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Beam, R. and Warming, R. (1980) Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative. SIAM Journal on Scientific and Statistical Computing, 1, 131-159.
https://doi.org/10.1137/0901007

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.