Stochastic Volatility Models with Additive and Multiplicative Noise
(Candidacy Exam Talk)
Ibukun Amusan, FSU
3/18/10
The unrealistic assumption of constant volatility under the Black-Scholes model has led to the development of several other models with non-constant volatility. Stochastic volatility models form a general class where volatility is assumed to follow its own diffusion process. The graph of kurtosis against skewness of the log of historical volatilities is found to be similar to the graph of kurtosis against skewness of simulated paths of a process that has the stochastic equation with additive and multiplicative noise. This suggests that the stochastic model with both additive and multiplicative noise might be more suitable for accounting for the skewness observed in the implied volatility smile curve.