SPAN and Portfolio Margining: How Derivative Margin Is Actually Computed

A clearinghouse stands in the middle of every cleared trade, and it worries about exactly one thing: if this counterparty defaults tomorrow, is the collateral I hold today enough to close out their positions without losing money? The entire machinery of derivatives margin is built around that question. SPAN — Standard Portfolio Analysis of Risk, developed by the Chicago Mercantile Exchange in 1988 — is the standard answer, and it has since become the de facto global methodology for derivatives margin (CME, 2014; BCBS-IOSCO, 2019).

SPAN replaced the historical “full collateral” approach with a scenario-based risk array that estimates the largest likely loss over a one-day horizon under stress. It is not quite VaR: its logic is “worst loss over a fixed set of scenarios,” a family of measures that is mathematically better behaved than quantile-style VaR (sub-additivity comes for free, for one) and that enjoys regulatory acceptance in every major jurisdiction. This article takes SPAN apart: the division of labor between the two kinds of margin, the scenarios and risk arrays, spread charges and credits, delivery considerations, and finally the places where the methodology fails.

Two Kinds of Margin, Two Tenses

Margin on a cleared position comes in two kinds, matching the two tenses of the clearinghouse’s question.

Initial margin (IM) handles the future tense. It is posted by both counterparties and covers the potential loss from tomorrow’s price moves. Its entire reason for existing is the opening question: if you default today, the clearinghouse takes your IM and can close out your position tomorrow without losing money. Variation margin (VM) handles the present tense. It is posted by the one counterparty whose position lost money today, settling today’s mark-to-market loss in cash. Rather than waiting for a default to tally the score, mark-to-market losses are settled daily — this is nothing other than the daily settlement mechanism of futures itself.

For a healthy position, IM is large and VM small (just the day’s loss); for a deeply underwater one, accumulated VM can exceed IM. One more layer to keep straight: the clearinghouse’s SPAN requirement is a floor. When you trade through a clearing broker, the broker typically requires more than the clearinghouse minimum, to cover the broker-client leg of default risk.

SPAN’s Answer: Scenarios and Risk Arrays

How does SPAN estimate “worst likely loss by tomorrow”? Not with a closed-form formula — by enumerating scenarios. Standard SPAN defines 16 scenarios per product, structured like this:

• Price moves at seven points: unchanged, up or down 1/3 of the scan range, up or down 2/3, up or down the full scan range; each price point paired with volatility shifted up or shifted down (by a volatility scan range the exchange sets). That’s 7 × 2 = 14 scenarios.
• Plus two extreme scenarios: price moving up or down a multiple of the scan range (commonly double), with the loss counted only at a fraction (commonly around a third) — capturing gap-risk tails without letting the extreme cells dictate the whole requirement.

In each scenario the position is repriced as if one day has passed (option time value decays accordingly), giving a per-scenario P&L. For each contract, those 16 numbers form its risk array. A sketch (downside direction only):

The upside mirrors it — longs fear the down scenarios, shorts fear the up scenarios, and the array carries both. Scale the array by position size, take the largest loss across the 16 scenarios, and you have the position’s scan risk.

The scan range itself is an exchange-published parameter, calibrated to cover a high quantile of one-day price moves. As a mental model you can write it as:

with $\sigma$ the daily volatility, $P$ the price, and $k$ a coverage multiple — but remember you never compute it yourself; the clearinghouse publishes it daily. Concretely: S&P 500 at 4000, 50% annualized volatility, daily vol around 2%, and suppose the exchange sets the scan range at $80. A single long delta-one future then loses $26.67 in the “down 1/3 of scan range” scenario, $53.33 at 2/3, and $80 at the full range; positions with vega pick up an additional volatility-shock-times-vega term in each cell:

For a plain future the vega term is zero, and the worst cell is the full scan-range move against you: raw scan risk of $80 per contract for the long.

Portfolios: What Offsetting Buys and What It Costs

A portfolio is rarely one contract; most positions are spreads — long one contract, short another. SPAN handles portfolios in the most direct way possible: within each scenario, sum the P&Ls of every contract in the portfolio, then take the worst across scenarios. Offsets don’t come from a correlation matrix; they happen naturally inside the vector addition.

Take a calendar spread: long 1 SPX September, short 1 SPX December, both at 4000. In the “down 1/3 range, vol roughly unchanged” cell, the long September loses about $26.67 and the short December gains about $26.67 (the time-dimension correction is second-order), so the combined P&L is roughly zero — the directional risks of the two legs eat each other in every cell.

Here hides the single most instructive detail in SPAN’s design: the combined scan calculation implicitly assumes all expiry months of the same underlying move in lockstep. In the real world there is basis risk between the September and December contracts — the spread itself moves. So SPAN adds an inter-month (calendar) spread charge on top of scan risk: for each pair of offsetting cross-month legs, an add-on charge, calibrated and published by the exchange, puts the basis risk that the scan netting erased back on the books. Part of what directional offsetting saved you, basis risk takes back.

To get a feel for the numbers: suppose the calibrated result is that one SPX calendar spread carries a net requirement of about $40, versus $80 per leg — $160 total — computed standalone. Holding 100 spreads:

A roughly 75% reduction. That is the value SPAN grants hedged portfolios: it recognizes that the two legs of a calendar spread move together directionally and charges only for the residual basis exposure. The converse also holds: a same-direction “false spread” (long September and long December) gets no offset at all — both legs lose in the same scenarios, and the losses simply add.

Across products is a separate layer. Between related-but-distinct products, SPAN grants inter-commodity spread credits — discounts calibrated from historical correlations and published by the clearinghouse. Within a product, offsets emerge from scenario addition; across products, they come from an explicit credit table. Don’t conflate the two mechanisms.

Expiration and Delivery

Contracts approaching expiration face one more test: will this position require delivery, and what does settlement cost? The delivery calculation compares the P&L of taking (physical or cash) delivery at expiration against closing out beforehand, and adds the largest of those losses as a charge. Most futures are cash-settled, so delivery risk is just the gap between final settlement and spot — usually small. Agricultural and physical commodity futures are the exception: with physical delivery, the logistics and settlement risk make this add-on genuinely material.

Assembling the Full Algorithm

Put the parts in order and SPAN’s computation for a portfolio reads:

1. Compute each contract’s 16-scenario risk array, scaled by position.
2. Within each product: sum P&L vectors scenario-by-scenario, take the worst across scenarios — the scan risk.
3. Add the inter-month spread charge (restoring the basis risk the combined scan erased).
4. Add the delivery charge for positions near expiry.
5. Subtract inter-commodity spread credits (hedge discounts between related products).
6. Take the maximum against the short option minimum — an exchange-set per-contract floor that stops deep out-of-the-money short options from margining at nearly zero.

In one line:

where $c$ ranges over the 16 scenarios and $\text{Loss}_i(c)$ is contract $i$‘s loss in scenario $c$. Every parameter — scan ranges, volatility scan ranges, spread charges and credits, option minimums — is computed and published daily by each clearinghouse in parameter files that carry the per-contract, per-scenario risk arrays. Your job is only to apply the algorithm to your own book. CME’s PC-SPAN and SPAN Risk Manager, and third-party systems like Calypso and Murex, exist to do exactly that.

Variation Margin and the Default Waterfall

The VM side is much simpler: the mark-to-market change from yesterday’s settle to today’s, in cash. Long SPX futures, settled 4000 yesterday and 4010 today: you are owed 10 points times the contract multiplier per contract. Computed end-of-day, posted by the underwater side, and generally not netted across product classes or counterparties.

The two margins combine into one procedure when a default actually happens. The clearinghouse: takes the defaulter’s IM collateral; collects whatever VM was already owed at the mark; closes out the defaulter’s positions, realizing the loss (or gain); and covers any shortfall from the IM reserve. IM is sized precisely so that, with high probability, IM plus accumulated VM covers the close-out loss. SPAN’s risk requirement is the clearinghouse’s estimate of that loss — the opening question, closed.

Portfolio Margining: Offsets Across Clearinghouses

SPAN’s offsets stop at the boundary of a single clearinghouse. Recognizing offsets across exchanges or asset classes takes explicit agreements between clearinghouses — portfolio margining / cross-margining arrangements. In the US, the OCC (Options Clearing Corporation) and CME run a cross-margining program for index products; on the securities side, portfolio margin accounts (equities, equity options) run on the OCC’s TIMS family of scenario-based methodology — same intellectual lineage as SPAN, different parameters.

Such accounts can recognize the offset between equity option delta exposure and index futures delta exposure, and for a well-hedged book the margin can fall to a small fraction of the standalone sum. The exact floors and account minimums are set by exchanges and regulators, with brokers typically layering their own requirements on top. For options-plus-futures books, SPAN itself already recognizes option-versus-underlying-future offsets through delta-equivalent positions — that’s the within-clearinghouse mechanism, not to be confused with the cross-clearinghouse agreements.

SPAN Versus VaR

SPAN’s risk requirement is conceptually VaR-like — a one-day loss not exceeded with high confidence — but the implementation differs at every step:

These differences are what make SPAN practical for futures and options clearing: it handles expiration effects and contract-level risk arrays correctly, its 16 scenarios carry more information than a single VaR number, and it is vastly cheaper than full Monte Carlo — and exactly reproducible. For a clearinghouse that must produce numbers for millions of accounts daily and have members able to verify them, reproducibility is not a small thing.

Where SPAN Fails

Three persistent problems, each one a shadow of the same design choice — 16 scenarios and a 1-day horizon.

The scenarios aren’t fat enough. Sixteen cells can’t cover the whole tail. A 1987-style one-day 20% crash sits outside the standard scenarios for most underlyings — the fractionally-counted extreme cells recover only part of it. And for products whose historical volatility has been low for years, the scan range thins out along with the history: the 2022 rates volatility shock exposed exactly this, forcing clearinghouses into repeated, large margin increases on fixed-income products during and after the move. SPAN’s parameters follow realized volatility, so at a regime break they are structurally late.

Offsets have a boundary. SPAN’s netting is intra-product and intra-clearinghouse. Systemic scenarios — the whole market halting, the clearinghouse itself under stress — are outside its ledger. The customer has a margin agreement with the clearinghouse, but the clearinghouse’s own exposure to the next Lehman-scale shock is a question SPAN does not answer.

One day may not be enough. The 1-day horizon assumes a defaulted book can be closed out by tomorrow. In a locked-limit or liquidity-starved market, unwinding a large illiquid position takes days — and IM calibrated to one day is then simply too short. More modern frameworks (Basel III’s FRTB, clearinghouse add-ons for concentrated positions) are pulling time-to-liquidate into the calibration, but for most listed derivatives the regulatory baseline remains SPAN-like.

Together these deliver the most important user-side lesson: SPAN’s requirement is a minimum, not a recommendation. Large institutional traders routinely hold more margin than SPAN demands — both because SPAN by design underestimates tails at regime breaks, and because the cost of meeting a margin call from an under-margined position is brutal. Firms that have lived through a liquidity-driven margin call learned this with real money. Retail traders can rely on PC-SPAN or their broker’s calculator (remembering the broker’s requirement exceeds the clearinghouse floor); institutions either use CME’s and third parties’ SPAN tools or implement the algorithm in-house with a more conservative overlay on top, holding whichever number is higher. Your IM is roughly the per-contract requirement times position size, updated daily; when it rises, you post collateral or cut positions. The clearinghouse’s question never changes — and your answer should be a little more conservative than its own.

References

Basel Committee on Banking Supervision & IOSCO. Margin Requirements for Non-centrally Cleared Derivatives, 2019.

Chicago Mercantile Exchange. CME SPAN Methodology, 2014.

Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. Springer.

McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools (2nd ed.). Princeton University Press.

Options Clearing Corporation. OCC Margin Manual. OCC Operations, 2023.

Securities and Exchange Commission. Customer Margin Rules for Security Futures. 17 CFR § 242.400-§ 242.406.