Central Clearing: formula sheet

Key formulas

Exposure of one trade

Exposure = max(V, 0)

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

Exposure without netting

Exposure = Σ max(Vi, 0)

Each trade is treated separately. Negative trades give no offset.

Exposure with close-out netting

Exposure = max(Σ Vi, 0)

Applies to trades in one legally enforceable netting set.

Exposure after collateral

Uncollateralised exposure = max(Net value − Collateral held, 0)

With a threshold H, collateral called is roughly max(Net value − H, 0), subject to the MTA.

Netting benefit

Netting benefit = Exposure without netting − Exposure with netting

Always zero or positive. It is zero when all trades have the same sign.

Net-to-gross ratio (NGR)

NGR = Net exposure ÷ Gross exposure

Lower NGR means more benefit from netting. Gross exposure is the sum of positive values.

Novation result

A–B trade → A–CCP trade + CCP–B trade

The original contract is extinguished. The CCP is the counterparty to both sides.

CCP net position

Σ long positions − Σ short positions = 0 (when all members perform)

The CCP is matched, so it has no net market exposure.

Number of bilateral links

n(n − 1) ÷ 2 bilateral relationships vs n links to a CCP

Shows how a CCP simplifies the web. For 10 firms: 45 vs 10.

Multilateral net exposure

Net exposure to CCP = Σ (positions across all trades with all counterparties)

Gains and losses offset across counterparties, which bilateral netting cannot do.

Default waterfall order

Defaulter's margin → defaulter's default fund contribution → CCP capital → surviving members' default fund contributions

Exact order and any CCP capital layers vary by CCP rules. Learn the logic: defaulter pays first.

Daily variation margin

VM = Current mark-to-market value − Previous mark-to-market value (paid by the party that lost)

For a long futures position: VM received = (F_t − F_t-1) × contract size × number of contracts. A negative result means you pay.

Margin period of risk scaling

IM ≈ z × σ_daily × √(MPOR in days) × Position value

A common simple approximation under normal returns with zero mean. z is 2.33 for 99% one-tailed and 1.645 for 95%. Real CCP models are more complex, but this appears in questions.

Default waterfall order

Defaulter's IM → Defaulter's default fund contribution → CCP's own capital → Surviving members' default fund contributions → further CCP tools (e.g., assessments)

Check the order given in the question. The defaulter's own resources always come first.

Loss to be mutualised

Loss after defaulter resources = Close-out loss − Defaulter's IM − Defaulter's default fund contribution

If the result is zero or negative, no one else is touched.

Cover standard

Cover 1: fund covers default of largest member. Cover 2: fund covers default of the two largest members.

Sizing is done under extreme but plausible scenarios.

Margin and loss-absorption order

Defaulter's initial margin → defaulter's default fund contribution → CCP's own capital (skin in the game) → surviving members' default fund contributions

Called the default waterfall. Exact layers vary by CCP, but the defaulter pays first and survivors' mutualized funds come later.

Variation margin

VM = change in mark-to-market value of the position, paid daily

Settles current exposure. It does not cover future moves, which initial margin covers.

Net exposure

Net exposure = max(Σ positive and negative values, 0)

Netting across contracts with the same party lowers exposure. Under multilateral CCP netting, a member faces one net position.

Reform pillars

Clear standardized OTC + trade on platforms + report to repositories + margin uncleared + higher capital

The core G20 reform list. Know all five.

Quick revision

• OTC trades are bilateral and customised, so each party bears the other's default risk.
• Novation replaces the original contract with two contracts, each facing the CCP.
• A CCP becomes the buyer to every seller and the seller to every buyer.
• Multilateral netting cuts total exposures compared with bilateral netting.
• Initial margin covers potential future losses if a member defaults, and is set to a high confidence level over a close-out period.
• Variation margin settles daily mark-to-market changes and is usually paid in cash.
• The default fund is mutualised: members share losses beyond the defaulter's own resources.
• The defaulter pays first, then the CCP's own capital, then surviving members' contributions.
• Central clearing concentrates risk, so a CCP failure would be systemic.
• Margin can be procyclical: it rises in stress and drains liquidity.
• Mutualisation can create moral hazard if members do not bear the cost of their own risk.
• Post-crisis reform pushed standardised OTC derivatives to CCPs and added margin rules for non-cleared trades.

Common mistakes

• Treating a negative trade value as an exposure. Fix: Use max(V, 0) for each trade. A negative value is zero exposure.
• Netting trades with different counterparties. Fix: Net only within a single legal netting agreement with one counterparty.
• Saying a CCP eliminates counterparty risk. Fix: Say it replaces many exposures with one exposure to the CCP, managed with margin and a default fund. Risk is concentrated.
• Thinking novation keeps the original contract alive. Fix: The original contract is extinguished and replaced by two new contracts with the CCP.
• Treating variation margin as a buffer that is returned. Fix: VM is a settlement of realised gains and losses. IM is the buffer held against future loss and returned when positions close.
• Using surviving members' default fund contributions before the defaulter's own resources. Fix: Always start with the defaulter's IM and its own default fund contribution. Others' funds come after the CCP's own capital in a standard waterfall.
• Saying central clearing eliminates counterparty risk. Fix: It transfers and concentrates risk in the CCP, and cuts it through netting and margin.
• Confusing procyclicality with moral hazard. Fix: Procyclicality is margin rising in stress. Moral hazard is weaker risk discipline because losses are shared or rescued.

Exam tips

• Always check whose perspective the values are quoted from before computing exposure.
• Look for the words 'enforceable' or 'legal opinion'. If netting is doubtful, compute exposure gross.
• Know the CSA terms: threshold, MTA, haircut, eligible collateral and margin period of risk. Questions often test them by definition.
• Be ready to compare bilateral and central clearing: flexibility and tailored terms versus standardisation, novation and mutualised default resources.
• Expect conceptual MCQs: pick the option that says the CCP becomes buyer to every seller and seller to every buyer.
• Reject any option claiming a CCP eliminates credit risk or removes the need for margin.
• In netting questions, compute net and gross exposure, then compare. Watch the sign of each position.
• Link standardization to benefits: it allows fungibility, valuation and close-out. Customized trades usually stay bilateral.