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