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No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate

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  • Xiaoyu Ji

    (Renmin University of China)

  • Hua Ke

    (Tongji University)

Abstract

In the stock models, the prices of the stocks are usually described via some differential equations. So far, uncertain stock model with constant interest rate has been proposed, and a sufficient and necessary condition for it being no-arbitrage has also been derived. This paper considers the multiple risks in the interest rate market and stock market, and proposes a multi-factor uncertain stock model with floating interest rate. A no-arbitrage theorem is derived in the form of determinants, presenting a sufficient and necessary condition for the new stock model being no-arbitrage. In addition, a strategy for the arbitrage is provided when the condition is not satisfied.

Suggested Citation

  • Xiaoyu Ji & Hua Ke, 2017. "No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 221-234, June.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:2:d:10.1007_s10700-016-9246-8
    DOI: 10.1007/s10700-016-9246-8
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    References listed on IDEAS

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    1. Galai, Dan & Masulis, Ronald W., 1976. "The option pricing model and the risk factor of stock," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 53-81.
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    3. Yoshida, Yuji, 2003. "The valuation of European options in uncertain environment," European Journal of Operational Research, Elsevier, vol. 145(1), pages 221-229, February.
    4. 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. Ziqiang Lu & Hongyan Yan & Yuanguo Zhu, 2019. "European option pricing model based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 199-217, June.

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