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The Russian option: Finite horizon

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  • Goran Peskir

Abstract

We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parallel with the best known results on the American put option with finite horizon. The key argument in the proof relies upon a local time-space formula. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, April.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:2:p:251-267
    DOI: 10.1007/s00780-004-0133-8
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    Citations

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    Cited by:

    1. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    2. Kimura, Toshikazu, 2008. "Valuing finite-lived Russian options," European Journal of Operational Research, Elsevier, vol. 189(2), pages 363-374, September.
    3. Duistermaat, J.J. & Kyprianou, A.E. & van Schaik, K., 2005. "Finite expiry Russian options," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 609-638, April.
    4. Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima in Diffusion Models with Finite Horizon," SFB 649 Discussion Papers SFB649DP2006-057, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Yerkin Kitapbayev, 2015. "The British Lookback Option with Fixed Strike," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 238-260, July.
    6. Bruno Buonaguidi, 2023. "Finite Horizon Sequential Detection with Exponential Penalty for the Delay," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 224-238, July.
    7. Woo, Min Hyeok & Choe, Geon Ho, 2020. "Pricing of American lookback spread options," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6300-6318.
    8. Denis Belomestny & Pavel V. Gapeev, 2006. "An Iteration Procedure for Solving Integral Equations Related to Optimal Stopping Problems," SFB 649 Discussion Papers SFB649DP2006-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    10. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes," Papers 2211.04095, arXiv.org, revised Dec 2023.
    11. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
    12. Gapeev, Pavel V., 2022. "Discounted optimal stopping problems in continuous hidden Markov models," LSE Research Online Documents on Economics 110493, London School of Economics and Political Science, LSE Library.
    13. Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.
    14. Gapeev, P.V. & Peskir, G., 2006. "The Wiener disorder problem with finite horizon," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1770-1791, December.

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