Calculating the Funding Valuation Adjustment (FVA) of Value-at-Risk (VAR) Based Initial Margin

Abstract

Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg, 2010, 2012a), under counterparty risk with unsecured funding costs (FVA) (Burgard and Kjaer, 2011a, 2011b, 2013) and in the presence of regulatory capital (KVA) (Green, Kenyon and Dennis, 2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of Burgard and Kjaer (2013), itself later extended by Green, Kenyon and Dennis (2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose a computationally efficient approach to the calculation of MVA through the use of regression techniques, Longstaff-Schwartz Augmented Compression (LSAC).