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

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

Economic Modelling, 2012, vol. 29, issue 3, 780-786

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.

Keywords: Fuzzy numbers; Option pricing; Jump diffusion; Crisp possibilistic mean value (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecmode:v:29:y:2012:i:3:p:780-786

DOI: 10.1016/j.econmod.2012.02.005

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