Properties of the American price function in the Heston-type models

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

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 MATHRISK - Mathematical Risk Handling
3 Università degli Studi di Roma Tor Vergata [Roma] = University of Rome Tor Vergata

We study some properties of the American option price in the stochastic volatility Heston model. We first prove that, if the payoff function is convex and satisfies some regularity assumptions, then the option value function is increasing with respect to the volatility variable. Then, we focus on the standard put option and we extend to the Heston model some well known results in the Black and Scholes world, most by using probabilistic techniques. In particular, we study the exercise boundary, we prove the strict convexity of the value function in the continuation region, we extend to this model the early exercise premium formula and we prove a weak form of the smooth fit property.

Mots clés: American options; Optimal stopping problem; Stochastic volatility

Domaines: Mathématiques [math]; Probabilités [math.PR]; Économie et finance quantitative [q-fin]; Finance quantitative [q-fin.CP]; Pricing [q-fin.PR]

Damien Lamberton, Giulia Terenzi. Properties of the American price function in the Heston-type models. 2019. ⟨hal-02088487⟩