Valuation equations for stochastic volatility models

Erhan Bayraktar, Constantinos Kardaras and Hao Xing

Papers from arXiv.org

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.

Date: 2010-04, Revised 2011-12
New Economics Papers: this item is included in nep-ore
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Working Paper: Valuation equations for stochastic volatility models (2012)
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