Accelerating CVA and CVA Sensitivities Using Quasi-Monte Carlo Methods

Abstract

We analyze the efficiency of the quasi Monte Carlo method (QMC) when used to compute credit valuation adjustment (CVA) and CVA sensitivities for various portfolios of interest rate swaps using a multi-currency extension to the Hull-White model. We find that QMC with Sobol’ sequences and the Brownian bridge discretization produces results as accurate as classical MC with 10,000 simulations when using roughly 800 simulations: a factor of 12 acceleration. The acceleration varies significantly across portfolios (increasing with moneyness and usually, but not always, decreasing with number of factors), calculation types (order from highest to lowest, usually, but not always, CVA, CR Deltas, IR and FX Deltas, and IR and FX Vegas), and the choice of model (local models usually outperform global models). QMC without the Brownian bridge discretization results in a more modest factor of 4 acceleration. Classical MC with antithetic sampling results in a factor of 2 acceleration. Randomized QMC (linear permutation of digits) with the Brownian bridge discretization improved the efficiency over the non-randomized sequences for smaller in-the-money portfolios. Randomization in combination with a direct and independent simulation approach of the risk factors produced extraordinary results in the limited tests we performed (CVA on a single currency swap), offering an additional factor of 6 acceleration over the pathwise simulation.

Keywords: XVA, CVA, Greeks, Monte Carlo, Quasi Monte Carlo, Sobol' Sequences, Hull-White

JEL Classification: C63