OIS (overnight indexed swap) discounting is the market-standard approach for defining the base value of derivatives from which xVA adjustments are computed. Under perfect collateralisation — where continuous, zero-threshold variation margin is exchanged in cash denominated in the transaction currency — the economically correct discount rate is the collateral remuneration rate, which in practice is the OIS rate (e.g. Fed Funds, EONIA/ESTER, SONIA). This is because the discount rate arises from the margin remuneration rate and not from any independent assessment of the “risk-free rate”, though OIS rates happen to be good proxies for risk-free rates.
The fundamental pricing equation of the xVA framework is: Actual Value = Base Value + xVA (Eq. 16.5 in Gregory). The base value uses OIS/collateral discounting as the starting point for all transactions, even uncollateralised ones, for several practical reasons: OIS rates approximate risk-free rates; this approach is operationally simple (requiring only knowledge of the margin agreement, not counterparty identity or funding costs); it creates a clean separation where originating trading desks value at the base price and the xVA desk handles all adjustments; and it is backwards-compatible with historical approaches.
When the collateral remuneration rate differs from the standard OIS rate in the transaction currency — for example, due to cross-currency collateral posting or cheapest-to-deliver optionality — this deviation is captured by ColVA. The push toward perfect collateralisation (through clearing mandates, bilateral margin rules, and CSA renegotiations) means that for an increasing proportion of the market, the base OIS-discounted value is close to the actual perfectly-collateralised value, and ColVA is small or zero.
Key Details
- Perfect collateralisation requires: continuous margin exchange, zero threshold, zero minimum transfer amount, cash in the transaction currency, and remuneration at the OIS rate.
- OIS discounting replaced LIBOR discounting as the market standard after the GFC, driven by the recognition that LIBOR contains a bank credit risk premium.
- For uncollateralised transactions, OIS discounting is still used as the starting point; the deviation from the “correct” price is then captured by xVA terms (especially FVA).
- Regulatory capital for market risk treats base value and xVA adjustments separately, so the choice of base valuation methodology has capital implications.
- Some desks historically continued using LIBOR discounting for uncollateralised trades even after the general move to OIS; Gregory notes this is “often sub-optimal for the management of xVA.”
Textbook References
The xVA Challenge (Gregory, 2020)
- Section 16.3.1 (pp. 480—482): The starting point for xVA is Actual Value = Base Value + xVA (Eq. 16.5). Collateral discounting uses the margin remuneration rate, not the “risk-free rate” per se. However, OIS discounting is appropriate for all transactions (collateralised or not) because: margin remuneration rates are good risk-free proxies; it is operationally simple; it cleanly separates the xVA desk’s role from the trading desk’s; and it is backwards compatible.
- Section 16.2.5 (pp. 479—480): Market trends toward perfect collateralisation and OIS discounting: CSA renegotiation, bilateral margin rules (zero thresholds, restricted collateral), and the clearing mandate (variation margin in the transaction currency). These trends reduce ColVA.
- Section 5.2.1 (p. 86): The base value is a “relatively simple calculation” conforming to a perfectly-collateralised or risk-free starting point. The xVA components are then the complicated corrections requiring knowledge of contractual terms and the economic impact of credit, funding, collateral, and capital.
- Section 16.3.2 (pp. 482—483): Starting from perfect collateralisation, xVA adjustments reflect deviations: ColVA for margin-type deviations, CVA/DVA for default risk, FVA for funding effects of under-collateralisation, KVA for capital costs, MVA for IM costs.