model
11.4.3 The Ho and Lee Model
11.4.4 The Hull and White Model
11.4.5 The Black-Derman-Toy Model
Volatility and Correlation
12.1 Historical Volatility
12.1.1 Historical Volatility from Close Prices
12.1.2 High-Low Volatility
12.1.3 High-Low-Close Volatility
12.1.4 Exponential Weighted Historical Volatility
12.1.5 From Annual Volatility to Daily Volatility
12.1.6 Confidence Intervals for the Volatility Estimate
12.1.7 Volatility Cones
12.2 Implied Volatility
12.2.1 The Newton-Raphson Method
12.2.2 The Bisection Method
12.2.3 Implied Volatility Approximations
12.2.4 Implied Forward Volatility
12.2.5 From Implied Volatility Surface to Local Volatility Surface
12.3 Confidence Interval for the Asset Price
12.4 Basket Volatility
12.5 Historical Correlation
12.5.1 Distribution of Historical Correlation Coefficient
12.6 Implied Correlations
12.6.1 Implied Correlation from Currency Options
12.6.2 Average Implied Index Correlation
12.7 Various Formulas
12.7.1 Probability of High or Low, the Arctangent Rule
12.7.2 Siegel�s Paradox and Volatility Ratio Effect
Distributions
13.1 The Cumulative Normal Distribution Function
13.1.1 The Hart Algorithm
13.1.2 Polynomial Approximations
13.2 The Inverse Cumulative Normal Distribution Function
13.3 The Bivariate Normal Density Function
13.3.1 The Cumulative Bivariate Normal Distribution Function
13.4 The Trivariate Cumulative Normal Distribution Function
Some Useful Formulas
14.1 Interpolation
14.1.1 Linear Interpolation
14.1.2 Log-Linear Interpolation
14.1.3 Exponential Interpolation
14.1.4 Cubic Interpolation: Lagrange's Formula
14.1.5 Cubic-Spline Interpolation
14.1.6 Two-Dimensional Interpolation2
14.2 Interest Rates
14.2.1 Future Value of Annuity
14.2.2 Net Present Value of Annuity
14.2.3 Continuous Compounding
14.2.4 Compounding Frequency
14.2.5 Zero-Coupon Rates from Par Bonds/Par Swaps
14.3 Risk-Reward Measures
14.3.1 Treynor's Measure
14.3.2 Sharpe Ratio
14.3.3 Confidence Ratio
14.3.4 Sortino Ratio
14.3.5 Burke Ratio
14.3.6 Return on VaR
14.3.7 Jensen's Measure
14.4 Appendix C Basic Useful Information
About Espen Gaardner Haug
Espen Gaarder Haug, has more than 15 years of experience in derivatives trading and research. He has worked as a proprietary option trader at J.P. Morgan Chase in New York, and as an option trader for the hedge funds Amaranth Advisors and Paloma Partners. Dr. Haug has published extensively in journals such as Quantitative Finance, International Journal of Theoretical and Applied Finance, and Wilmott Magazine. He is also a popular lecturer on option pricing, hedging, and risk management and an Adjunct Associate Professor at Norwegian University of Science and Technology.
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