Central Clearing: formula sheet

Key formulas

Exposure on a single trade

Exposure = max(V, 0)

V is the mark-to-market value to you. Only positive value is at risk if the counterparty defaults.

Exposure without netting

Gross exposure = Σ max(Vᵢ, 0)

Each trade is treated separately. Losing trades are ignored.

Exposure with close-out netting

Net exposure = max(Σ Vᵢ, 0)

Applies to trades in one legally enforceable netting set. Never below zero.

Exposure after collateral

Exposure after collateral = max(Net value − Collateral held, 0)

Add any initial margin posted by the counterparty and subtract collateral you posted if it is not segregated.

Netting benefit

Netting benefit = Gross exposure − Net exposure

Always zero or positive. It is zero if all trades have the same sign of value.

Net-to-gross ratio (NGR)

NGR = Net exposure ÷ Gross exposure

Between 0 and 1. Lower means more netting benefit.

Novation result

Original trade A ↔ B becomes A ↔ CCP and CCP ↔ B

Terms stay identical. The CCP is buyer to every seller and seller to every buyer.

CCP net market position

Σ long positions − Σ short positions = 0 (when all trades are cleared)

The CCP's book is matched, so its exposure is to member default, not market direction.

Bilateral vs multilateral netting

Multilateral net exposure ≤ Sum of bilateral net exposures

Holds when netting is legally enforceable. Bilateral netting works only within each pair of counterparties.

Clearing chain

Client ↔ Clearing member ↔ CCP

The client has no direct contract with the CCP. The member guarantees the client's obligations.

Variation margin call

VM call = MtM(today) − MtM(at last settlement) (paid by the party whose position lost value)

Settles realised losses. Sign matters: the loser pays, the gainer receives.

Initial margin (VaR-based)

IM = VaR(α, MPOR) of the portfolio's P&L over the margin period of risk

Typically at 99% or higher. It covers loss after default, not past loss.

Square-root-of-time scaling

VaR(MPOR) ≈ VaR(1 day) × √(MPOR in days)

Valid only if daily returns are independent and identically distributed with the same volatility. Autocorrelation or fat tails make it approximate.

Parametric VaR for IM

IM = z(α) × σ(daily) × √MPOR × Position value

z(99%) ≈ 2.33. z(99.5%) ≈ 2.58. Zero-mean assumption.

Margin period of risk (components)

MPOR = time from last VM payment to default + time to close out and hedge

Longer remargining intervals and slower liquidation both lengthen it.

Typical waterfall order

Defaulter's margin → defaulter's default fund contribution → CCP skin in the game → survivors' default fund contributions → recovery tools

Defaulter-pays resources always come first. Check the order the question gives, since CCP rulebooks differ.

Cover 1 standard

Pre-funded resources ≥ loss from default of the single largest participant (with affiliates) in extreme but plausible conditions

Minimum standard for a CCP under CPMI-IOSCO principles.

Cover 2 standard

Pre-funded resources ≥ combined loss from default of the two largest participants (with affiliates) in extreme but plausible conditions

Applies to CCPs with a more complex risk profile or systemic importance in multiple jurisdictions.

Loss remaining after a layer

Remaining loss = max(0, Loss − resources used so far)

Apply layer by layer. A layer is only used if the loss is still positive.

Bilateral netting exposure

Net exposure to a counterparty = max(Σ MtM of all trades with that counterparty, 0)

Nets only within one legal netting set between two parties.

Multilateral netting (CCP)

Member net position = Σ MtM of all its cleared trades with the CCP

Nets across all counterparties through novation, within the same CCP and, at many CCPs, the same netting set or clearing service.

Netting efficiency

Netting benefit = (Gross exposure − Net exposure) ÷ Gross exposure

Higher means more exposure removed. Usually lower when trades are split across CCPs.

Default waterfall order

Defaulter's initial margin → defaulter's default fund contribution → CCP's own capital (skin in the game) → surviving members' default fund contributions → further loss allocation or recovery tools

This is the standard stylised order. Exact order and tools vary by CCP. Know the principle: defaulter pays first.

Cover standard (PFMI)

Systemically important CCP: prefunded resources ≥ loss from default of the 2 largest participants (with affiliates) in extreme but plausible conditions

Cover 1 is the minimum for less complex CCPs. Check which one the question asks about.

Default waterfall order

Typical order: Defaulter's initial margin → defaulter's default fund contribution → CCP's own capital (skin in the game) → non-defaulters' default fund contributions → further recovery tools

This is a typical waterfall, and CCP rules vary. For example, some CCPs add a second tranche of their own capital after the non-defaulters' contributions. Order of the waterfall is a common MCQ. Defaulter pays first.

Trade exposure risk weight (QCCP)

Risk weight = 2% on a clearing member's trade exposure to a QCCP. A client exposure also gets 2% if the Basel client-protection conditions are met, and 4% if they are not.

Non-QCCP: trade exposure gets the standardised counterparty risk weight, while funded default fund contributions to a non-QCCP are risk-weighted at 1250%. The 1250% rule applies to funded contributions.

Exposure at default for trade exposure

RWA = RW × EAD, with EAD for QCCP trade exposure = counterparty credit risk exposure measured under the Basel standardised approach (SA-CCR), including margin where permitted

Capital = RWA × minimum capital ratio. The 8% ratio used in simple questions is only a simplifying assumption, so use the ratio the question gives.

Quick revision

• Novation replaces the original contract with two contracts: the CCP faces each clearing member.
• The CCP becomes buyer to every seller and seller to every buyer, so it must stay matched.
• Variation margin passes current mark-to-market changes, usually daily or more often.
• Initial margin covers potential future exposure over the margin period of risk if a member defaults.
• Initial margin is usually set from a high-confidence loss estimate, so it rises when volatility rises.
• The waterfall starts with the defaulter's own resources: initial margin, then its default fund contribution.
• The CCP's own capital contribution then comes before surviving members' default fund contributions, in the typical structure.
• Loss mutualization means surviving members share residual losses through the default fund.
• Multilateral netting can reduce exposures compared with bilateral netting, but only within one CCP.
• Fragmented clearing across CCPs can reduce netting benefits.
• Procyclical margin calls can create liquidity stress in a crisis.
• Recovery tools aim to keep the CCP running; resolution applies when recovery fails.

Common mistakes

• Netting across trades under different master agreements Fix: Net only within one netting set under the same enforceable agreement.
• Allowing negative exposure Fix: Floor exposure at zero. A net amount owed by you is not credit exposure to the counterparty.
• Saying the CCP eliminates counterparty risk. Fix: Say the CCP transforms and concentrates counterparty risk. Risk moves to the CCP and its default resources.
• Thinking novation changes the price or maturity of the trade. Fix: Novation changes only the counterparty. All economic terms stay the same.
• Treating VM as a buffer against future default losses. Fix: VM settles realised mark-to-market changes. Only IM covers the potential loss during the MPOR.
• Using a 1-day horizon for IM when a multi-day MPOR is stated. Fix: Scale by √MPOR (under i.i.d. returns) before multiplying by z and exposure.
• Using survivors' default fund contributions before the defaulter's own contribution Fix: Split it in two: the defaulter's contribution is used first. Survivors' contributions come after CCP skin in the game.
• Treating skin in the game as the largest layer Fix: It is usually small compared with the default fund. Its role is incentive alignment, not main loss absorption.
• Saying central clearing eliminates counterparty risk. Fix: Counterparty risk moves to the CCP and its members. Say it is reduced and concentrated, not removed.
• Treating multilateral netting as the same as bilateral netting with more trades. Fix: Bilateral nets within one pair. Multilateral nets each member against the CCP across all counterparties.

Exam tips

• Read whether trades share one netting set. Questions often add a trade under a separate agreement as a trap.
• Check the sign convention: values are usually given from the bank's side.
• Floor every exposure at zero before choosing an answer.
• For legal questions, link the benefit of close-out netting to enforceability and prevention of cherry picking.
• In comparison questions, contrast bilateral risk spread across counterparties with CCP concentration and mutualised losses.
• Questions often ask who bears the risk after novation. Answer with the CCP's counterparty and its default resources, not 'no risk'.
• Read carefully whether the question is about a member or a client. The default fund and direct CCP contract belong to members only.
• In netting questions, compute net per member, then check that the CCP's total nets to zero. This catches arithmetic slips.