If You Measure Premium Monthly, Measure Risk Monthly Too
29 July 2026 · 6 min read
At a fixed delta, a weekly put and a monthly put look almost identical on the risk numbers most tools report, while one of them earns roughly two and a half times the annualised rate. That is not a free lunch, and the gap between those two facts is where a real modelling error lives — one we shipped, ran on a live book for a while, and only found by asking why our own optimizer kept preferring the shortest expiry on the board.
Every figure below comes from the same pricing engine behind levelbox, at a fixed 0.10 delta and 60% implied volatility, stressed at a 25% drawdown with volatility expanding into it.
The number that surprised us
Start with the assumption we had been carrying: that shorter-dated puts are safer in a crash, because there is less time value in them to lose.
That's true as far as it goes. What it misses is that at a fixed delta the strike moves with the tenor. A 3-day 0.10-delta put sits about 6.6% below spot; a 30-day one sits about 18.3% below; a 60-day one about 24.1% below. Delta is a statement about standard deviations, and three days holds far fewer of them than thirty.
So in a 25% drop the short-dated strike goes far deeper in the money, while the long-dated one keeps more time value and more vega. Those two effects very nearly cancel:
| At 0.10 delta, 60% IV | 3 DTE | 14 DTE | 30 DTE | 60 DTE |
|---|---|---|---|---|
| Strike, below spot | 6.6% | 13.3% | 18.3% | 24.1% |
| Modelled crash loss, as share of collateral | 19.8% | 18.6% | 20.2% | 23.4% |
| Annualised premium on collateral | 34.3% | 17.6% | 13.1% | 10.3% |
Crash loss per dollar of collateral is essentially flat across the whole range. Annualised premium is not — it is more than three times higher at the short end, because premium scales roughly with the square root of time while the number of days you hold it scales linearly.
If your only risk gate is a drawdown number, that table says sell the shortest thing available. Ours did exactly that, and it was right by its own lights.
Where the mismatch actually is
The error was not in the crash model. It was in the units of two numbers sitting next to each other.
Our premium figure was a rate: credit scaled to a thirty-day run, because that is how anyone thinks about income. Our assignment budget was a stock: the probability of assignment times strike times contracts, summed across the positions held at that instant.
An objective measured per month, constrained by a risk figure measured per instant. A weekly book and a monthly book at the same delta and the same collateral consume near-identical assignment budget, while the weekly book books several times the premium. The constraint had no way to see tenor. Not approximately — not at all.
Here are two positions at the same delta and near-identical collateral, one at 3 days and one at 30:
| 3 DTE | 30 DTE | |
|---|---|---|
| Premium per month | $1,820 | $704 |
| Expected assignment, snapshot | $7,199 | $8,730 |
| Expected assignment, over 30 days | $45,027 | $8,730 |
| Premium per assignment-dollar, snapshot | 0.253 | 0.081 |
| Premium per assignment-dollar, over 30 days | 0.040 | 0.081 |
Read the last two rows. On the snapshot measure the short-dated position looks three times more efficient. On the same clock as the premium, the ranking inverts.
Assignment compounds, and saturates
The reason is not subtle once you look for it. A 0.10-delta put has roughly a 12% chance of finishing in the money. Sell one a month and that is your exposure. Sell one every three days and you have taken that 12% draw ten times.
| Tenor | Cycles in 30 days | Chance of at least one assignment |
|---|---|---|
| 3 DTE | 10 | ~72% |
| 14 DTE | 2.1 | ~24% |
| 30 DTE | 1 | ~12% |
| 60 DTE | 0.5 | ~6% |
The maths has to saturate — one minus the survival probability compounded, not the per-cycle figure multiplied by the cycle count. Multiplying would claim more expected assignment dollars than you have capital to be assigned with, which is nonsense: once you are assigned, that collateral has become shares and the sequence stops.
And it assumes each cycle is independent, which markets plainly are not. Volatility clusters; trends persist; the cycle after a bad one is not a fresh draw. So the real figure is lower than this. We report it anyway, because being conservative on a risk measure is the correct direction to be wrong in, and we say on the page that it is not a calibrated probability.
What this changes if you sell premium
You do not need our tooling for any of this to apply.
If you quote yourself an annualised yield, quote yourself an annualised assignment risk beside it. A 34% rate against a 72% monthly chance of being handed stock is a coherent trade if you want the shares. It is a very different trade from the same rate presented next to a 12% figure that quietly described a single position rather than a month of them.
Check what units your risk numbers are in. This is the general lesson and it is not specific to assignment. If an objective is a flow and a constraint is a stock, the constraint will not restrain the objective in the dimension where they disagree — and it will look like it is working the whole time, because it returns a plausible number on every run.
Weeklies are not free money and not a trap. They pay more per unit of time for a reason you can now put a number on. Whether that is worth it depends entirely on whether assignment is something you want — which, for anyone running the wheel, is a real question rather than a rhetorical one.
What we did about it
Our assignment budget is now a thirty-day run-rate on the same clock as the premium figure it constrains, and the instantaneous snapshot ships beside it so the change is visible rather than silent. On a short-dated book the two differ several-fold.
That change also let us open something we had kept deliberately shut. Target delta and expiry had both been pinned to a single setting, because with a tenor-blind constraint an optimizer allowed to choose freely would simply run to the shortest, closest-to-the-money contract on the board — the corner of the grid where the reported numbers looked best and the real risk was worst. With the constraint on the right clock, both can be opened up and let the budgets do the restraining. That is the whole point of a budget. It has a price, though: budgeting a whole book against several capacities at once makes the allocation a knapsack problem of the kind with no exact answer, so what comes back is a heuristic rather than a proven best plan.
The premium optimizer now also computes a target shape for the option layer against a clean-slate copy of your capital, so what it suggests is measured against what your book should look like rather than accreting on top of what it already holds. And because a short-dated book turns over quickly — the one that prompted this work released its entire option layer within twenty-four days — it reports when each tranche of collateral comes free, which turns out to be the thing that actually schedules the next month of trades.
None of this is a recommendation about tenor. Shorter expiries suit some books and some temperaments; the point is only that the numbers you use to decide should be measured on the same clock, or the comparison is not the one you think you are making.
Analytical and educational tooling, not investment advice. Crash figures are model estimates from our own conservative TIMS-lite margin model with volatility expanding into the drawdown, not your broker's numbers. Assignment probabilities are risk-neutral, which is a price-implied quantity rather than a forecast, and the thirty-day figure additionally assumes independence between cycles. Options carry the risk of assignment and of loss; work through the numbers on your own book and decide for yourself.
Common questions
- Are weekly or monthly cash-secured puts better?
- It depends on what you measure. At a fixed delta, weeklies pay a much higher annualised rate on the same collateral — around 34% against 13% for a 30-day put on a 60%-volatility name at 0.10 delta. But they also reset far more often, and assignment risk compounds with every reset. A 0.10-delta put carries roughly a 12% chance of finishing in the money; run ten of them in a month and the chance of being assigned at least once is closer to 72%. The higher rate is real, and so is the reason you are being paid it.
- Does selling shorter-dated puts reduce crash risk?
- Not meaningfully, at a fixed delta. It is a common assumption because a short-dated option has less time value to lose, but that misses the other half: at the same delta a short-dated strike sits much closer to the money. A 3-day 0.10-delta put on a 60%-volatility name is about 6.6% out of the money where a 30-day one is about 18.3% out. In a 25% drop the near strike goes far deeper in the money. Priced through a stress engine, the two land within about a point and a half of each other as a share of collateral — roughly 20% either way.
- Why can a risk budget fail to distinguish weekly from monthly puts?
- Because most risk figures are snapshots and most income figures are rates. Expected assignment computed as probability times strike times contracts describes the positions you hold at one instant. Premium quoted per month describes a flow. Put a weekly book and a monthly book side by side at the same delta and collateral and the snapshot returns nearly the same number for both, while the weekly book books several times the premium. The fix is to put both on the same clock.
- How do you measure assignment risk over a month instead of an instant?
- Take the per-cycle probability of assignment, work out how many cycles fit in the window, and compute the chance of at least one assignment: 1 minus (1 minus p) to the power of the cycle count. It saturates rather than growing without limit, which matters because you can only be assigned once against a given pool of collateral — after that the cash has become shares and the sequence stops. The measure assumes each cycle is independent, which real markets violate, so it overstates slightly. That is the honest direction to be wrong in.
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