Exercise strategies for American exotic options under ambiguity

Tatjana Chudjakow and Jörg Vorbrink
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Tatjana Chudjakow: Center for Mathematical Economics, Bielefeld University
Jörg Vorbrink: Center for Mathematical Economics, Bielefeld University

No 421, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We analyze several exotic options of American style in a multiple prior setting and study the optimal exercise strategy from the perspective of an ambiguity averse buyer in a discrete time model of Cox-Ross-Rubinstein style. The multiple prior model relaxes the assumption of a known distribution of the stock price process and takes into account decision maker's inability to completely determine the underlying asset's price dynamics. In order to evaluate the American option the decision maker needs to solve a stopping problem. Unlike the classical approach ambiguity averse decision maker uses a class of measures to evaluate her expected payoffs instead of a unique prior. Given time-consistency of the set of priors an appropriate version of backward induction leads to the solution as in the classical case. Using a duality result the multiple prior stopping problem can be related to the classical stopping problem for a certain probability measure - the worst-case measure. Therefore, the problem can be reduced to identifying the worst-case measure. We obtain the form of the worst-case measure for different classes of exotic options explicitly exploiting the observation that the option can be decomposed in simpler event-driven claims.

Keywords: Ambiguity aversion; Worst-case measure; Binomial methods; Optimal exercise; American exotic options (search for similar items in EconPapers)
Date: 2011-08-16
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (1)

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