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margin value adjustment

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Margin value adjustment (MVA) is the present value of the lifetime cost of funding initial margin (IM) posted against a derivatives portfolio. Unlike FVA, which captures the cost of funding uncollateralised positions and variation margin asymmetries, MVA specifically addresses the opportunity cost of segregated IM that earns at most a sub-overnight rate while the posting bank’s cost of funds is higher. MVA is driven by two regulatory developments: the clearing mandate (requiring standardised OTC derivatives to be centrally cleared via CCPs with upfront IM) and bilateral margin rules (requiring two-way IM posting under ISDA SIMM for non-cleared trades from September 2016).

The MVA formula, following Kenyon and Green (2015), is:

MVA = - integral from 0 to infinity of E[IM(u)] x FS(u) du, approximately equal to - sum of EIM(t_i) x FS(t_{i-1}, t_i) x (t_i - t_{i-1})

where EIM(t) is the discounted expected initial margin profile at time t and FS(u) is the funding spread reflecting the type of margin posted (cash, government bonds) and any related remuneration or repo rate. The main computational challenge lies in calculating the EIM term, which requires simulating future IM requirements using the specific methodology (CCP proprietary models or ISDA SIMM), accounting for portfolio ageing, and capturing the dynamic recalibration of IM models over time. This is a “simulation within a simulation” problem: at each future time step in the outer Monte Carlo, the IM model must be evaluated, which may itself require an inner simulation or sensitivity computation.

Initial margin represents over-collateralisation: it is additional collateral posted on top of variation margin to provide a buffer against potential losses during the close-out period following a counterparty default. Unlike variation margin, initial margin does not offset the current mark-to-market but rather covers potential future adverse moves, so it constitutes a pure funding cost for the posting party. Default fund contributions (for clearing members) can also be captured under the MVA definition.

MVA is purely a cost (asymmetric), unlike FVA which has both cost and benefit components. This asymmetry arises because regulatory IM received must typically be segregated and cannot be rehypothecated, providing no funding benefit to the receiver. Both MVA and FVA are fundamentally funding costs, but they reflect opposite sides of the collateralisation spectrum: FVA is the cost of being under-collateralised, while MVA is the cost of being over-collateralised. From an xVA perspective, posting IM reduces CVA and KVA (by reducing counterparty risk and capital requirements) but creates MVA, illustrating the “conservation of xVA” principle where value is pushed between components rather than eliminated.

MVA interacts importantly with KVA: in a bilateral margin regime, posting IM increases MVA but received IM may reduce KVA by providing capital relief. The joint optimisation of MVA and KVA is essential — for example, posting a small discretionary bilateral IM can be optimal when the KVA reduction exceeds the MVA increase, though posting the full regulatory amount is typically not optimal. The MVA-KVA trade-off also gives rise to the CCP basis, a price differential across clearing venues driven by dealer-specific incremental IM costs.

Key Details

  • MVA is a cost only (no symmetric benefit), distinguishing it from FVA
  • IM is funded at a spread over the sub-overnight remuneration rate; eligible securities (government bonds) at the repo rate are usually more efficient than cash for IM posting
  • The EIM calculation is computationally demanding: it requires future simulation of IM under the relevant methodology (CCP models or SIMM), capturing portfolio ageing, model recalibration, and potential future trades
  • Contingent MVA arises from the LCR requirement to hold HQLAs against potential additional IM upon a three-notch rating downgrade (Section 4.3.3); CCP IM may have larger contingent components than SIMM due to its dynamic recalibration
  • The CCP basis is the price differential for the same trade cleared at different venues, driven by dealer-specific incremental MVA costs at each CCP
  • Default fund contributions to CCPs can logically be included alongside IM in the MVA calculation
  • As of 2020, approximately 50% of banks were charging MVA and just under 20% were accounting for it (IACPM 2018 survey)
  • MVA accounting follows the same logic as FVA: if funding costs are reported via FVA, then IM costs should also be reported via MVA, though adoption has been slower due to the difficulty of charging MVA to clients
  • For centrally-cleared transactions, MVA is typically the dominant xVA cost, as CVA and FVA are negligible
  • IM can be posted in various assets (cash, government bonds, etc.), creating optionality similar to ColVA that may be incorporated in the determination of funding costs rather than adjusted directly
  • MVA has not yet become an explicit component of accounting fair value, though some banks include it implicitly within FVA

Textbook References

The xVA Challenge (Gregory, 2020)

  • Section 3.2.1 (p. 54): Initial margin represents over-collateralisation and a funding cost; it is required by central clearing and bilateral margin rules.
  • Section 3.2.3 (p. 57): MVA defines the cost of posting initial margin over the lifetime of the transaction.
  • Section 5.2.5 (pp. 90—91): For centrally-cleared and overcollateralised bilateral trades, MVA is the dominant xVA cost (Table 5.2). The clearing mandate and bilateral margin rules create MVA but reduce CVA and KVA.
  • Section 16.3.2 (pp. 482—483): MVA defines the cost of posting initial margin; default fund contributions can also be captured under this definition. Both FVA and MVA are funding costs, but “the former is the cost of being undercollateralised, whereas the latter is the cost of being overcollateralised.”
  • Section 20.1 (pp. 591—593): Overview of MVA drivers: the clearing mandate imposes CCP IM; bilateral margin rules (from September 2016) require two-way IM under SIMM. Discretionary IM (independent amount) differs from regulatory IM in being one-way, non-segregated, and often linked to rating triggers (Table 20.1). Table 20.2 summarises the impact of segregated vs. non-segregated IM on CVA, KVA, and MVA.
  • Section 20.2.2 (pp. 594—595): The MVA formula (Equation 20.1): MVA = - integral of E[IM(u)] x FS(u) du. Table 20.3 contrasts FVA and MVA: FVA funds assets and cash flows (potentially symmetric), MVA funds IM posting (asymmetric, cost only).
  • Section 20.2.3 (pp. 595—596): The main computational challenge is calculating EIM. CCP IM methodologies are dynamic and can change significantly during stress (e.g., the switch from relative to absolute returns). SIMM is more static but still recalibrated annually.
  • Section 20.3.1 (pp. 602—603): MVA pricing considerations. Banks often lack industrial capability for rigorous MVA calculation and may only consider it material for large client trades. Whether MVA will become as rigorously treated as CVA remains uncertain.
  • Section 20.3.2 (pp. 603—604): MVA accounting parallels the FVA debate. Andersen et al. (2016) show that total firm value is invariant to IM payments (wealth transfer from shareholders to derivatives creditors), but shareholders still need compensation via MVA.
  • Section 20.3.3 (pp. 603—604): Contingent MVA arises from the LCR requirement to hold HQLAs against potential IM increases upon rating downgrade. CCP contingent IM may be more expensive than SIMM contingent IM due to dynamic recalibration.
  • Section 20.3.4 (pp. 604—606): The CCP basis: a dealer quoting different prices for the same trade cleared at different CCPs, driven by incremental MVA costs. Persistent across all dealers when clients systematically prefer a different CCP than dealers.
  • Section 20.4 (pp. 606—608): MVA-KVA interaction. Table 20.6: bilateral IM creates MVA cost but potential KVA benefit; central clearing creates MVA cost but lower KVA from favourable capital charges. Figures 20.10 and 20.11 show that optimal bilateral IM is below the regulatory requirement under SA-CCR, with the optimal point depending on the bank’s cost of capital vs. cost of funding.

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