MVA: Margin Valuation Adjustment#

Margin Valuation Adjustment, or MVA, is the cost of funding the initial margin that a firm has to post over the life of a derivative. Initial margin is collateral posted upfront, in addition to the variation margin that follows the daily mark-to-market. It is there to cover the potential loss on the position during the time it would take to close out a defaulting counterparty.

MVA is closely related to FVA, but it is a separate adjustment because initial margin behaves differently from variation margin:

  • it is posted by both sides, and it is held by a third party or segregated, so the receiver cannot reuse it

  • it is sized on a potential future move, not on the current mark, so it is posted even when the trade is at zero value

  • the firm funds the margin it posts at its own funding rate, but earns only a low rate on it, so there is a net cost of carry

Why MVA matters#

Before the margin rules, much bilateral business was uncollateralised or only exchanged variation margin, so the main funding cost was captured by FVA. Two changes made initial margin a material cost:

  • Central clearing: cleared trades require initial margin to be posted to the central counterparty (CCP), and the amount is set by the CCP’s own model.

  • Uncleared margin rules (UMR): for large bilateral counterparties, regulators now require initial margin to be exchanged on uncleared derivatives, usually calculated with the ISDA Standard Initial Margin Model (SIMM).

For a long-dated portfolio, the initial margin has to be funded for many years, so the cost accumulates and can be a significant part of the XVA of a trade.

How it is calculated#

MVA depends on the future initial margin, so it needs the same Monte Carlo framework as the other adjustments, with an extra step:

  1. Simulate the risk factors over the life of the portfolio, as for CVA.

  2. At each future date on each path, calculate the initial margin that would be required, using the CCP model or SIMM.

  3. Take the expected initial margin profile over time.

  4. Multiply by the funding spread and discount.

A simplified form is:

\[\text{MVA} \approx \sum_t \text{E}[\text{IM}_t] \times s_{f,t} \times \Delta t \times \text{DF}_t\]

where \(\text{E}[\text{IM}_t]\) is the expected initial margin at time \(t\) and \(s_{f,t}\) is the spread between the firm’s funding rate and the rate earned on the margin.

The difficulty is the cost of the calculation. The margin models are themselves sensitivity based, so a full calculation would need sensitivities inside the simulation, a nested calculation. Banks use approximations, such as regressing the margin on the simulated state, or scaling the current margin by the exposure profile.

Hedging and management#

MVA is a cost that is charged to the trade, in the same way as the other adjustments. It is partly managed by:

  • choosing between clearing and bilateral trading, depending on which gives the lower margin

  • compressing the portfolio, which removes offsetting trades and reduces the margin

  • optimising the allocation of trades between netting sets and CCPs, where the margin is set per portfolio

MVA and FVA overlap in principle, as both are funding costs. A valuation framework should state clearly which funding cost is in which adjustment, so that none is counted twice. This is covered further in FVA: Funding Valuation Adjustment.

A valuation control view#

MVA adds some specific points to the valuation control checks:

  • Margin models: the accuracy of the SIMM or CCP model replication, and the stability of the result when the inputs move.

  • Approximation methods: the regression or scaling used to estimate future margin must be validated against a full calculation on a sample of portfolios.

  • Completeness: the margin terms, such as the thresholds and whether a counterparty is in scope of the rules, must be correct in the trade and agreement data.

  • Funding spread: the spread used is a judgement and should be consistent with the one used for FVA.