Margin (Collateral) and Settlement: formula sheet

Key formulas

Credit support amount (one-way view)

Call = max(0, Exposure − Threshold − Collateral already held)

Exposure is the receiver's mark-to-market. Include any independent amount if the CSA requires it.

Minimum transfer amount test

Transfer only if |Call| ≥ MTA

If the call is below the MTA, nothing moves. Some CSAs round the transfer to a set unit.

Haircut collateral value

Collateral value = Market value × (1 − haircut)

Needed to find how much market value must be posted: Market value required = Value needed ÷ (1 − haircut).

Uncollateralised exposure left

Residual ≈ Threshold + MTA gap + price change over margin period of risk

A rule of thumb for what stays unsecured, not an exact formula.

Variation margin call

Call = max(0, V − Collateral held − Threshold), subject to the MTA and rounding

V is the net portfolio value to the caller. The call is made only if it exceeds the MTA.

Collateralized exposure at default

Exposure ≈ max(V(t + MPOR) − C, 0)

C is collateral held at the start of the MPOR. Collateral is not updated during the MPOR.

Volatility over the MPOR

σ(MPOR) = σ(daily) × √(MPOR in days)

Assumes independent, identically distributed daily changes. Use business days consistently.

Approximate residual exposure (normal model)

Residual exposure at confidence c ≈ z(c) × σ(daily) × √MPOR + Threshold

Applies when the portfolio is fully covered up to the threshold. Add MTA effects if relevant.

Components of MPOR

MPOR ≈ remargining period + call, dispute and settlement time + close-out and replacement time

Use this to explain changes in MPOR. The Basel floor is 10 business days for daily-margined OTC netting sets.

Scaling between MPORs

Exposure(new) ≈ Exposure(old) × √(MPOR new ÷ MPOR old)

Fast comparison when only the MPOR changes.

Uncleared margin IM calibration

IM ≈ 99% one-tailed VaR over a 10-day horizon, stress-calibrated

BCBS-IOSCO standard for non-centrally cleared derivatives; netting is allowed only within a legally enforceable netting set.

Scaling VaR to a margin period

VaR(T days) = VaR(1 day) × √T

Valid under i.i.d. returns and normality; a rough approximation only. Example: √10 ≈ 3.162.

Parametric IM for a position

IM = z × σ(daily) × √T × Position value

z = 2.326 for 99% one-tailed under normality.

SIMM aggregation within a bucket

K = √( Σ WSᵢ² + ΣΣ(i≠j) ρᵢⱼ × WSᵢ × WSⱼ )

WS = risk weight × sensitivity; ρ = prescribed correlation. Results then aggregate across buckets and risk classes.

Net IM exposure to the poster

Loss to poster on collector default = IM posted − recovery of segregated IM

If segregated and bankruptcy-remote, recovery should be full; if not segregated or rehypothecated, the poster may be an unsecured creditor.

Collateral value after haircut

Adjusted value = Market value × (1 − H)

H is the haircut as a decimal. Use it for each asset separately.

Net exposure after collateral

Net exposure = max(0, Exposure − Σ adjusted collateral)

Exposure cannot be negative for the receiver. Ignores threshold and minimum transfer amount unless given.

Gross-up for a required haircut

Market value needed = Required value ÷ (1 − H)

Use when asked how much collateral to post to cover a given amount.

Combined haircut (price and FX)

Adjusted value = Market value × (1 − H_price) × (1 − H_FX)

Basel treats these as separate adjustments. Some questions simply add them, so follow the stated method.

Haircut from volatility

H ≈ z × σ × √T

σ is the volatility per unit time, T is the margin period of risk in the same unit, z is the normal quantile (for example 2.33 at 99%). It is an approximation that assumes normal returns.

Novation

Trade A–B → A–CCP and CCP–B

The CCP becomes buyer to every seller and seller to every buyer. Original counterparties no longer face each other.

Variation margin

VM payment = change in mark-to-market value of the position

Paid at least daily. It resets current exposure and covers losses already incurred, not future ones.

Initial margin

IM ≈ loss at a high confidence level (VaR or ES) over the margin period of risk

Covers potential future exposure between the last margin call and close-out. Longer close-out periods and higher volatility raise IM.

Default waterfall order (typical)

Defaulter's IM → defaulter's default fund → CCP capital → non-defaulters' default fund → further recovery tools

Defaulter pays first. Always check the order given in the question, as CCP rules vary.

Cover-N standard

Default fund sized to cover default of the largest member (Cover 1) or two largest (Cover 2) under extreme but plausible conditions

Cover 2 applies to CCPs that are systemically important or have complex risk profiles under international standards.

Netting benefit

Net exposure = Σ(MtM across netting set), floored at zero

Positive and negative values within a netting set offset. Multilateral netting at a CCP extends this across all members.

Settlement risk exposure

Exposure = full principal of the leg you have paid and not yet received

The loss can be the whole amount, not just replacement cost.

Pre-settlement risk exposure

Exposure = max(MTM replacement cost, 0)

Applies from trade date to settlement date. Much smaller than principal.

Settlement risk window

Window = time between irrevocable payment of your leg and confirmed receipt of the other leg

Time zone differences in FX widen this window.

DvP and PvP rule

DvP: security ↔ cash. PvP: currency A ↔ currency B. Each leg final only if the other is final

Both remove principal risk; neither removes market risk before settlement.

Multilateral netting of pay-ins

Net pay-in per currency = Σ amounts to pay − Σ amounts to receive

Used by CLS to lower funding needs. Gross trade value is much larger than net pay-in.

Quick revision

• Collateral reduces exposure to a counterparty but does not remove it.
• Variation margin settles current mark-to-market changes; initial margin covers potential future moves during close-out.
• The margin period of risk is the time from the last successful margin exchange to close-out and replacement of the position.
• A longer margin period of risk means larger potential exposure, even with daily margining.
• Thresholds and minimum transfer amounts leave uncollateralised exposure.
• Segregation protects posted initial margin if the collateral taker fails; rehypothecation reuses collateral and adds risk for the poster.
• A haircut cuts the credit given for collateral to allow for price and FX volatility; riskier or more volatile assets get larger haircuts.
• Wrong-way risk arises when collateral value or exposure moves adversely with the counterparty's credit quality.
• Margin calls in stress can drain liquidity and create procyclical funding pressure.
• A CCP becomes buyer to every seller and seller to every buyer through novation, and relies on margin and default resources.
• Settlement risk includes principal risk, where one leg is paid and the other is not; payment-versus-payment arrangements reduce it in foreign exchange.
• Delivery-versus-payment links the transfer of securities to the transfer of cash and cuts principal risk.

Common mistakes

• Treating the threshold as a deductible that is paid only once Fix: The threshold is the exposure left unsecured at all times. The call is exposure minus threshold, every time.
• Applying the MTA to the exposure instead of the call Fix: Compute the call first. The MTA is tested against the call amount.
• Assuming daily margining means zero exposure. Fix: Always think of residual exposure over the MPOR. Collateral is fixed while the portfolio keeps moving.
• Scaling exposure linearly with the MPOR. Fix: Use √time for volatility under the standard model. Doubling MPOR multiplies exposure by about 1.41.
• Treating IM and VM as the same thing. Fix: IM covers potential future loss over the MPOR; VM tracks current mark-to-market and is exchanged to remove current exposure.
• Saying IM is netted between the two counterparties. Fix: Under the uncleared rules, both parties post IM to each other on a gross basis. Netting applies only within a netting set to compute each side's amount.
• Multiplying by H instead of (1 − H). Fix: The haircut is the cut. Value kept = (1 − H). A 10% haircut on 100 gives 90.
• Adding the FX haircut to the price haircut when the question gives a multiplicative rule, or the reverse. Fix: Use the method the question states. If none is stated, multiply the two (1 − H) factors and say so.
• Saying a CCP eliminates counterparty risk. Fix: Say it replaces many bilateral exposures with one exposure to the CCP and concentrates risk.
• Mixing up initial and variation margin. Fix: VM settles current gains and losses. IM protects against future losses during close-out.

Exam tips

• Always list threshold, MTA and haircut before calculating. Questions often hide one of them in the text.
• Watch the direction of the haircut. Divide to size a posting, multiply to value holdings.
• For concept questions, link IM to the margin period of risk and VM to current mark-to-market.
• Expect interpretation questions on residual risk. Name the threshold, MTA, gaps in timing and wrong-way risk.
• Read the MPOR components in the stem. Dispute time and close-out time are often added to the remargining interval.
• If a question changes the MPOR, reach for square-root scaling first, then add any fixed threshold.
• Name the concept precisely: variation margin covers current exposure, while the MPOR creates the residual exposure.
• Remember the Basel floor of 10 business days for daily-margined non-cleared OTC netting sets, and that it increases in stress or for illiquid portfolios.