Multilevel monte carlo method for the heston model

Abstract

The Heston model is a widely used financial model which incorporates stochastic volatility. The Monte Carlo method is one of the popular simulation method, particularly good at estimating the price of complex financial derivatives via random number generation. The multilevel Monte Carlo method is a computationally efficient version of Monte Carlo method, but the target model should satisfy conditions for it to be applicable. We show that such conditions are met in the Heston model by analytically proving the $L^{p}$ -covergence of the Heston model. In the latter part of the thesis, we consider the hitting time of the Heston model as well as some representative financial options. Our numerical results show that the multilevel Monte Carlo method is an efficient numerical technique whose performance exceeds that of the standard Monte Carlo method.