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Valuation equations for stochastic volatility models

Bayraktar, Erhan, Kardaras, Constantinos and Xing, Hao (2012) Valuation equations for stochastic volatility models. SIAM Journal on Financial Mathematics, 3 (1). pp. 351-373. ISSN 1945-497X

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Abstract

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model behavior: the volatility process in our model can potentially reach zero and either stay there or instantaneously reflect, and the asset-price process may be a strict local martingale. Our main result is a necessary and sufficient condition on the uniqueness of classical solutions to the valuation equation: the value function is the unique nonnegative classical solution to the valuation equation among functions with at most linear growth if and only if the asset price is a martingale

Item Type: Article
Official URL: https://www.siam.org/journals/sifin.php
Additional Information: © 2012 SIAM
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 04 May 2012 10:20
URL: http://eprints.lse.ac.uk/43460/

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