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Finite expiry Russian options

Author

Listed:
  • Duistermaat, J.J.
  • Kyprianou, A.E.
  • van Schaik, K.

Abstract

We consider the Russian option introduced by Shepp and Shiryayev (Ann. Appl. Probab. 3 (1993) 631, Theory Probab. Appl. 39 (1995) 103) but with finite expiry and show that its space-time value function characterizes the unique solution to a free boundary problem. Further, using a method of randomization (or Canadization) due to Carr (Rev. Financ. Stud. 11 (1998) 597) we produce a numerical algorithm for solving the aforementioned free boundary problem.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:115:y:2005:i:4:p:609-638
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    References listed on IDEAS

    as
    1. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    2. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    3. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181.
    4. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, April.
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    Cited by:

    1. Eisenbaum, Nathalie, 2006. "Local time-space stochastic calculus for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 757-778, May.
    2. Kimura, Toshikazu, 2008. "Valuing finite-lived Russian options," European Journal of Operational Research, Elsevier, vol. 189(2), pages 363-374, September.
    3. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
    4. Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima of some Jump-Diffusion Processes," SFB 649 Discussion Papers SFB649DP2006-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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