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In its fifth edition, this book presents the most significant equity derivatives models used these days. It is not a book around esoteric or cutting-edge models, but rather a book on relatively simple and standard models, viewed from the angle of a practitioner.
A few key subjects explained in this book are:

• cash dividends for European, American, or exotic options
• advanced finite difference techniques: grid stretching, payoff smoothing, the solution of the linear complementary problem under negative rates, and explicit super-time-stepping schemes.
• issues of the Dupire local volatility model and possible fixes
• Non-parametric regression for American options in Monte-Carlo, randomized simulations
• the particle method for stochastic-local-volatility model with quasi-random numbers
• Numerical methods for the variance and volatility swaps, including some popular variations around those.
• quadratures for options under stochastic volatility models
• VIX options and dividend derivatives
• backward/forward representation of exotics.
• arbitrage-free representations for implied volatilities.

• vanilla option pricing under the spot piecewise-lognormal model has been reworked and now include newer approximations.
• Asian option pricing also includes newer approximations.
• Time-dependent piecewise-constant stochastic volatility vanilla pricing, calibration and simulation.
• a small section on forward variance model calibration.

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