The Missing Term in the FVA Calculation

Abstract

In the aftermath of the Global Financial Crisis, many large banks moved to include Funding Value Adjustment (FVA) in their derivative valuations, despite controversy in the industry over its appropriateness. This paper examines the mathematical derivations of FVA-inclusive valuation formulas in an influential paper advocating FVA inclusion and identifies an implicit assumption that is unrealistic yet crucial, and hence creates problems for the derivation. We examine what happens when the assumption is abandoned and find that it can still be theoretically sound to include FVA in valuations, and to use formulas derived in the paper, subject to some modifications in either the discount rates used, or in what other valuation adjustments are included. Different types of FVA calculation are appropriate when the valuation is from a shareholder-only perspective from when it is from a whole-of-bank perspective (ie including the interests of debtholders). It is also observed that a bank that uses what are here termed 'full-FVA-inclusive valuations', may find that, in cases where the FVA is an asset, prudential supervisors require them to deduct that asset from measures of prudential capital such as CET1.