Accelerating CVA and CVA Sensitivities Using Quasi-Monte Carlo Methods

Abstract

We compare the efficiency of quasi-Monte Carlo (QMC) methods to classical Monte Carlo (MC) method and MC with antithetic sampling in computing credit valuation adjustment (CVA) and CVA sensitivities for various portfolios of interest rate swaps using a multi-currency extension to the Hull-White model. For uncollateralized portfolios using local models, we find that QMC with Sobol' sequences and the Brownian bridge discretization can produce results as accurate as classical MC with 10,000 simulations when using on average roughly only 800 simulations, a speed-up by a factor of 12. However, we also find that the acceleration varies significantly across portfolios increasing with moneyness and usually, but not always, decreasing with the number of factors), calculation types (order from highest to lowest, usually, but not always, CVA and CR Deltas, IR and FX Deltas, and IR and FX Vegas), and the choice of model (local models usually outperform global models). While the Brownian bridge discretization is less effective on the collateralized portfolios, the so-called Brownian bridge portfolio interpolation technique significantly improves the results. Randomization of Sobol' sequences, a technique shown to increase the convergence rate of QMC on a particular class of integrands, is found to be most effective on test cases with small numbers of dimensions.

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

JEL Classification: C