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Options pricing with time changed Lévy processes under imprecise information

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Abstract

This study evaluates a time changed Lévy model for European call options under a fuzzy environment. The proposed model is characterized by high frequency jumps, stochastic volatility, and stochastic volatility with the jumps, existing in the returns process of financial assets. Moreover, to consider imperfect and unpredictable accounting information, this study uses fuzzy logic to account for the impreciseness of the accounting information, which can not be described in extant models, and provides reasonable reference instruments for future research on option pricing under a jump diffusion model with imprecise market information. Our empirical results also show that the fuzzy time changed Lévy model has better fitting performance when compared with the time changed Lévy and the Black and Scholes model when using S&P 500 index option data.

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Notes

  1. Cont (2001) carried out an empirical study of various types of financial markets, and found that the asset returns distribution has several statistical properties, including the leverage effect, asymmetric time scale, high peaks, heavy tails, and so on.

  2. Triangular fuzzy numbers resemble trapezoidal fuzzy numbers. When using trapezoidal fuzzy numbers, the most likely value lies in the same period, \(a\) and \(b\), as the triangular fuzzy number. To increase both the reliability and simplicity of the model, this study uses the most popular sharp function, the triangular fuzzy function, as the sharp function.

  3. The definition of the exponential martingale represents that the expectation of Eq. (18) is equivalent to one.

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Acknowledgments

We thank Shu-Cherng Fang (the editor) and the anonymous reviewers for helpful comments and suggestions.

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Authors and Affiliations

  1. City College, Wenzhou University, Chashan University Town, Wenzhou City, Zhejiang, People’s Republic of China

    Zhi-Yuan Feng

  2. Department of International Business, Soochow University, No. 56, Sec. 1, Guiyang St., Zhongzheng District, Taipei City, 10048, Taiwan, Republic of China

    Johnson T.-S. Cheng

  3. Graduate Institute of Finance and Banking, Department of Accountancy, National Cheng Kung University, Tainan City, 70101, Taiwan, Republic of China

    Yu-Hong Liu

  4. Faculty of Finance, College of Management, Yuan Ze University, No. 135, Yuan-Tung Road, Chung-Li, Taoyuan, 32003, Taiwan, Republic of China

    I-Ming Jiang

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  1. Zhi-Yuan Feng
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  2. Johnson T.-S. Cheng
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Correspondence to I-Ming Jiang.

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Feng, ZY., Cheng, J.TS., Liu, YH. et al. Options pricing with time changed Lévy processes under imprecise information. Fuzzy Optim Decis Making 14, 97–119 (2015). https://doi.org/10.1007/s10700-014-9191-3

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  • DOI: https://doi.org/10.1007/s10700-014-9191-3

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