Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure

The Barndorff-Nielsen and Shephard (BNS) model is a representative jump-type stochastic volatility model. Still, no method exists to compute option prices numerically for the non martingale case with infinite active jumps. In this paper, selecting the minimal martingale measure (MMM) as a representative martingale measure, we develop two simulation methods for the BNS model under the MMM. The first method simulates the asset price at maturity and the Radon-Nikodym density of the MMM separately. On the other hand, the second method directly computes the asset price distribution under the MMM. In addition, we implement some numerical experiments to evaluate the performance of our simulation methods.