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Computing option price for Levy process with fuzzy parameters

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  • Nowak, Piotr
  • Romaniuk, Maciej

Abstract

In the following paper we propose the method for option pricing based on application of stochastic analysis and theory of fuzzy numbers. The process of underlying asset trajectory belongs to a subclass of Levy processes with jumps. From practical point of view some parameters of such trajectory cannot be precisely described. Therefore, some degree of the market uncertainly has to be reflected in the description of the model itself. For example, the parameters (like interest rate, volatility) of financial market fluctuate from time to time and experts may have different opinions about such parameters. Using theory of fuzzy numbers and stochastic analysis enables us to take into account many sources of uncertainty, not only the probabilistic one. In our paper we apply the theory of Levy characteristics and present some numerical experiments based on Monte Carlo simulations. In detail, we present pricing formula for classical example of European call option.

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  • Nowak, Piotr & Romaniuk, Maciej, 2010. "Computing option price for Levy process with fuzzy parameters," European Journal of Operational Research, Elsevier, vol. 201(1), pages 206-210, February.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:1:p:206-210
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    2. 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.
    3. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    4. Jorge de Andrés-Sánchez, 2023. "Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    5. 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.
    6. Wei-Guo Zhang & Zhe Li & Yong-Jun Liu & Yue Zhang, 2021. "Pricing European Option Under Fuzzy Mixed Fractional Brownian Motion Model with Jumps," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 483-515, August.
    7. Marroquı´n-Martı´nez, Naroa & Moreno, Manuel, 2013. "Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?," European Journal of Operational Research, Elsevier, vol. 225(3), pages 429-442.
    8. Lin, Zhongguo & Han, Liyan & Li, Wei, 2021. "Option replication with transaction cost under Knightian uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    9. Katarína Čunderlíková, 2020. "Martingale Convergence Theorem for the Conditional Intuitionistic Fuzzy Probability," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    10. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.

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