Application of Stochastic Mesh Method to Efficient Approximation of CVA

TL;DR

This paper explores two stochastic mesh methods to efficiently approximate Credit Valuation Adjustment (CVA) for large financial systems using Monte Carlo simulations, focusing on convergence rates.

Contribution

It introduces two novel stochastic mesh techniques for CVA computation and analyzes their convergence properties, enhancing computational efficiency.

Findings

First method accurately estimates future derivative values.

Second method efficiently determines the positivity of future values.

Both methods show promising convergence rates.

Abstract

In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, stochastic mesh method is used only to judge whether future value of the derivative contracts is positive or not. He discusses the rate of convergence to the real CVA value of these methods.