Variational formulation of American option prices in the Heston Model

Damien Lamberton; Giulia Terenzi

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arXiv · 1711.11311

Variational formulation of American option prices in the Heston Model

Damien Lamberton·Giulia Terenzi

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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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Damien Lamberton, Giulia Terenzi. 2017-11-30. Variational formulation of American option prices in the Heston Model. https://arxiv.org/abs/1711.11311

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