The simulation of the implied distribution and other smile consistent stochastic volatility models: An overview

This review paper focuses on the smile-consistent stochastic volatility models. Smile-consistent stochastic volatility models take the European options' market prices as given, and they try to explain the stochastic evolution of implied volatilities over time across strikes and maturities. The main ideas behind the models by Derman and Kani (1998), Ledoit and Santa-Clara (1999), and Britten-Jones and Neuberger (1999) are highlighted. In addition, the concept and the applications of a new methodology for smile-consistent stochastic volatility pricing, that of the simulation of the implied distribution, arc discussed. The simulation model by Skiadopoulos and Hodges (2001) is explained