Variational formulation of American option prices in the Heston Model

Damien Lamberton (1, 2) , Giulia Terenzi (1, 3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 MATHRISK - Mathematical Risk handling
3 Dipartimento di Matematica [Rome]

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.

Mots clés: degenerate parabolic obstacle problem; optimal stopping problem; American options

Domaines: Probabilités [math.PR]

Damien Lamberton, Giulia Terenzi. Variational formulation of American option prices in the Heston Model. 2017. ⟨hal-01649496v1⟩