Path Dependent Options and the Effect of Stochastic Volatility

In modern asset price models, stochastic volatility plays a crucial role explaining several stylized facts of returns. Recently, Barndorff-Nielsen and Shephard [4] introduced a class of stochastic volatility models (the so called BNS SV model) based on superposition of Ornstein-Uhlenbeck processes driven by subordinators. The BNS SV model forms a flexible class, which can easily explain heavy-tails and skewness in returns and the typical time-dependency structures seen in asset return data. In this paper the effect of stochastic volatility on path-dependent options is studied. This is done by simulation studies of comparable models, one with and one without stochastic volatility.