Bermudan Option Pricing using Almost-Exact Scheme under Heston-type Models

Sammanfattning

Black and Scholes have proposed a model for pricing European options where the underlying asset follows a so-called geometric Brownian motion which assumes constant volatility. The proposed Black-Scholes model has an exact solution. However, it has been shown that such an assumption of constant volatility is not realistic, and numerous extensions have been developed. In addition, models usually do not have a closed-form solution which makes pricing a challenging task. The thesis focuses on pricing Bermudan options under two stochastic volatility Heston-type models using an Almost-Exact scheme for simulation. Namely, we focus on deriving the Almost-Exact scheme for Heston and Double Heston model and numerically study the behaviour of the scheme. We show that the AES works well when the number of simulated steps is equal to the number of exercise dates which makes it efficient.