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Abergel, F. and Tachet, R. (2010) A Nonlinear Partial Integrodifferential Equation from Mathematical Finance. Discrete and Continuous Dynamical Systems, 27, 907-917.
https://doi.org/10.3934/dcds.2010.27.907

has been cited by the following article:

• 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.