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Superreplication in stochastic volatility models and optimal stopping

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  • RØdiger Frey

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

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    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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    Bibliographic Info

    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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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Stochastic volatility; optimal stopping; incomplete markets; superreplication;

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    Cited by:
    1. Pierre Henri-Labordère & Nizar Touzi & Alfred Galichon, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    2. Wei Chen, 2013. "G-Doob-Meyer Decomposition and its Application in Bid-Ask Pricing for American Contingent Claim Under Knightian Uncertainty," Papers 1401.0677, arXiv.org.
    3. Haishi Huang, 2009. "Convertible Bonds: Risks and Optimal Strategies," Bonn Econ Discussion Papers bgse07_2010, University of Bonn, Germany.
    4. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
    5. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0ck8ecp is not listed on IDEAS

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