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A new look at pricing of the “Russian Option”

L. A. Shepp^a, A. N. Shiryaev<sup>b

a</sup> AT&T Bell Laboratories, New Jersey, USA
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The “Russian option” was introduced and calculated with the help of the solution of the optimal stopping problem for a two-dimensional Markov process in [10]. This paper proposes a new derivation of the general results [10]. The key idea is to introduce the dual martingale measure which permits one to reduce the “two-dimensional” optimal stopping problem to a “one-dimensional” one. This approach simplifies the discussion and explain the simplicity of the answer found in [10].

Keywords: diffusion model of the $(B,S)$-market, bank account, rational option price, rational expiration time, optimal stopping rules, smooth sewing condition, the Stephan problem, diffusion with reflection.

Received: 05.07.1993

 English version: Theory of Probability and its Applications, 1994, 39:1, 103–119

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