Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 218, Issue -, Pages 223-234Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2023.11.029
Keywords
Barndorff-Nielsen and Shephard model; Stochastic volatility model; Minimal martingale measure; Monte Carlo simulation
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The Barndorff-Nielsen and Shephard model is a jump-type stochastic volatility model, and this paper proposes two simulation methods for computing option prices under a representative martingale measure. The performance of these methods is evaluated through numerical experiments.
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.
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