Gaussian process regression for derivative portfolio modeling and application to credit valuation adjustment computations

Stéphane Crépey and Matthew F. Dixon

Abstract

Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all trades between each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for the over-the-counter derivative portfolio valuation involved in credit valuation adjustment (CVA) computation. Our approach avoids nested simulation or simulation and regression of cashflows 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, imposing the spatial covariancestructure 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, including a counterparty portfolio of interest rate swaps.