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The double exponential jump diffusion model for pricing European options under fuzzy environments

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  • Zhang, Li-Hua
  • Zhang, Wei-Guo
  • Xu, Wei-Jun
  • Xiao, Wei-Lin

Abstract

The interest rate and volatility may have different values in the different commercial banks and financial institutions. Moreover, the fluctuations of the underlying assets are rare events, and there are not enough historical data to estimate the jump intensity in a precise sense. This paper considers European option pricing problems with the fuzzy interest rate, fuzzy drift, fuzzy volatility and fuzzy jump intensity. We present the fuzzy pricing formula of European options based on the Kou's double exponential jump diffusion model. We also obtain the crisp possibilistic mean option pricing formula in fuzzy double exponential jump diffusion model by using the crisp possibilistic mean values of the fuzzy numbers. Comparing with B-S formula, numerical analysis and empirical results show that the fuzzy double exponential jump diffusion formula and the crisp possibilistic mean option pricing formula are reasonable and can be taken as reference pricing tools for the financial investors.

Suggested Citation

  • Zhang, Li-Hua & Zhang, Wei-Guo & Xu, Wei-Jun & Xiao, Wei-Lin, 2012. "The double exponential jump diffusion model for pricing European options under fuzzy environments," Economic Modelling, Elsevier, vol. 29(3), pages 780-786.
    • Handle: RePEc:eee:ecmode:v:29:y:2012:i:3:p:780-786
    DOI: 10.1016/j.econmod.2012.02.005
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    References listed on IDEAS

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    6. Xianfei Hui & Baiqing Sun & Hui Jiang & Indranil SenGupta, 2021. "Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters," Papers 2101.08984, arXiv.org, revised Feb 2022.
    7. Li, Xiao-Ping & Feng, Yun & Wu, Chong-Feng & Xu, Wei-Dong, 2013. "Response of the term structure of forward exchange rate to jump in the interest rate," Economic Modelling, Elsevier, vol. 30(C), pages 863-874.
    8. Anatoliy Swishchuk & Maksym Tertychnyi & Robert Elliott, 2014. "Pricing Currency Derivatives with Markov-modulated Levy Dynamics," Papers 1402.1953, arXiv.org.
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