Alethograph

funding value adjustment

5 min read

Funding value adjustment (FVA) is the valuation adjustment that captures the cost and benefit arising from the funding of uncollateralised (or partially uncollateralised) derivative positions. It is often decomposed into a funding cost adjustment (FCA), reflecting the cost of funding a positive exposure (asset) at a spread above the risk-free rate, and a funding benefit adjustment (FBA), reflecting the benefit of receiving funding from a negative exposure (liability) at that same spread.

FVA arises because institutions must borrow to finance their activities, and this borrowing cost includes a credit spread reflecting the institution’s own creditworthiness. For uncollateralised derivatives, a positive mark-to-market value represents an asset that must be funded but generates no offsetting collateral inflow. The FVA captures this lifetime funding cost (or benefit). Collateralised transactions, where variation margin offsets the mark-to-market, have negligible FVA because the margin effectively provides the required funding.

FVA has become a relatively standard component of financial reporting since around 2012, with major banks (e.g. Barclays, JP Morgan) explicitly including it in their accounts. However, FVA creates theoretical tensions: it is entity-specific (different banks have different funding costs), it violates the law of one price, and accounting standards state that fair value should be “a market-based measurement, not an entity-specific measurement”. The overlap between FBA and DVA remains a significant conceptual issue, as both reflect aspects of the institution’s own credit risk.

Key Details

  • FVA pricing implicitly assumes the bank will issue unsecured debt as a result of each transaction, even though in practice the funding position changes only discretely.
  • FVA is the cost of being under-collateralised, while MVA is the cost of being over-collateralised; both are fundamentally funding costs.
  • FVA may include contingent liquidity provisions (e.g. buffers of high-quality liquid assets against contractual clauses).
  • The general xVA formula applies: FVA = integral of funding_spread(t) * D(t) * E[exposure(t)] dt.

Textbook References

The xVA Challenge (Gregory, 2020)

  • Section 3.2.1 (pp. 54—55): Funding costs are directly related to counterparty risk: greater balance-sheet risk means higher cost of funding. FVA is introduced alongside other “beyond counterparty risk” costs.
  • Section 3.2.3 (pp. 56—57): FVA is defined as the cost and benefit arising from the funding of the transaction, divided into FCA and FBA.
  • Section 5.2.4 (pp. 89—90): Table 5.1 traces the evolution from “funding costs accrued on a daily basis” (traditional) to “FVA inception pricing, valuation, and management” (market-standard xVA approach).
  • Section 5.3.4 (pp. 98—99): FVA has become fairly standard in accounting despite not being explicitly mandated; banks justify it as a component of the exit price. Both IFRS 13 and FASB 157 state fair value is “a market-based measurement, not an entity-specific measurement”, creating tension with entity-specific funding costs.
  • Section 16.3.2 (pp. 482—483): FVA defines the cost and benefit arising from being uncollateralised or partially uncollateralised. Both FVA and MVA are funding costs, but FVA reflects under-collateralisation and MVA reflects over-collateralisation.
  • Section 18.1 (pp. 529—530): FVA overview. Assets create funding costs (EPE), liabilities create benefits (ENE). FVA was negligible pre-GFC when bank funding was near risk-free. FVA does not include MVA (initial margin funding) or KVA (equity funding).
  • Section 18.2.2 (pp. 531—534): Source of funding costs. The most accurate definition is “total value minus total reusable margin” (Eq. 18.1). Four options in order of sophistication: uncollateralised value, total margin posted, collateralised value, total value minus total margin.
  • Section 18.2.4 (pp. 535—537): Symmetric FVA formula. FVA = -sum EFV(t_i) x FS(t_{i-1},t_i) x dt (Eq. 18.2—18.3). Decomposition: FCA = -sum EPE x FS x dt, FBA = -sum ENE x FS x dt (Eq. 18.4a—c). Symmetric FVA is additive across trades and equivalent to discounting at the funding rate. Survival probabilities may or may not be included (market practice is divided, Figure 18.3).
  • Section 18.2.5 (pp. 539—544): The Burgard-Kjaer framework. FCA = -integral FS D_{r+lambda_P+lambda_C} EPE du (Eq. 18.5). DVA = FBA under FS = LGD_P x lambda_P. Two consistent frameworks: (i) CVA + FCA + FBA (symmetric, shareholder value), (ii) CVA + DVA + FCA (bilateral, total firm value). Table 18.2—18.3: one-way margin agreements produce only CVA + FCA (no FBA); non-reusable margin mitigates CVA but not FCA.
  • Section 18.2.6 (pp. 546—548): The FVA debate. Hull and White (2012a): FVA violates risk-neutral pricing and Modigliani-Miller; “DVA2” (benefit from defaulting on general funding liabilities) cancels FCA. Counterarguments: no “market” for uncollateralised derivatives (Kenyon and Green 2014); CVA + FVA maximises shareholder value (Andersen et al. 2016). The remaining undisputed FVA component is the liquidity premium (bond-CDS basis).
  • Section 18.2.7 (pp. 548—551): FVA accounting. Banks use “blended market cost of funds” for accounting vs own cost for pricing. J.P. Morgan’s 25m/bp sensitivity, largely offsetting DVA sensitivity of ~$23m/bp. “Incremental FBA” (= FBA - DVA) is used by some banks to avoid double-counting.
  • Section 18.3 (pp. 551—563): Asymmetric FVA. Four regimes: no FVA (borrow/lend at OIS), symmetric (same unsecured rate), asymmetric (borrow unsecured/lend risk-free), partially asymmetric (borrow unsecured/lend short-term unsecured). Asymmetric FCA is computed at funding-set level (Eq. 18.8). NSFR invariance pricing approximately doubles the cost vs asymmetric FVA. Contingent FVA from LCR rating triggers (Eq. 18.11—18.14). Wrong-way funding risk from correlation between funding spreads and market variables.

concept

Graph View

Backlinks