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.
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
\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://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RH52800006}
Linking options:
https://www.mathnet.ru/eng/tvp3766
https://www.mathnet.ru/eng/tvp/v39/i1/p191
This publication is cited in the following 10 articles:
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