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

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  • Arai, Takuji
  • Imai, Yuto

Abstract

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.

Suggested Citation

  • Arai, Takuji & Imai, Yuto, 2024. "Monte Carlo simulation for Barndorff–Nielsen and Shephard model under change of measure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 223-234.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:223-234
    DOI: 10.1016/j.matcom.2023.11.029
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    Cited by:

    1. Takuji Arai & Yuto Imai, 2024. "Option pricing for Barndorff-Nielsen and Shephard model by supervised deep learning," Papers 2402.00445, arXiv.org.

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