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From perpetual strangles to Russian options
Journal article   Peer reviewed

From perpetual strangles to Russian options

Hans U Gerber and Elias S.W Shiu
Insurance, mathematics & economics, Vol.15(2), pp.121-126
1994
DOI: 10.1016/0167-6687(94)90787-0

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Abstract

The owner of a Russian option on a stock receives the historical maximum value of the stock prices upon exercising the option. There is no fixed exercise date since it is a perpetual American option. As the payoff is path-dependent, it is remarkable that there are simple formulas for the price. This paper derives two (equivalent) pricing formulas by means of the optional sampling theorem.
Perpetual American options Optional sampling theorem Smooth pasting condition Option-pricing theory Russian option Optimal stopping Perpetual American strangle Smooth fitting condition Risk-neutral measure High contact condition

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