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| Introduction | |
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| Acknowledgments | |
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| What Is New in the Second Edition? | |
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| Option Pricing Formulas Overview | |
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| Glossary of Notations | |
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| Black-Scholes-Merton | |
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| Black-Scholes-Merton | |
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| The Black-Scholes Option Pricing Formula | |
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| Options on Stock Indexes | |
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| Options on Futures | |
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| Margined Options on Futures | |
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| Currency Options | |
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| The Generalized Black-Scholes-Merton Option Pricing Formula | |
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| Parities and Symmetries | |
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| Put-Call Parity for European Options | |
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| At-the-Money Forward Value Symmetry | |
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| Put-Call Symmetry | |
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| Put-Call Supersymmetry | |
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| Black-Scholes-Merton on Variance Form | |
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| Before Black-Scholes-Merton | |
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| The Bachelier Model | |
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| The Sprenkle Model | |
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| The Boness Model | |
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| The Samuelson Model | |
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| Appendix A: The Black-Scholes-Merton PDE | |
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| Ito's Lemma | |
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| Dynamic Hedging | |
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| Black-Scholes-Merton Greeks | |
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| Delta Greeks | |
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| Delta | |
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| Delta Mirror Strikes and Assets | |
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| Strike from Delta | |
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| Futures Delta from Spot Delta | |
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| DdeltaDvol and DvegaDspot | |
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| DvannaDvol | |
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| DdeltaDtime, Charm | |
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| Elasticity | |
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| Gamma Greeks | |
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| Gamma | |
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| Maximal Gamma and the Illusions of Risk | |
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| GammaP | |
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| Gamma Symmetry | |
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| DgammaDvol, Zomma | |
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| DgammaDspot, Speed | |
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| DgammaDtime, Color | |
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| Vega Greeks | |
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| Vega | |
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| Vega Symmetry | |
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| Vega-Gamma Relationship | |
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| Vega from Delta | |
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| VegaP | |
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| Vega Leverage, Vega Elasticity | |
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| DvegaDvol, Vomma | |
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| DvommaDvol, Ultima | |
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| DvegaDtime | |
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| Variance Greeks | |
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| Variance Vega | |
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| DdeltaDvar | |
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| Variance Vomma | |
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| Variance Ultima | |
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| Volatility-Time Greeks | |
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| Theta Greeks | |
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| Theta | |
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| Theta Symmetry | |
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| Rho Greeks | |
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| Rho | |
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| Phi/Rho-2 | |
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| Carry Rho | |
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| Probability Greeks | |
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| In-the-Money Probability | |
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| DzetaDvol | |
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| DzetaDtime | |
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| Risk-Neutral Probability Density | |
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| From in-the-Money Probability to Density | |
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| Probability of Ever Getting in-the-Money | |
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| Greeks Aggregations | |
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| Net Weighted Vega Exposure | |
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| At-the-Money Forward Approximations | |
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| Approximation of the Black-Scholes-Merton Formula | |
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| Delta | |
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| Gamma | |
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| Vega | |
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| Theta | |
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| Rho | |
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| Cost-of-Carry | |
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| Numerical Greeks | |
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| First-Order Greeks | |
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| Second-Order Greeks | |
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| Third-Order Greeks | |
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| Mixed Greeks | |
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| Third-Order Mixed Greeks | |
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| Greeks from Closed-Form Approximations | |
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| Appendix B: Taking Partial Derivatives | |
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| Analytical Formulas for American Options | |
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| The Barone-Adesi and Whaley Approximation | |
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| The Bjerksund and Stensland (1993) Approximation | |
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| The Bjerksund and Stensland (2002) Approximation | |
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| Put-Call Transformation American Options | |
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| American Perpetual Options | |
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| Exotic Options-Single Asset | |
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| Variable Purchase Options | |
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| Executive Stock Options | |
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| Moneyness Options | |
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| Power Contracts and Power Options | |
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| Power Contracts | |
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| Standard Power Option | |
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| Capped Power Option | |
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| Powered Option | |
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| Log Contracts | |
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| Log(S) Contract | |
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| Log Option | |
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| Forward Start Options | |
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| Fade-in Option | |
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| Ratchet Options | |
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| Reset Strike Options-Type 1 | |
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| Reset Strike Options-Type 2 | |
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| Time-Switch Options | |
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| Chooser Options | |
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| Simple Chooser Options | |
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| Complex Chooser Options | |
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| Options on Options | |
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| Put-Call Parity Compound Options | |
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| Compound Option Approximation | |
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| Options with Extendible Maturities | |
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| Options That Can Be Extended by the Holder | |
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| Writer-Extendible Options | |
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| Lookback Options | |
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| Floating-Strike Lookback Options | |
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| Fixed-Strike Lookback Options | |
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| Partial-Time Floating-Strike Lookback Options | |
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| Partial-Time Fixed-Strike Lookback Options | |
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| Extreme-Spread Options | |
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| Mirror Options | |
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| Barrier Options | |
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| Standard Barrier Options | |
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| Standard American Barrier Options | |
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| Double-Barrier Options | |
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| Partial-Time Single-Asset Barrier Options | |
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| Look-Barrier Options | |
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| Discrete-Barrier Options | |
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| Soft-Barrier Options | |
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| Use of Put-Call Symmetry for Barrier Options | |
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| Barrier Option Symmetries | |
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| First-Then-Barrier Options | |
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| Double-Barrier Option Using Barrier Symmetry | |
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| Dual Double-Barrier Options | |
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| Binary Options | |
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| Gap Options | |
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| Cash-or-Nothing Options | |
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| Asset-or-Nothing Options | |
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| Supershare Options | |
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| Binary Barrier Options | |
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| Double-Barrier Binary Options | |
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| Double-Barrier Binary Asymmetrical | |
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| Asian Options | |
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| Geometric Average-Rate Options | |
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| Arithmetic Average-Rate Options | |
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| Discrete Arithmetic Average-Rate Options | |
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| Equivalence of Floating-Strike and Fixed-Strike Asian Options | |
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| Asian Options with Volatility Term-Structure | |
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| Exotic Options on Two Assets | |
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| Relative Outperformance Options | |
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| Product Options | |
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| Two-Asset Correlation Options | |
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| Exchange-One-Asset-for-Another Options | |
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| American Exchange-One-Asset-for-Another Option | |
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| Exchange Options on Exchange Options | |
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| Options on the Maximum or the Minimum of Two Risky Assets | |
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| Spread-Option Approximation | |
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| Two-Asset Barrier Options | |
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| Partial-Time Two-Asset Barrier Options | |
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| Margrabe Barrier Options | |
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| Discrete-Barrier Options | |
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| Two-Asset Cash-or-Nothing Options | |
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| Best or Worst Cash-or-Nothing Options | |
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| Options on the Minimum or Maximum of Two Averages | |
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| Currency-Translated Options | |
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| Foreign Equity Options Struck in Domestic Currency | |
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| Fixed Exchange Rate Foreign Equity Options | |
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| Equity Linked Foreign Exchange Options | |
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| Takeover Foreign Exchange Options | |
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| Greeks for Two-Asset Options | |
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| Black-Scholes-Merton Adjustments and Alternatives | |
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| The Black-Scholes-Merton Model with Delayed Settlement | |
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| The Black-Scholes-Merton Model Adjusted for Trading Day Volatility | |
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| Discrete Hedging | |
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| Hedging Error | |
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| Discrete-Time Option Valuation and Delta Hedging | |
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| Discrete-Time Hedging with Transaction Cost | |
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| Option Pricing in Trending Markets | |
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| Alternative Stochastic Processes | |
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| Constant Elasticity of Variance | |
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| Skewness-Kurtosis Models | |
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| Definition of Skewness and Kurtosis | |
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| The Skewness and Kurtosis for a Lognormal Distribution | |
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| Jarrow and Rudd Skewness and Kurtosis Model | |
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| The Corrado and Su Skewness and Kurtosis Model | |
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| Modified Corrado-Su Skewness-Kurtosis Model | |
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| Skewness-Kurtosis Put-Call Supersymmetry | |
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| Skewness-Kurtosis Equivalent Black-Scholes-Merton Volatility | |
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| Gram Charlier Density | |
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| Skewness-Kurtosis Trees | |
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| Pascal Distribution and Option Pricing | |
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| Jump-Diffusion Models | |
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| The Merton Jump-Diffusion Model | |
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| Bates Generalized Jump-Diffusion Model | |
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| Stochastic Volatility Models | |
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| Hull-White Uncorrelated Stochastic Volatility Model | |
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| Hull-White Correlated Stochastic Volatility Model | |
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| The SABR Model | |
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| Variance and Volatility Swaps | |
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| Variance Swaps | |
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| Volatility Swaps | |
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| More Information | |
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| Trees and Finite Difference Methods | |
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| Binomial Option Pricing | |
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| Cox-Ross-Rubinstein American Binomial Tree | |
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| Greeks in CRR Binomial Tree | |
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| Rendleman Bartter Binomial Tree | |
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| Leisen-Reimer Binomial Tree | |
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| Convertible Bonds in Binomial Trees | |
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| Binomial Model with Skewness and Kurtosis | |
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| Trinomial Trees | |
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| Exotic Options in Tree Models | |
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| Options on Options | |
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| Barrier Options Using Brownian Bridge Probabilities | |
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| American Barrier Options in CRR Binomial Tree | |
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| European Reset Options Binomial | |
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| American Asian Options in a Tree | |
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| Three-Dimensional Binomial Trees | |
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| Implied Tree Models | |
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| Implied Binomial Trees | |
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| Implied Trinomial Trees | |
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| Finite Difference Methods | |
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| Explicit Finite Difference | |
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| Implicit Finite Difference | |
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| Finite Difference in ln(S) | |
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| The Crank-Nicolson Method | |
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| Monte Carlo Simulation | |
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| Standard Monte Carlo Simulation | |
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| Greeks in Monte Carlo | |
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| Monte Carlo for Callable Options | |
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| Two Assets | |
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| Three Assets | |
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| N Assets, Cholesky Decomposition | |
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| Monte Carlo of Mean Reversion | |
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| Generating Pseudo-Random Numbers | |
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| Variance Reduction Techniques | |
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| Antithetic Variance Reduction | |
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| IQ-MC/Importance Sampling | |
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| IQ-MC Two Correlated Assets | |
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| Quasi-Random Monte Carlo | |
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| American Option Monte Carlo | |
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| Options on Stocks That Pay Discrete Dividends | |
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| European Options on Stock with Discrete Cash Dividend | |
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| The Escrowed Dividend Model | |
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| Simple Volatility Adjustment | |
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| Haug-Haug Volatility Adjustment | |
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| Bos-Gairat-Shepeleva Volatility Adjustment | |
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| Bos-Vandermark | |
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| Non-Recombining Tree | |
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| Black's Method for Calls on Stocks with Known Dividends | |
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| The Roll, Geske, and Whaley Model | |
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| Benchmark Model for Discrete Cash Dividend | |
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| A Single Dividend | |
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| Multiple Dividends | |
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| Applications | |
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| Options on Stocks with Discrete Dividend Yield | |
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| European with Discrete Dividend Yield | |
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| Closed-Form American Call | |
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| Recombining Tree Model | |
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| Commodity and Energy Options | |
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| Energy Swaps/Forwards | |
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| Energy Options | |
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| Options on Forwards, Black-76F | |
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| Energy Swaptions | |
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| Hybrid Payoff Energy Swaptions | |
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| The Miltersen-Schwartz Model | |
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| Mean Reversion Model | |
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| Seasonality | |
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| Interest Rate Derivatives | |
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| FRAs and Money Market Instruments | |
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| FRAs From Cash Deposits | |
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| The Relationship between FRAs and Currency Forwards | |
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| Convexity Adjustment Money Market Futures | |
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| Simple Bond Mathematics | |
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| Dirty and Clean Bond Price | |
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| Current Yield | |
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| Modified Duration and BPV | |
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| Bond Price and Yield Relationship | |
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| Price and Yield Relationship for a Bond | |
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| From Bond Price to Yield | |
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| Pricing Interest Rate Options Using Black-76 | |
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| Options on Money Market Futures | |
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| Price and Yield Volatility in Money Market Futures | |
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| Caps and Floors | |
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| Swaptions | |
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| Swaption Volatilities from Caps or FRA Volatilities | |
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| Swaptions with Stochastic Volatility | |
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| Convexity Adjustments | |
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| European Short-Term Bond Options | |
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| From Price to Yield Volatility in Bonds | |
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| The Schaefer and Schwartz Model | |
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| One-Factor Term Structure Models | |
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| The Rendleman and Bartter Model | |
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| The Vasicek Model | |
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| The Ho and Lee Model | |
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| The Hull and White Model | |
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| The Black-Derman-Toy Model | |
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| Volatility and Correlation | |
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| Historical Volatility | |
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| Historical Volatility from Close Prices | |
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| High-Low Volatility | |
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| High-Low-Close Volatility | |
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| Exponential Weighted Historical Volatility | |
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| From Annual Volatility to Daily Volatility | |
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| Confidence Intervals for the Volatility Estimate | |
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| Volatility Cones | |
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| Implied Volatility | |
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| The Newton-Raphson Method | |
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| The Bisection Method | |
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| Implied Volatility Approximations | |
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| Implied Forward Volatility | |
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| From Implied Volatility Surface to Local Volatility Surface | |
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| Confidence Interval for the Asset Price | |
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| Basket Volatility | |
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| Historical Correlation | |
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| Distribution of Historical Correlation Coefficient | |
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| Implied Correlations | |
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| Implied Correlation from Currency Options | |
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| Average Implied Index Correlation | |
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| Various Formulas | |
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| Probability of High or Low, the Arctangent Rule | |
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| Siegel's Paradox and Volatility Ratio Effect | |
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| Distributions | |
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| The Cumulative Normal Distribution Function | |
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| The Hart Algorithm | |
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| Polynomial Approximations | |
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| The Inverse Cumulative Normal Distribution Function | |
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| The Bivariate Normal Density Function | |
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| The Cumulative Bivariate Normal Distribution Function | |
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| The Trivariate Cumulative Normal Distribution Function | |
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| Some Useful Formulas | |
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| Interpolation | |
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| Linear Interpolation | |
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| Log-Linear Interpolation | |
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| Exponential Interpolation | |
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| Cubic Interpolation: Lagrange's Formula | |
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| Cubic-Spline Interpolation | |
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| Two-Dimensional Interpolation | |
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| Interest Rates | |
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| Future Value of Annuity | |
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| Net Present Value of Annuity | |
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| Continuous Compounding | |
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| Compounding Frequency | |
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| Zero-Coupon Rates from Par Bonds/Par Swaps | |
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| Risk-Reward Measures | |
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| Treynor's Measure | |
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| Sharpe Ratio | |
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| Confidence Ratio | |
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| Sortino Ratio | |
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| Burke Ratio | |
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| Return on VaR | |
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| Jensen's Measure | |
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| Appendix C: Basic Useful Information | |
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| The Option Pricing Software | |
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| Bibliography | |
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| Index | |