Calibrating and pricing with local volatility models

Consistently fitting vanilla option surfaces when pricing volatility derivatives such as Vix options or interest rate/equity hybrids is an important issue. Yong Ren, Dilip Madan and Michael Qian Qian show how this can be accomplished, using a stochastic local volatility model as the main example. They also give, for the first time, quanto corrections in local volatility models

Local volatility models introduced by Dupire (1994) and Derman & Kani (1994) are now widely used to price and manage the risks of structured products. The dimensionality of risks to be simultaneously managed continues to expand with the demand for hybrid products and the growth of markets directly trading volatility. The formulation and implementation of local volatility models in these higher-dimensional Markov contexts is now becoming an important issue. Of particular interest to the financial