FRM Part I · FRM Exam Part I

Exchanges and OTC Markets: formula sheet

Full chapter guide

Key formulas

Exchange-traded profile: Standardized + public prices + clearing house + daily margin; Higher liquidity and transparency, lower counterparty risk, less flexibility.
OTC profile: Customized + bilateral + dealer-based + credit exposure unless cleared or collateralized; Higher flexibility and closer hedge, lower liquidity and transparency.
Counterparty exposure on an OTC trade: Exposure = max(V, 0), where V is the mark-to-market value to you; You lose only if the contract has positive value to you when the counterparty defaults. Collateral reduces it.
Net exposure with a netting agreement: Net exposure = max(ΣVi, 0); Compare with the gross sum of Σ max(Vi, 0) without netting. Netting never increases exposure.
Daily margin balance: New balance = Old balance + (Settlement price today − Settlement price yesterday) × Contract size × Number of contracts (long position); For a short position, the sign of the price change is reversed. Add any deposits, subtract any withdrawals.
Margin call trigger: Margin call if balance < maintenance margin; deposit = initial margin − balance; The deposit restores the account to initial margin, not to maintenance.
Bid-ask spread: Spread = Ask − Bid; Half-spread cost = Spread ÷ 2; A round trip (buy then sell at the same quotes) costs the full spread.
Order trigger rules: Buy limit: price ≤ limit. Sell limit: price ≥ limit. Sell stop: triggers when price ≤ stop. Buy stop: triggers when price ≥ stop.; A triggered stop becomes a market order, so the fill can differ from the stop price.
Position gain or loss: P&L = (Exit price − Entry price) × Contract size × Contracts (long); reverse for short; Total P&L equals the sum of daily margin flows.
Novation result: A ↔ B becomes A ↔ CCP ↔ B; The CCP is the buyer to every seller and the seller to every buyer. Its net position is zero.
Variation margin: VM = change in mark-to-market value of the position since the last settlement; Paid or received daily. The side with a loss pays. It is not a deposit that is returned.
Multilateral netting: Net exposure to CCP = Σ gains and losses across all trades with the CCP; Netting works across all of a member's cleared trades in the same netting set, so the CCP exposure is lower than the sum of bilateral gross exposures.
Initial margin purpose: IM ≈ potential loss over the margin period of risk at a high confidence level; Usually calculated with a VaR-type or scenario-based model. It rises when volatility rises.
Default waterfall order (typical): Defaulter IM → defaulter default fund → CCP own capital → survivors' default fund → other loss-allocation tools; State this as typical, not universal. The defaulter's own resources are always used first.
Net exposure with close-out netting: Net exposure = max(Σ Vi, 0); Sum the values of all trades in the netting set from your viewpoint, then floor at zero. Without netting: Σ max(Vi, 0).
Netting benefit: Benefit = Σ max(Vi, 0) − max(Σ Vi, 0); Always ≥ 0. It is zero when all trades have positive value or all are negative or zero.
Collateral call (CSA): Required collateral = max(Net exposure − Threshold, 0) + Independent amount; Compare with collateral already held. Make a transfer only if the difference is at least the MTA. Conventions on independent amounts vary, so follow the stem.
Uncollateralised exposure after a call: Residual exposure ≈ Net exposure − Collateral held × (1 − haircut); Non-cash collateral is valued after haircut. Add exposure change over the margin period of risk.
Mandatory clearing: Standardized OTC derivatives → cleared through a CCP; Applies to standardized, sufficiently liquid products. Exemptions exist for some end users and non-financial firms below thresholds.
Trade reporting: All OTC derivative trades → reported to trade repositories; Applies to both cleared and non-cleared trades. Its aim is regulator transparency, not risk reduction through collateral.
Trading platform rule: Cleared and eligible standardized swaps → traded on exchange or SEF (US); Dodd-Frank uses SEFs. EMIR refers to regulated markets and similar venues.
Non-cleared margin rule: Non-cleared trade → VM (daily) + IM (covers potential future exposure); BCBS-IOSCO framework. IM is segregated and is not rehypothecated, and posted and received IM are not netted.
BCBS-IOSCO IM calibration: IM ≈ potential loss over a 10-day margin period of risk at 99% confidence; IM is calibrated to a period of significant financial stress. Models may be a regulatory schedule or an approved internal model.
Margin threshold: Bilateral IM threshold up to €50 million (or equivalent); Applies to the IM exchange between covered entities. Check the specific minimum transfer amounts in your reading.
Notional versus risk: Gross market value (absolute sum of positive and negative fair values) < Notional amount; Notional is a scale for payments, not the amount at risk. Gross market value is the better proxy for replacement cost.
Gross market value: Gross market value = Σ |fair value of each contract|; Positive and negative values are summed as absolute amounts, with no offsetting between counterparties.
Net exposure to a counterparty: Net exposure = max(Σ fair values under an enforceable netting agreement, 0); Netting applies only when legally enforceable. Collateral then reduces the exposure further.
Gross market value ratio: Gross market value ÷ Notional = relative size of replacement cost; A small ratio shows that notional greatly overstates economic exposure.

Quick revision

Exchange-traded contracts are standardized and cleared centrally; OTC contracts are customized and traditionally bilateral.
A CCP becomes the buyer to every seller and the seller to every buyer, removing bilateral counterparty exposure between members.
Variation margin settles daily gains and losses; initial margin covers potential loss while a defaulter is closed out.
A margin call arises when the account falls below the maintenance level, and the investor must restore it to the initial margin level.
CCP resources are used in layers: the defaulter's margin first, then the default fund, with further loss sharing among members.
Netting lets the non-defaulting party combine positive and negative values across a netting set, so it owes or claims only the net amount.
A CSA sets the terms for collateral: thresholds, minimum transfer amounts, eligible collateral and haircuts.
Haircuts reduce the credited value of collateral to allow for price changes.
Central clearing concentrates risk in the CCP, which makes the CCP systemically important.
Post-crisis reforms push standardized OTC derivatives toward central clearing and trade reporting, and set higher requirements for uncleared trades.
Uncleared bilateral trades face margin requirements to reduce risk and make clearing relatively more attractive.
Securitization can spread and hide credit risk when structures are complex and opaque.

Common mistakes

Saying OTC trades always carry more counterparty risk than exchange trades. Fix: Say OTC trades carry bilateral credit risk unless they are centrally cleared or collateralized.
Assuming all derivatives like swaps are OTC and all like futures are exchange-traded with no exceptions. Fix: Treat the lists as typical. Some standardized swaps are cleared, and some options trade both ways.
Thinking a stop order guarantees the stop price. Fix: A stop becomes a market order once triggered, so the fill can be worse in fast markets. Only a stop-limit caps the price.
Placing a buy stop below the market or a sell stop above it. Fix: A sell stop sits below the current price and a buy stop above it. A buy limit sits below and a sell limit above.
Treating initial margin and variation margin as the same thing. Fix: IM is a buffer against future losses after a default. VM settles gains and losses that have already occurred, daily.
Thinking novation means the CCP guarantees nothing is lost. Fix: Novation moves credit risk to the CCP. The CCP still depends on margin, its capital and member contributions. It can fail.
Adding only positive trade values when netting applies Fix: With enforceable close-out netting, sum all values including negatives, then floor the total at zero.
Applying the threshold before netting Fix: Collateral is computed on the net exposure of the whole netting set. Net first, then subtract the threshold.
Saying all OTC derivatives must be centrally cleared. Fix: Say that standardized, sufficiently liquid contracts are subject to clearing. Bespoke trades stay bilateral but face margin rules.
Confusing trade reporting with clearing. Fix: Reporting goes to trade repositories and gives regulators information. Clearing goes to a CCP and transfers counterparty risk.

Exam tips

Read for words like customized, standardized, cleared, collateralized and netted. They decide the answer.
Be wary of options with always or never about counterparty risk.
For exposure questions, set negative values to zero first, then apply netting only if the question says it is enforceable.
Link the topic to central clearing and margining: questions often ask how those features change OTC risk.
Expect numerical margin-call questions. Build a small table: day, price change, balance, call.
Watch the direction of the position. Questions often switch between long and short.
Know the trigger side for each order type. A common trap is placing a stop on the wrong side of the market.
Remember that the call restores initial margin, and that a market maker earns the spread but bears inventory risk.