TITLE:
Nonparametric Model Calibration for Derivatives
AUTHORS:
Frédéric Abergel, Rémy Tachet des Combes, Riadh Zaatour
KEYWORDS:
Local Stochastic Volatility, Calibration, Derivative Pricing, Partial Integro-Differential Equations
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.7 No.3,
July
13,
2017
ABSTRACT: Consistently fitting vanilla option surface 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.