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. The January 2025 fifth edition all in color brings the following minor updates: - 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.