Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations (Part II)

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 MC simulation or simulation and regression of cash flows by learning a metamodel for the mark-to-market cube of a derivative portfolio. We model the joint posterior of the derivatives as a Gaussian over function space, with the spatial covariance structure imposed only on the risk factors. Monte-Carlo simulation is then used to simulate the dynamics of the risk factors. This approach quantifies the uncertainty in portfolio valuation from the Gaussian process approximation. Numerical experiments demonstrate the accuracy and convergence properties of our strategy for CVA computations. This is joint work with Stephane Crepey (Paris Saclay).

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning