OIS Discounting and Credit Risk in Collateralized Swaps
Summary
The document outlines post-crisis swap valuation using overnight indexed swap rates for discounting, followed by adjustments for counterparty credit, funding, and other costs. It contrasts this approach with older conventions that used government yields or LIBOR-based swap rates as risk-free proxies, noting that unsecured bank borrowing rates embed credit risk.
Collateral does not always eliminate counterparty exposure. Variation margin may lag market value during the margin period of risk, and thresholds or transfer minimums can leave residual exposure. The discussion says that initial and variation margin together can largely remove counterparty credit risk, while creating initial-margin funding costs captured by an MVA. Practices may differ for some non-bank institutions operating under distinct capital frameworks. The document gives a conceptual overview rather than a detailed valuation model, and its claims depend on the collateral agreement and applicable framework.
Key ideas
- OIS discounting is commonly used as the baseline for post-crisis swap valuation.
- Counterparty credit and funding costs can be applied as valuation adjustments after discounting.
- Variation margin leaves residual exposure because collateral can lag and agreements can include thresholds.
- Initial margin can reduce counterparty exposure while introducing funding costs reflected in MVA.
- Some non-bank institutions may use different discounting conventions under distinct capital frameworks.
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Full text
# Collateralized / uncollateralized swap # Collateralized / uncollateralized swap Is a fully collateralized interest rate swap considered free of counterparty credit risk? Or close to risk free? Therefore discounted by the rate that best proxies the risk-free rate (which is the OIS-rate)? And then you have the fair value, no more adjustments? For a swap that is not collateralized, or not fully collateralized, the practice is to derive the risk-free value by OIS-discounting, and then perform any applicable value adjustments (CVA, DVA, FVA)? Or is practice divided on uncollateralized swaps? Do some people adjust for credit risk directly, by using a discount rate other than OIS? ## Answer by byouness (score 1, accepted) https://quant.stackexchange.com/a/39927 #### 1. Discount Yes, usually, people discount using the risk free rate, and then adjust for the counterparty credit risk (CVA), funding cost (FVA), and so on. #### 2. Collateral In the case of default, the counterparty will usually stop posting collateral for a given period of time before being closed-out. This period is called the margin period of risk: $MPOR$. As a result, for credit exposures computation, the collateral used is computed based on market values that are lagged by $MPOR$: $$Collateral(t, \omega) = f(MtM(t - MPOR, \omega))$$ The above, combined with the fact that collateral agreements are not perfect (thresholds, minimum transfer amounts, etc.), implies that a swap that is subject to variation margin can still have some counterparty credit risk. However, if the swap is subject both to initial margin and variation margin then nothing will be left in terms of counterparty credit risk. In this case the CCR is essentially replaced by other costs (e.g. the initial margin gives rises to a new adjustment called the MVA to account for funding costs of this IM). ## Answer by rrg (score 1) https://quant.stackexchange.com/a/40014 The pre-crisis concept of a risk-free rate was either government securities or LIBOR-based swap rates. As LIBOR is unsecured bank borrowing-lending rate, this was clearly an approximation too far. Counterparty credit adjustments for a bank, and post-crisis discounting: The value is derived by discounting at the overnight (OIS) rate, and then apply xVA adjustments, including to margin (@byouness). You may find that non-bank institutions, especially those that are permitted to measure credit risk and supply capital using a framework that diverges from BCBS i.e. SII, use a discount rate other than LIBOR or OIS.
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