Stochastic volatility models and option prices

Abstract

It is an observed fact in the market that the implied volatility of traded options vary from day to day. An alternative and straight-forward explanation is that the instantaneous volatility of a stock is a stochastic quantity itself. The assumptions of the Black and Scholes model no longer hold. This is, therefore, one reason why Black and Scholes prices can differ from market prices of options. Having decided to make the instantaneous volatility stochastic, it is necessary to decide what sort of process it follows. The article analyzes three stochastic volatility models and considers how stochastic volatility can be incorporated into model prices of options. The investigation of stochastic volatility influence for pricing options traded in the SEB Vilnius Bank is done. © Springer-Verlag Berlin Heidelberg 2006.