CVA-VaR

19 Pages Posted: 6 Jun 2011 Last revised: 14 Feb 2012

See all articles by Shahram Alavian

Shahram Alavian

Royal Bank of Scotland (RBS); Barclays Capital; Toronto-Dominion (TD) Bank Financial Group - TD Securities; Lehman Brothers Europe

Etienne Koehler

Université Paris I Panthéon-Sorbonne

Date Written: December 13, 2011

Abstract

Usage of Monte Carlo simulation for pricing requires a well defined and accurate market implied distribution of risk factors. Overlay, on top of these simulated risk factors, one can also generate conditional prices based on the set of underlying risk factors at future time horizons. The ability to generate these forward conditional prices is not limited to options with early exercise feature. It is a general scheme that can be extended to any other other asset-equivalent values such as expected exposures and CVAs. These distributions, provide a wealth of information on the dynamics of the price changes as a function of the changes in the underlying risk factors. By obtaining the forward distributions of expected exposures and CVAs at a time horizon of less than one-day in to the future, this paper proposes a scheme that can be used for calculating the VaR on CVA. It can provide the dependency to any order of non-linear terms, in one single CVA calculation. The method is applied to cases where both exposures and hazard rates are simultaneously simulated (Method-I) and in cases where the exposure is simulated in isolation from the credit states (Method-II). In both cases, the variations that are needed for the final calculations of VaR are modeled using linear regression against the changes in the driving risk factors, therefore, requiring only one simulation run. For a numerical example, an uncollateralized portfolio of a long European power put option, to address the non-linear effects, is considered. For the case of zero correlation between the exposure and the credit, VaR of the portfolio is calculated using Method-I and Method-II for various strike levels. Results of both approaches are then compared to the actual re-valuating the CVA for each of the historical elements in the time series. For the cases where the exposure is correlated with the credit, Method-I is used to provide the VaR of the CVA at the presence of wrong way risk.

Keywords: CVA, VaR, Basel III, Regulatory Capital

JEL Classification: C12, C13, C15, C18

Suggested Citation

Alavian, Shahram and Koehler, Etienne, CVA-VaR (December 13, 2011). Available at SSRN: https://ssrn.com/abstract=1858633 or http://dx.doi.org/10.2139/ssrn.1858633

Shahram Alavian (Contact Author)

Royal Bank of Scotland (RBS) ( email )

135, Bishopsgate
EC2M 3UR London
United Kingdom

HOME PAGE: http://www.shahramalavian.net

Barclays Capital ( email )

5 Colonade
London E14 5LE
United Kingdom
022031346761 (Phone)

Toronto-Dominion (TD) Bank Financial Group - TD Securities ( email )

6th Floor
TD Tower, 66 Willington Street West
Toronto, Ontario M5K 1A2
Canada

Lehman Brothers Europe ( email )

London
United Kingdom

Etienne Koehler

Université Paris I Panthéon-Sorbonne ( email )

17, rue de la Sorbonne
Paris, IL 75005
France

Register to save articles to
your library

Register

Paper statistics

Downloads
328
Abstract Views
2,249
rank
91,644
PlumX Metrics