Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations

31 Pages Posted: 11 Feb 2019

See all articles by Stéphane Crépey

Stéphane Crépey

Université d'Évry - Equipe d'Analyse et Probabilites

Matthew Francis Dixon

Illinois Institute of Technology

Date Written: January 30, 2019

Abstract

Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA computation. Our approach avoids nested simulation or simulation and regression of cash flows by learning a Gaussian metamodel for the mark-to-market cube of a derivative portfolio. We model the joint posterior of the derivatives as a Gaussian process over function space, with the spatial covariance structure imposed on the risk factors. Monte-Carlo simulation is then used to simulate the dynamics of the risk factors. The uncertainty in portfolio valuation arising from the Gaussian process approximation is quantified numerically. Numerical experiments demonstrate the accuracy and convergence properties of our approach for CVA computations.

Keywords: Gaussian Processes, Kriging, OTC Derivatives, CVA

JEL Classification: C14, C63, C45, G32

Suggested Citation

Crépey, Stéphane and Dixon, Matthew Francis, Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations (January 30, 2019). Available at SSRN: https://ssrn.com/abstract=3325991 or http://dx.doi.org/10.2139/ssrn.3325991

Stéphane Crépey

Université d'Évry - Equipe d'Analyse et Probabilites ( email )

Boulevard des Coquibus
F-91025 Evry Cedex
France

Matthew Francis Dixon (Contact Author)

Illinois Institute of Technology ( email )

Department of Math
W 32nd St., E1 room 208, 10 S Wabash Ave, Chicago,
Chicago, IL 60616
United States

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