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

Abstract

Central counterparties (CCPs) require initial margin (IM) to be postedfor derivative portfolios cleared through them. Additionally, the BaselCommittee on Banking Supervision has proposed (BCBS-261 2013) thatall significant OTC derivatives trading must also post IM by 2019. IMis typically calculated using Value-at-Risk (VAR) or Conditional Value-at-Risk (CVAR, aka Expected Shortfall), based on historical simulation.As previously noted (Green 2013b), (Green 2013a) IM requirements giverise to a need for unsecured funding similar to FVA on unsecured deriva-tives. The IM cost to the derivatives originator requires an integral of thefunding cost over the funding profile which depends on VAR- or CVAR-based calculation. VAR, here, involves running a historical simulationMonte Carlo inside a risk-neutral Monte Carlo simulation. Brute forcecalculation is computationally unfeasible. This paper presents a compu-tationally effcient method of calculating IM costs for any derivative port-folio: Longstaff-Schwartz Augmented Compression (LSAC). Essentially,Longstaff-Schwartz is used with an augmented state space to retain accu-racy for VAR-relevant changes to the state variables. This method allowsrapid calculation of IM costs both for portfolios, and on an incrementalbasis. LSAC can be applied wherever historic simulation VAR is requiredsuch as lifetime cost of market risk regulatory capital using internal mod-els. We present example costs for IM under (BCBS-261 2013) for interestrate swap portfolios of up to 10000 swaps and 30 year maturity showingsignificant IM FVA costs and two orders of magnitude speedup comparedto direct calculation.