On Stochastic Volatility in the Valuation of European Options

Abstract

This paper presents stochastic volatility in the valuation of European options. Stochastic volatility models treat the volatility of the underlying asset as a random process rather than the constant volatility assumption of the Black-Scholes model. By changing the model parameters, almost all kinds of asset distributions can be generated by a negative correlation between the stock price process and the volatility process. It is observed that an asset’s log-return distribution is non-Gaussian which is characterized by heavy tails and high peaks. Heston model presents a new approach for a closed form valuation of options specifying the dynamics of the squared volatility as a square-root process and applying Fourier inversion techniques for the pricing procedure. Determination of the market growth rate of the stock share was considered. We also considered the effect of volatility and correlation parameter on the kurtosis and skewness of the density function.