4.7.4 Collateral, Netting & SA-CCR

Basic Prerequisites: PFE and 03 · CVA & DVA.

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1. Intuition & Practical Objective

There are exactly two ways to reduce counterparty exposure: netting (combine trades so opposite values cancel) and collateral (post margin against the current value). Both are powerful, and both are routinely over-estimated. This page builds the mitigation machinery and then the regulatory exposure formula - SA-CCR - that Basel uses when a bank cannot model exposure itself.

The core discipline:

• Netting only works inside a legally enforceable netting set. Two offsetting trades with different counterparties produce two exposures, not zero.
• Collateral never reaches zero exposure. The gap is the margin period of risk (MPoR) - the time from the last margin exchange to close-out after default (regulatory: 10 business days for bilateral non-cleared OTC, 5 days for cleared). During the MPoR the position moves unhedged and uncollateralised, and a large cash flow inside that window creates an exposure spike that margin does not cover.
• SA-CCR is deliberately conservative. Its $\alpha =1.4$ grosses exposure by 40%; industry studies found SA-CCR EAD runs at roughly 2.5× the internal-model (IMM) number overall, and an order of magnitude higher for well-margined books (ISDA-AFMR 2017).

The reported mitigation, in numbers. Below: netting cuts a two-trade portfolio’s average EPE from $23.6$ to $9.0$ (62%), and a zero-threshold CSA with a 10-day MPoR cuts a single forward’s EPE by 7.6× - not to zero. The residual is the MPoR.

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2. Mathematical Ground Truth & Derivations

2.1 Netting

Close-out netting aggregates the values $V_k$ of all trades in a netting set into a single claim:

$$V_{\text{NS}}(t)=\sum _{k\in \text{NS}}{V}_k(t),\text{exposure}=V_{\text{NS}}(t{)}^{+}.$$

The net-to-gross ratio measures how much offsetting is captured:

$$\text{NGR}=\frac{{\text{RC}}_{\text{NS}}}{{\sum }_k\max (V_k,0)}.$$

Basel’s standardised initial-margin formula uses it to hand back only part of the benefit:

$$\text{Net standardised IM}=(0.4+0.6\text{NGR})\times \text{Gross IM}\text{\hspace{1em}(Gregory 7.4)}$$

• i.e. 60% of the current netting benefit is recognised for future exposure.

2.2 Collateral: the credit support amount

Let $V$ be the portfolio value, $K_C$ the counterparty threshold, $C$ the margin already held, and $\text{IM}$ the independent amount. The receiving party’s margin call is (Gregory 7.2–7.3)

$$\text{Margin due}=\max (V-K_C,0)+\text{IM},$$ $$\text{Credit support amount}=\max (V-K_C,0)-\max (-V-K_P,0)-C.$$

Threshold and MTA are additive ($\text{TH}+\text{MTA}$ must be breached before a call), and IM is the mathematical opposite of a threshold (a negative threshold). Exposure after collateral is the position valued with a look-back of one MPoR:

$${\text{Positive exposure}}_t=\max (V_t-C_{t-\text{MPoR}},0).\text{\hspace{1em}(Gregory 15.3)}$$

Two consequences the formula hides: (i) MTAs make margin path-dependent - the credit support balance at $t$ depends on history; (ii) collateral spikes - a settled cash flow is not netted against margin, so it creates an exposure lasting ~one MPoR.

2.3 SA-CCR - the regulatory exposure formula

The Basel standardised approach (BCBS 2014, paras 129–149) defines exposure at default as

$$\boxed{\text{EAD}=\alpha (\text{RC}+\text{PFE}),\alpha =1.4}\text{\hspace{1em}(13.16)}$$

with replacement cost for margined trades

$$\text{RC}=\max \{V-C,\text{TH}+\text{MTA}-\text{NICA},0\}\text{\hspace{1em}(13.19)}$$

and potential future exposure

$$\text{PFE}=\text{multiplier}\times {\text{AddOn}}^{\text{aggregate}},{\text{AddOn}}^{\text{aggregate}}=\sum _a{\text{AddOn}}^{(a)},$$ $${\text{AddOn}}_i={\text{SF}}_i\times {\text{SD}}_i,\text{SD}=\frac{1-e^{-0.05M}}{0.05},$$ $$\text{multiplier}=\min \left\{1,\text{Floor}+(1-\text{Floor})\exp \left(\frac{V-C}{2(1-\text{Floor}){\text{AddOn}}^{\text{aggregate}}}\right)\right\},\text{Floor}=5\%.\text{\hspace{1em}(13.21)}$$

• ${\text{SF}}_i$ = supervisory factor (one-year loss): IR 0.50%, FX 4.00%, credit single-name 0.38–6.00% by rating, equity single-name 32%, commodity 18% (electricity 40%).
• $\text{NICA}$ = net independent collateral amount = collateral received less non-segregated collateral posted (segregated posted margin is bankruptcy-remote and ignored).
• The multiplier recognises excess collateral: it falls toward the 5% floor as $V-C$ becomes more negative (out-of-the-money portfolios), but never reaches zero.
• The VM horizon factor for margined PFE is $\frac{3}{2}\sqrt{\text{MPR}/250}$, so a 10-day MPoR gives $\frac{3}{2}\sqrt{10/250}=0.30$.

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3. Computational Implementation - netting, collateral and SA-CCR

Simulate a two-trade portfolio, measure the netting benefit and the collateral benefit, then compute SA-CCR EAD for a 6-year interest-rate swap and the excess-collateral multiplier ladder. Standard library only.

Points to read: (i) netting captures 62% of the gross exposure but leaves $9.0$ of EPE - netting is neither free nor complete; (ii) a perfect zero-threshold CSA still leaves 13% of the uncollateralised EPE, because the 10-day MPoR is a real unhedged window; (iii) SA-CCR’s $\alpha$ and the multiplier turn a $10m IR swap into an EAD of $362,854 unmargined / $108,856 margined - versus CEM’s $150,000 (Gregory §13.4.2, §13.5.1), which is why SA-CCR replaced CEM. (Note: Gregory’s worked text prints $249,182 for the product $10\text{m}\times 0.5\%\times 5.18$; the arithmetic is 259,182, as the book itself uses two paragraphs later - a typo in the source.)

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4. Failure Modes & First-Principles Breakdowns

1. Netting mis-scoping. Applying netting across counterparties, legal entities, or margin agreements that do not share an enforceable master agreement overstates the benefit. SA-CCR forces netting sets to be split when more than one margin agreement applies (conservative).
2. MPoR under-estimation. The MPoR is a model parameter, not a literal close-out time. It absorbs delayed default declaration, portfolio liquidation, disputes, and higher post-default volatility - doubling volatility is roughly equivalent to quadrupling the MPoR (Gregory §9.1.2). The regulatory floor is 10 days bilateral / 5 days cleared, but illiquid or hard-to-replace books require ≥20 days.
3. Collateral spikes. A settled cash flow inside the MPoR is uncollateralised and not covered by variation margin, producing a transient exposure spike - a dominant residual EPE even under full initial margin (Gregory §7.3.6, §15.6.6).
4. Wrong-way collateral. Posting one’s own bonds/equity as margin, or a cross-currency swap collateralised in one of the two currencies, makes the collateral itself correlated with the exposure - margin that evaporates exactly when it is needed (§17.6.6).
5. Rating triggers & cliff-edge. Threshold linked to a credit rating means a downgrade can trigger a large margin call (AIG: $20bn on a downgrade); Basel gives no capital benefit for rating triggers and the LCR requires pre-funding of the outflows.
6. SA-CCR is a floor, not a model. Using it as if it were risk-sensitive over-capitalises well-hedged books; two offsetting same-bucket swaps give zero EAD, while FX triangles (USD/EUR, GBP/USD, EUR/GBP) generate capital on all three legs (Gregory §13.5.1) - counter-intuitive artefacts of the asset-class bucketing.

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5. References

• Gregory, Jon: The xVA Challenge (5th ed., 2025)
• BCBS (2014): The Standardised Approach for Measuring Counterparty Credit Risk Exposures (BIS d317)
• Hull, Options, Futures, and Other Derivatives
• BCBS-IOSCO (2015): Margin requirements for non-centrally cleared derivatives

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6. Connected Graph Bridges

• Back: 03 · CVA & DVA
• Forward: 05 · Failure Modes & Practice · Index Hub
• Sibling: Liquidity Risk & Margin Spirals (the margin–funding spiral that collateral creates) · Value at Risk & Expected Shortfall