Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization

Vincent Lemaire (1) , Thibaut Montes (1) , Gilles Pagès (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show, based on calibrated parameters, that this model produce a steeper smile for short maturities than the Standard Heston model. We also present numerical solution based on Product Recursive Quantization for the evaluation of exotic options (Bermudan and Barrier options).

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

Vincent Lemaire, Thibaut Montes, Gilles Pagès. Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization. Quantitative Finance, 2022, 22 (4), pp.611-629. ⟨10.1080/14697688.2021.2023205⟩. ⟨hal-02434232v2⟩