  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, including a
counterparty portfolio of interest rate swaps.
