Exotic option prices simulated by Monte Carlo method on market driven by diffusion with Poisson jumps and stochastic volatility

Abstract

We consider a broad class of stochastic models of a financial market generalizing the classical Black-Scholes model, which comprise both: stochastic volatility of Brownian type and jumps at random times. We restrict ourselves to the model, where volatility is described by the diffusion which comprises the Heston stochastic volatility defined as a diffusion of Brownian type and the Poisson jump diffusion. We provide an argument that such models perfectly match typical real-life financial phenomena comparing the so-called logarithmic returns. Applying computer simulations methods we investigate the dependence of prices of a few selected contingent claims (specifying some different options) on the parameters of our stochastic model. © Springer-Verlag Berlin Heidelberg 2005.