This article is cited in 10 papers

Short Communications

On the rational pricing of the “Russian Option” for the symmetrical binomial model of a $(B,S)$-market

D. O. Kramkov, A. N. Shiryaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We present in the binomial model of Cox, Rubinstein and Ross the closed form solution for the “Russian option”, i.e., the American type option with the reward sequence $f=(f_n)_{n\ge 0}$ given by
$$ f_n(\omega)=\beta^n\max_{k\le n}S_k(\omega), $$
where $\beta$ is some discounting factor, $0<\beta<1$. This option was introduced earlier by L. Sheep and A. N. Shiryaev [3], in the framework of the diffusion model of Black and Sholes.

Keywords: the binomial Cox, Rubinstein, and Ross model, American option, “Russian option”, symmetric geometrical random walk, optimal stopping rules.

Received: 05.07.1993

 English version: Theory of Probability and its Applications, 1994, 39:1, 153–162

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