Valuation equations for stochastic volatility models

Erhan Bayraktar, Constantinos Kardaras and Hao Xing

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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

Keywords: stochastic volatility models; valuation equations; strict local martingale; Feynman-Kac theorem (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2012-04
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Citations: View citations in EconPapers (15)

Published in SIAM Journal on Financial Mathematics, April, 2012, 3(1), pp. 351-373. ISSN: 1945-497X

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Related works:
Working Paper: Valuation equations for stochastic volatility models (2011)
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