Least Squares Monte Carlo Credit Value Adjustment with Small and Unidirectional Bias

14 Pages Posted: 18 Jan 2016 Last revised: 8 Apr 2016

See all articles by Mark S. Joshi

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Oh Kang Kwon

The University of Sydney - Discipline of Finance

Date Written: January 12, 2016

Abstract

Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued analytically at each simulation step, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their values. However, these functions do not necessarily provide accurate approximations to product values over all simulated paths and can result in biases that are difficult to control. Motivated by a novel characterization of the CVA as the value of an option with an early exercise opportunity at a stochastic time, we provide an approximation for CVA and other credit charges that rely only on the sign of the regression functions. The values are determined, instead, by pathwise deflated cash flows. A comparison of CVA for Bermudan swaptions and cancellable swaps show that the proposed approximation results in much smaller errors than the standard approach of using the regression function values.

Keywords: Credit value adjustment, least squares regression, Monte Carlo simulation

JEL Classification: C15, C63, G13

Suggested Citation

Joshi, Mark and Kwon, Oh Kang, Least Squares Monte Carlo Credit Value Adjustment with Small and Unidirectional Bias (January 12, 2016). Available at SSRN: https://ssrn.com/abstract=2717250 or http://dx.doi.org/10.2139/ssrn.2717250

Mark Joshi

University of Melbourne - Centre for Actuarial Studies (deceased) ( email )

Melbourne, 3010
Australia

Oh Kang Kwon (Contact Author)

The University of Sydney - Discipline of Finance ( email )

Discipline of Finance
Codrington Building H69
The University of Sydney, NSW 2006
Australia

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