CVA and FVA Modeling and Implementation

Abstract

CVA/FVA modeling is complex, mainly because: The potential credit/funding exposures are generally non-linear. For a linear fixed-for-floating interest rate swap, one may value the swap based on discounting of cash flows; however, the CVA/FVA exposures would depend on the distribution of the interest rate, and it is really a swaption. CVA/FVA must be calculated on a net basis. If you have done a thousand trades across different asset classes with one counterparty, you have to net all the future exposures while calculating the default loss or funding cost/benefit. This means you would need to have a consistent simulation framework for all the risk factors involved across different asset classes. CVA/FVA calculations have to deal with complex CSAs, such as ratings-based threshold, and automatic/discretionary triggers/terminations, among other things. This means the rating migrations must be incorporated in the CVA/FVA calculations. There may exist significant correlations between credit and market risk factors, which need to be accounted for in CVA/FVA calculations. This means the market risk factors and credit risk factors have to be consistently simulated. For FVA, funding and collaterals are involved, which means multi-currency/asset collateral curves and collateral choice options must be dealt with, as well as the firm’s own funding curves. When asymmetric funding curve is used, one may have to deal with funding set and netting set issues. There are other legal issues surrounding the enforceability of CSAs in different jurisdictions and authorities, which could introduce extra dimension of issues in calculating CVA properly.