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Pricing power options with a generalized jump diffusion

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  • Juan Liao
  • Huisheng Shu
  • Chao Wei

Abstract

In this article, the valuation of power option is investigated when the dynamic of the stock price is governed by a generalized jump-diffusion Markov-modulated model. The systematic risk is characterized by the diffusion part, and the non systematic risk is characterized by the pure jump process. The jumps are described by a generalized renewal process with generalized jump amplitude. By introducing NASDAQ Index Model, their risk premium is identified respectively. A risk-neutral measure is identified by employing Esscher transform with two families of parameters, which represent the two parts risk premium. In this article, the non systematic risk premium is considered, based on which the price of power option is studied under the generalized jump-diffusion Markov-modulated model. In the case of a special renewal process with log double exponential jump amplitude, the accurate expressions for the Esscher parameters and the pricing formula are provided. By numerical simulation, the influence of the non systematic risk’s price and the index of the power options on the price of the option is depicted.

Suggested Citation

  • Juan Liao & Huisheng Shu & Chao Wei, 2017. "Pricing power options with a generalized jump diffusion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(22), pages 11026-11046, November.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:22:p:11026-11046
    DOI: 10.1080/03610926.2016.1257138
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    Cited by:

    1. Anqi Zou & Jiajie Wang & Chiye Wu, 2023. "Pricing Variance Swaps under MRG Model with Regime-Switching: Discrete Observations Case," Mathematics, MDPI, vol. 11(12), pages 1-30, June.

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