The volatility smile is a well-known phenomenon observed with the Black-Scholes option pricing model. This suggests that stock price volatility is certainly not constant as assumed in the Black-Scholes model. Heston amongst others introduced stochastic volatility models for the stock price process. However empirical research has shown that a combined stochastic volatility and jump-diffusion model actually works better. We also consider American-style versions of these option when the underlying asset is modelled by a combined SV-JD process.
Contact: Gerald Cheang
GHL Cheang, C Chiarella & Andrew Ziogas, 'The Representation of American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics', Quantitative Finance, 2011.