This short book evolved out of lecture notes for a course offered several times over the past few years at New York University. It describes financial engineering models that assume non-constant volatility for pricing equity derivatives. This allows the models to be calibrated to—or at least better fit—observed volatility skew.

The first half of the book focuses on theory. It covers stochastic volatility models and local volatility models. It delves into the popular Heston stochastic volatility model and variants. A chapter extends the discussion to incorporate jumps. The book then takes a diversion into structural and intensity credit risk models and discusses arbitrage between credit and equity derivatives for issues with poor credit. There are two chapters exploring the asymptotic and dynamic behavior of the volatility surface. The last three chapters focus on specific instruments: barrier options, exotic cliquets and volatility derivatives.