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A direct solution method for pricing options involving the maximum process

Author

Listed:
  • Masahiko Egami

    (Kyoto University)

  • Tadao Oryu

    (Tokyo Metropolitan University)

Abstract

One often encounters options involving not only the stock price, but also its running maximum. We provide, in a fairly general setting, explicit solutions for optimal stopping problems concerned with a diffusion process and its running maximum. Our approach is to use excursion theory for Markov processes and rewrite the original two-dimensional problem as an infinite number of one-dimensional ones. Our method is rather direct without presupposing the existence of an optimal threshold or imposing a smooth-fit condition. We present a systematic solution method by illustrating it through classical and new examples.

Suggested Citation

  • Masahiko Egami & Tadao Oryu, 2017. "A direct solution method for pricing options involving the maximum process," Finance and Stochastics, Springer, vol. 21(4), pages 967-993, October.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:4:d:10.1007_s00780-017-0343-5
    DOI: 10.1007/s00780-017-0343-5
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    References listed on IDEAS

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    1. Hongzhong Zhang & Olympia Hadjiliadis, 2012. "Drawdowns and the Speed of Market Crash," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 739-752, September.
    2. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
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    Citations

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    Cited by:

    1. Zbigniew Palmowski & Tomasz Serafin, 2020. "A Note on Simulation Pricing of π -Options," Risks, MDPI, vol. 8(3), pages 1-19, August.
    2. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    3. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, January.
    4. Liu, Zhenya & Zhan, Yaosong, 2022. "Investor behavior and filter rule revisiting," Journal of Behavioral and Experimental Finance, Elsevier, vol. 33(C).

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    More about this item

    Keywords

    60G40; 60J75;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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