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Exact simulation pricing with Gamma processes and their extensions

Author

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  • Lancelot F. James
  • Dohyun Kim
  • Zhiyuan Zhang

Abstract

Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV model that parallels the notable Heston SV model in the sense of admitting exact path simulation as studied by Broadie and Kaya. The instantaneous volatility process of the proposed model is driven by a Gamma process. Extensions to the model including superposition of independent instantaneous volatility processes are studied. Numerical results show that the proposed model outperforms the Heston model and two other L\'evy driven SV models in terms of model fit to the real option data. The ability to exactly simulate some of the path-dependent derivative prices is emphasized. Moreover, this is the first instance where an infinite-activity volatility process can be applied exactly in such pricing contexts.

Suggested Citation

  • Lancelot F. James & Dohyun Kim & Zhiyuan Zhang, 2013. "Exact simulation pricing with Gamma processes and their extensions," Papers 1310.6526, arXiv.org, revised Nov 2013.
  • Handle: RePEc:arx:papers:1310.6526
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    References listed on IDEAS

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    Cited by:

    1. Chengwei Zhang & Zhiyuan Zhang, 2017. "Sequential Sampling for CGMY Processes via Decomposition of their Time Changes," Papers 1708.00189, arXiv.org, revised Aug 2018.
    2. Fan Jiang & Xin Zang & Jingping Yang, 2020. "Asymptotic expansion for the transition densities of stochastic differential equations driven by the gamma processes," Papers 2003.06218, arXiv.org.
    3. Chengwei Zhang & Zhiyuan Zhang, 2018. "Sequential sampling for CGMY processes via decomposition of their time changes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 522-534, September.

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