CVA-VaR

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