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Variational formulation of American option prices in the Heston Model

Damien Lamberton 1, 2 Giulia Terenzi 1, 3
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
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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Submitted on : Monday, December 10, 2018 - 2:44:48 PM
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Damien Lamberton, Giulia Terenzi. Variational formulation of American option prices in the Heston Model. SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics 2019, 10 (1), pp.261-368. ⟨10.1137/17M1158872⟩. ⟨hal-01649496v2⟩

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