Superreplication in stochastic volatility models and optimal stopping

RØdiger Frey ()
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RØdiger Frey: Swiss Banking Institute, University of Zurich, Zurich, Plattenstrasse 14, CH-8032 Zurich, Switzerland Manuscript

Finance and Stochastics, 2000, vol. 4, issue 2, 187 pages

Abstract: In this paper we discuss the superreplication of derivatives in a stochastic volatility model under the additional assumption that the volatility follows a bounded process. We characterize the value process of our superhedging strategy by an optimal-stopping problem in the context of the Black-Scholes model which is similar to the optimal stopping problem that arises in the pricing of American-type derivatives. Our proof is based on probabilistic arguments. We study the minimality of these superhedging strategies and discuss PDE-characterizations of the value function of our superhedging strategy. We illustrate our approach by examples and simulations.

Keywords: Stochastic volatility; optimal stopping; incomplete markets; superreplication (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2000-02-10
Note: received: June 1998; final version received: April 1999
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Citations: View citations in EconPapers (17)

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