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Superreplication in stochastic volatility models and optimal stopping

  • RØdiger Frey

    ()

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

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    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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    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 4 (2000)
    Issue (Month): 2 ()
    Pages: 161-187

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    Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:161-187
    Note: received: June 1998; final version received: April 1999
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    Order Information: Web: http://www.springer.com/mathematics/quantitative+finance/journal/780/PS2

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    9. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
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