Stochastic volatility models with application in option pricing

In this paper, we develop a new method for pricing derivatives under stochastic volatility models by viewing the call price as an expected value of a truncated lognormal distribution under the risk neutral measure. We also obtain the formula for the estimate of the variance of the call price with the stochastic volatility. Using return data, we estimate the mean and variance of the stochastic volatility of the Black-Scholes model. An extensive empirical analysis of the European call option valuation for S & P 100 Index shows: (i) our method outperforms other compelling stochastic volatility pricing models, (ii) the pricing errors when using our method are quite small even though our estimation procedure is based only on historical return data. Formulas for option pricing and variances derivation for Heston’s (1993) continuous time stochastic volatility model and for Taylor’s (1973) discrete time stochastic volatility model are also discussed in some detail. © 2010 Taylor & Francis Group, LLC. All rights reserved.