Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit simulation. In particular, CVA estimation requires pricing each counterparty portfolio as an option on the portfolio under simulated market and credit spread moves. Moreover, Greeks are required for hedging CVA and 10 day CVA VaR is required under Basel III, necessitating layers of nested MC simulations.
Following Spiegeleer et al.'s approach to Gaussian Process Regression for derivative pricing, this talk develops a kernel learning approach for estimating CVA, including CVA greeks and VaR. Numerical experiments demonstrate the accuracy of this approach and viability for real-time CVA estimation.