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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 | |