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Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate

Author

Listed:
  • Xiaoyu Tan

    (Department of Mathematics, School of Science, Zhejiang University, Hangzhou 310058, China)

  • Shenghong Li

    (Department of Mathematics, School of Science, Zhejiang University, Hangzhou 310058, China)

  • Shuyi Wang

    (Department of Mathematics, School of Science, Zhejiang University, Hangzhou 310058, China)

Abstract

This paper extends the traditional jump-diffusion model to a comprehensive general Lévy process model with the stochastic interest rate for European-style options pricing. By using the Girsanov theorem and Itô formula, we derive the uniform formalized pricing formulas under the equivalent martingale measure. This model contains not only the traditional jump-diffusion model, such as the compound Poisson model, the renewal model, the pure-birth jump-diffusion model, but also the infinite activities Lévy model.

Suggested Citation

  • Xiaoyu Tan & Shenghong Li & Shuyi Wang, 2020. "Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:731-:d:354368
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    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
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    4. Fu, Jun & Yang, Hailiang, 2012. "Equilibruim approach of asset pricing under Lévy process," European Journal of Operational Research, Elsevier, vol. 223(3), pages 701-708.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. 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.
    7. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Hirsa, Ali & Neftci, Salih N., 2013. "An Introduction to the Mathematics of Financial Derivatives," Elsevier Monographs, Elsevier, edition 3, number 9780123846822.
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    Cited by:

    1. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu, 2022. "Multiple-Trigger Catastrophe Bond Pricing Model and Its Simulation Using Numerical Methods," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    2. Xianfei Hui & Baiqing Sun & Hui Jiang & Yan Zhou, 2022. "Modeling dynamic volatility under uncertain environment with fuzziness and randomness," Papers 2204.12657, arXiv.org, revised Oct 2022.

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