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Super-replication in stochastic volatility models under portfolio constraints

Cvitanić, Jakša and Pham, Huyên and Touzi, Nizar (1999) Super-replication in stochastic volatility models under portfolio constraints. Journal of Applied Probability, 36 (2). pp. 523-545. ISSN 0021-9002. http://resolver.caltech.edu/CaltechAUTHORS:CVIjap99

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Abstract

We study a financial market with incompleteness arising from two sources: stochastic volatility and portfolio constraints. The latter are given in terms of bounds imposed on the borrowing and short-selling of a `hedger' in this market, and can be described by a closed convex set K. We find explicit characterizations of the minimal price needed to super-replicate European-type contingent claims in this framework. The results depend on whether the volatility is bounded away from zero and/or infinity, and also, on if we have linear dynamics for the stock price process, and whether volatility process depends on the stock price. We use a previously known representation of the minimal price as a supremum of the prices in the corresponding shadow markets, and we derive a PDE characterization of that representation.


Item Type:Article
Additional Information:1999 © Applied Probability Trust. Received 8 May 1997; revision received 21 October 1997. The research of the first author (J.C.) was partially supported by NSF grant #DMS-95-03582. He is also grateful to CREST for its hospitality in July 1996, when this research was initiated. We are grateful to Victoria Pikovsky for the numerical calculations in Section 8.3, to H. Mete Soner for providing us with some 'viscosity tips', and to Yuri Kabanov for helpful comments that prompted the introduction of Lemma 4.1.
Subject Keywords:Stochastic volatility; portfolio constraints; hedging options; viscosity solution
Record Number:CaltechAUTHORS:CVIjap99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CVIjap99
Alternative URL:http://dx.doi.org/10.1239/jap/1032374469
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10919
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:17 Jun 2008
Last Modified:26 Dec 2012 10:06

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