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Finance and Stochastics

, Volume 9, Issue 2, pp 251–267 | Cite as

The Russian option: Finite horizon

  • Goran PeskirEmail author
Article

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.

Keywords:

Russian option finite horizon arbitrage-free price optimal stopping smooth-fit geometric Brownian motion free-boundary problem nonlinear integral equation local time-space calculus curved boundary 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of AarhusAarhusDenmark

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