Variational formulation of American option prices in the Heston Model

2017/11/30 by Lamberton, Damien, Terenzi, Giulia
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.11311

Abstract

We give an analytical characterization of the price function of an American option in Heston-type models. Our approach is based on variational inequalities and extends recent results of Daskalopoulos and Feehan (2011). We study the existence and uniqueness of a weak solution of the associated degenerate parabolic obstacle problem. Then, we use suitable estimates on the joint distribution of the log-price process and the volatility process in order to characterize the analytical weak solution as the solution to the optimal stopping problem. We also rely on semi-group techniques and on the affine property of the model.

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