NONPARAMETRIC MODEL CALIBRATION FOR DERIVATIVES

Frédéric Abergel (1, 2) , Rémi Tachet (3, 2) , Riadh Zaatour (1, 2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 FiQuant - Chaire de finance quantitative
3 Senseable City Laboratory

Consistently fitting vanilla option surfaces is an important issue in derivative modelling. In this paper, we consider three different models: local and stochastic volatility, local correlation, hybrid local volatility with stochastic rates, and address their exact, nonparametric calibration. This calibration process requires solving a nonlinear partial integro-differential equation. A modified alternating direction implicit algorithm is used, and its theoretical and numerical analysis is performed.

Domaines: Finance quantitative [q-fin.CP]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Frédéric Abergel, Rémi Tachet, Riadh Zaatour. NONPARAMETRIC MODEL CALIBRATION FOR DERIVATIVES. 2016. ⟨hal-01399542v1⟩