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.
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Received: March 2004,
Mathematics Subject Classification (2000):
91B28, 35R35, 45G10, 60G40, 60J60
JEL Classification:
G13
Goran Peskir: Centre for Analytical Finance (funded by the Danish Social Science Research Council) and Network in Mathematical Physics and Stochastics (funded by the Danish National Research Foundation).
The first draft of the present paper has been completed in September 2002. I am indebted to Albert Shiryaev for useful comments.
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Peskir, G. The Russian option: Finite horizon. Finance Stochast. 9, 251–267 (2005). https://doi.org/10.1007/s00780-004-0133-8
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DOI: https://doi.org/10.1007/s00780-004-0133-8