From perpetual strangles to Russian options
type: Item
instance of: scholarly article
title: From perpetual strangles to Russian options
zbMATH Open document ID: 0822.60042
DOI: 10.1016/0167-6687(94)90787-0
published in: Insurance Mathematics \& Economics
publication date: 1995-07-03T00:00:00Z
review text: Let \(\{S(t); t\geq 0\}\) be a geometric Brownian motion modeling the stock price process. Define the process \(M(t) = \max \{M, \max[S(u)\mid 0 \leq u \leq t]\}\), \(t \geq 0\), where \(M \geq S(0)\). \(M(t)\) is called the historical maximum of the stock prices up to time \(t\). The `Russian option' is a perpetual American option such that, if its owner exercises it at time \(t \geq 0\), he receives the amount \(M(t)\) at that time. The price at time 0 of the option is the supremum, over all stopping times \(T\), of \(E[\text{exp} (-rT) M(T)]\). The authors derive two pricing formulas by means of the optional sampling theorem. In particular, an alternative derivation of the Shepp-Shiryaev pricing formula for Russian option is provided.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62P05
zbMATH DE Number: 768795
zbMATH Keywords: geometric Brownian motion modeling the stock price process
zbMATH Keywords: historical maximum of the stock prices
zbMATH Keywords: optional sampling theorem
zbMATH Keywords: pricing formula for Russian option
author: H. U. Gerber
author: E. S. W. Shiu
reviewed by: Vigirdas Mackevičius
MaRDI profile type: Publication
full work available at URL: 0167-6687(94)90787-0
OpenAlex ID: W2035089054
cites work: Q4035104
cites work: Q4320690
cites work: The Russian option: Reduced regret
cites work: Q4172681
description: scientific article; zbMATH DE number 768795