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Teor. Veroyatnost. i Primenen., 1994, Volume 39, Issue 1, Pages 191–200 (Mi tvp3766)  

This article is cited in 3 scientific papers (total in 3 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.

Full text: PDF file (442 kB)

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

Bibliographic databases:

Received: 05.07.1993

Citation: D. O. Kramkov, A. N. Shiryaev, “On the rational pricing of the “Russian Option” for the symmetrical binomial model of a $(B,S)$-market”, Teor. Veroyatnost. i Primenen., 39:1 (1994), 191–200; Theory Probab. Appl., 39:1 (1994), 153–162

Citation in format AMSBIB
\Bibitem{KraShi94}
\by D.~O.~Kramkov, A.~N.~Shiryaev
\paper On the rational pricing of the ``Russian Option'' for the symmetrical binomial model of a $(B,S)$-market
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 1
\pages 191--200
\mathnet{http://mi.mathnet.ru/tvp3766}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1348194}
\zmath{https://zbmath.org/?q=an:0836.90013}
\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 1
\pages 153--162
\crossref{https://doi.org/10.1137/1139006}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RH52800006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math., 237 (2002), 192–202  mathnet  mathscinet  zmath
    2. R. V. Ivanov, “Calculating the American options in the default model”, Autom. Remote Control, 68:3 (2007), 513–522  mathnet  crossref  mathscinet  zmath  elib  elib
    3. Christensen S., Irle A., “A General Method For Finding the Optimal Threshold in Discrete Time”, Stochastics, 91:5 (2019), 728–753  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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