Variational Formulation of American Option Prices in the Heston Model
Damien Lamberton, Giulia Terenzi
Source 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 [ Existence, Uniqueness and Global Regularity for Degenerate Elliptic Obstacle Problems in Mathematical Finance, preprint, 2011; J. Differential Equations, 260 (2016), pp. 5043--5074] and Feehan and Pop [ Trans. Amer. Math. Soc., 367 (2015), pp. 981--1031; Adv. Differential Equations, 20 (2015), pp. 361--432]. 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 semigroup techniques and on the affine property of the model.
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