Option Vega and Portfolio Vega: What Premium Sellers Are Really Short

Vega measures how much an option is worth per point of implied volatility. If you sell premium you are short it, which means you lose when implied volatility rises — and implied volatility rises in precisely the conditions where your positions are already hurting. Most sellers know this in the abstract. Fewer have looked at how much vega they are carrying, or noticed that the number grows as a trade moves against them.

The figures below all come from the same contract, priced with the engine behind levelbox: a put struck 10% below a $100 stock, 30 days out, 30% implied volatility, 4% risk-free rate. It prints at $0.40 with a delta of −0.096. A 10-delta put, roughly — the kind of strike a lot of people sell by default.

Vega, briefly

Vega is one of five sensitivities that fall out of an option pricing model; the full set is covered here. It is positive for any long option and largest for at-the-money contracts with plenty of time left. Convention quotes it per 1.00 of volatility, meaning a move of 100 volatility points, so the practical number is that figure divided by 100.

Our $0.40 put carries $0.049 of vega per volatility point, or $4.90 per contract. Sell it and you lose $4.90 for every point implied volatility climbs, before the stock has moved at all.

That sounds small. It stops sounding small once volatility actually moves. Push implied volatility from 30% to 40% and hold the stock at $100 — no price change whatsoever — and the put reprices from $0.40 to $1.00. You collected $40 and you are down $60 on a stock that did nothing.

Worth noting what the vega number itself predicted: $0.049 × 10 points = $0.49, against an actual move of $0.60. Vega understated the loss by about 22%, because vega is a local derivative and it rises as volatility rises. Any single vega figure is a tangent line to a curve that bends the wrong way for a seller.

The number moves against you twice

The more useful thing about vega is that it is not a constant. Hold the same 30-day contract and walk the stock down toward the strike:

Spot	Delta	Vega per vol point
$100	−0.096	$0.049
$97	−0.171	$0.071
$94	−0.279	$0.091
$91	−0.417	$0.102

Vega roughly doubles while the put is still out of the money. So a sell-off hands a short put three separate problems at once: delta losses as the stock falls, accelerating losses from short gamma, and a volatility exposure that is quietly growing the whole way down — right as the market is repricing volatility upward.

This is the specific reason a headline vega figure taken at today's spot flatters the position. It is measuring the exposure in the state of the world where you do not care about it.

Theta per vega: what you are paid for the risk

If vega is the risk, theta is the payment. The ratio between them says what you are being paid per unit of volatility exposure, and it turns out to depend almost entirely on tenor. Same strike, same stock, same volatility, varying only days to expiry:

DTE	Credit	Theta per day	Vega per vol point	Theta per unit of vega
7	$0.01	$0.004	$0.002	7.72
14	$0.08	$0.015	$0.014	3.82
30	$0.40	$0.023	$0.049	1.74
45	$0.76	$0.024	$0.077	1.14
60	$1.11	$0.023	$0.100	0.84
90	$1.77	$0.021	$0.138	0.55

Look at the theta column on its own. From 30 days out to 90 days out, daily decay goes from 2.3 cents to 2.1 cents. It does not improve. The 90-day contract pays a bigger headline credit only because there are more days in it, not because any individual day pays better.

Now look at vega over the same stretch: 5 cents to 14 cents. Close to triple.

So selling the 90-day contract instead of the 30-day one earns slightly less per day, ties up the capital three times as long, and carries almost three times the volatility exposure. The approximation behind this is clean — for an at-the-money option the ratio comes out near σ/2T, so doubling tenor roughly halves your carry per unit of vol risk. Longer tenors are not a free upgrade to a bigger number. They are a worse rate on the same risk.

Portfolio vega does not net the way delta does

Everything above is one contract. The part that gets skipped is what happens when you add twenty of them up.

Delta nets. Long one name, short another, and the book's directional exposure is genuinely smaller than the sum of its parts — that is ordinary diversification, and it works because stock returns are imperfectly correlated.

Vega mostly does not net, because implied volatility across unrelated names moves together far more tightly than the underlying prices do. A macro shock reprices volatility on almost everything at once, in the same direction. Twenty short puts across twenty tickers, in twenty different sectors, are not twenty independent volatility bets. They are close to one position held twenty times.

That makes portfolio vega the least diversifiable exposure a premium-selling book carries, and the one most likely to be uncounted. A wheel book that has carefully spread its delta across sectors, capped its position sizes, and kept its assignment odds in check can still be running a concentrated short-volatility position without anyone having written the number down.

Not every name's volatility moves by the same multiple

One wrinkle that trips people up when they try to estimate this: the quiet names move proportionally more.

When VIX printed above 65 intraday on 5 August 2024, having sat in the mid-teens a fortnight earlier, that is roughly a fourfold move on a low base. A name already trading at 60% implied volatility does not go to 240%. It might go to 90%. In absolute volatility points the high-volatility name moved more; as a multiple, the sleepy index moved far more.

The practical consequence is that the instinct to scale volatility shocks by a name's current volatility level is backwards. Doing so overstates the shock on your most volatile holdings and understates it on the boring ones, which is exactly wrong if you are trying to work out what a market-wide volatility event does to a book.

Where it actually bites: margin

For a cash-secured seller, a volatility spike is a mark-to-market event you can sit through. On portfolio margin it is a squeeze from both sides at once.

Margin models reprice your positions under stress scenarios, and those scenarios include volatility expansion. So a volatility spike raises your margin requirement at the same moment it lowers your account value. Requirement up, equity down, and the gap closes from both ends. The forced-liquidation risk in a short-premium book usually arrives through this door rather than through any single position going wrong.

What a drawdown model does and does not cover

Worth being straight about the limits here, including our own.

The risk engine behind levelbox prices volatility expansion into its drawdown scenarios. It does not model a crash with volatility held flat, which would badly understate the damage to a short-premium book. What a scenario like that gives you is the size of the loss, not its composition — how much came from spot and how much from volatility. The composition is the part that determines the fix, because if the loss is mostly spot you trim notional, and if it is mostly volatility you shorten tenor, and doing the first when you needed the second leaves the exposure exactly where it was.

There is also a shape of event that a drawdown ladder cannot reach at all. Implied volatility is modelled as a function of the spot move, so "volatility spikes while the stock barely moves" — the 5 August 2024 shape, or the 5 February 2018 one — does not appear anywhere in the table, at any depth. Anyone stressing a short-premium book off spot scenarios alone inherits that blind spot, whatever tool they are using.

Both of those now ship

The composition is available. The risk page reprices the whole book a second time against a volatility-free copy of the same assumptions and takes the difference, which gives an exact split rather than a sum of vegas — and summing vega is precisely what you cannot do here, because vega itself moves as spot falls. The interaction between the two is not attributed to either side; splitting it would need an arbitrary ordering convention that quietly flatters whichever leg you sequenced first, so it is reported as its own term and labelled as such.

The volatility-spike scenario ships as its own ladder — market implied volatility at 1.5×, 2× and 3× today's, each paired with a mild spot move rather than a crash — and can be turned on as a third budget alongside the crash and assignment ones. It is off by default, because a budget that silently changes your plan the day it appears is worse than no budget at all.

Two things we learned building it are worth passing on, because neither was obvious in advance.

The first is that a "mild" paired spot move is harder to specify than it sounds. Our first version scaled that move by each name's beta and capped it with the same cap the crash row uses. A short-premium book is systematically high-volatility, so almost every name pinned that cap, and the "mild −5%" became −15%. The spot term then swamped the volatility term by roughly ten to one: the volatility row was a second crash row wearing a different label, and a budget set against it was mostly budgeting direction. It needed its own, tighter cap to become the thing it claimed to be.

The second is that a short-dated book barely registers on this scenario, and not because the model is wrong. Vega scales with the square root of time, so weeklies have very little of it left to shock. Run the same book with its expiries pushed out to thirty days and the pure volatility loss nearly triples. If your volatility number looks reassuring, check the tenor of the book it was computed on before you take comfort from it.

What is still an assumption

The calibration gap is real and unclosed. Doing this properly means measuring how each name's implied volatility responds to a market-wide move, and that takes a long run of paired observations spanning more than one volatility regime — quiet stretches teach you very little about how a name behaves when volatility triples. Our implied-volatility history is a few weeks deep and not one of the two hundred-odd symbols we track has the twenty-plus observations a credible estimate would need.

So the per-name volatility response runs on a stated assumption rather than a measurement, and the page says so in those words. Fitting that relationship on a short, calm sample would produce a number carrying far more authority than information. It is the same reasoning behind our implied-volatility rank showing "building history" rather than a percentile computed from too few snapshots. An acknowledged gap is more useful than a confident number with nothing behind it, and it is a single function to swap when the history matures.

The practical takeaways stand on their own arithmetic regardless of what any risk model tells you. Shorter tenors pay a better rate per unit of volatility risk — though that rate has to be read against a risk figure on the same clock, or the comparison flatters the short end. Vega grows as a position moves against you, so the exposure you measured at entry understates the one you are holding in a drawdown. And volatility risk is the exposure your diversification does least to help with, which makes it the one most worth adding up deliberately.

levelbox.ai exists to make this layer legible — the premium, the yield, the assignment odds and the risk behind each candidate, with the assumptions and the gaps stated rather than hidden. Analytical and educational tooling, not investment advice. Nothing here is a recommendation to buy or sell anything; work through the numbers on your own book.