Volatility surface
The volatility surface is implied volatility across both strike and expiry at once, the smile of every expiry laid along the term structure; traders usually read it by delta rather than by strike, so expiries compare on equal terms.
Two dimensions
The smile is IV across strikes for one expiry; the term structure is at-the-money IV across expiries. Put them together and every listed option has a point on one surface: IV as a function of strike and time. A strategy whose legs sit at different strikes and expiries, a calendar or a double diagonal, depends on several points of it at once.
Why traders read it by delta
A fixed strike means different things at different expiries. With BTC at $100,000, a $91,000 put is a typical 25-delta put at 30 days, but at 7 days it is about a 9-delta put, far out of the money, and at 90 days about a 32-delta put, much closer to the money. Comparing IVs strike by strike across expiries compares different kinds of options.
Delta fixes that: a 25-delta put is roughly as likely to finish in the money at any expiry, so it is the same kind of bet. Quoting the surface by delta also follows the volatility level, since the 25-delta strike moves further out when IV rises.
A worked example
| Expiry | 25Δ put IV | ATM IV | 25Δ call IV | 25Δ put strike | 25Δ call strike |
|---|---|---|---|---|---|
| 7 days | 50% | 44% | 43% | ≈ $95,700 | ≈ $104,300 |
| 30 days | 55% | 50% | 47% | ≈ $91,000 | ≈ $110,500 |
| 90 days | 58% | 54% | 52% | ≈ $85,800 | ≈ $123,100 |
Read down the ATM column and you see contango, 44% to 54%. Read across each row and you see the skew: risk reversals of −7, −8 and −6 points, put skews of 6, 5 and 4. The strike columns show why delta is the better axis: the same 25-delta put sits $4,300 below the forward at 7 days and $14,200 below it at 90 days.
Reading the surface
A healthy surface changes smoothly in both directions. What deserves attention is where it breaks pattern: one expiry whose ATM IV stands out from its neighbors (an event inside it), a wing much richer than the same wing one expiry over, or a term structure that has flipped to backwardation. A calendar spread trades the difference between two points of one column; a combo trades the tilt of one row.
How BOSS builds it
For each listed expiry, BOSS reports three points: ATM IV, the average of the at-the-money call's and put's IV, and the IV at the 25-delta put and the 25-delta call, interpolated linearly in delta between the two out-of-the-money quotes whose venue-reported deltas bracket ±0.25. There is no fitted model and no extrapolation: an expiry without a bracketing pair shows no wing value, and every IV is the venue's own mark IV.
Live on BOSS
IV by expiry at the 25-delta put, at the money and at the 25-delta call on the selected venue. Read down a column for the term structure and across a row for that expiry's skew.
| Days to expiry | 25Δ put IV | ATM IV | 25Δ call IV |
|---|---|---|---|
| 0.1 | — | 39.3% | 46.2% |
| 1.1 | 40.7% | 40.3% | 41.9% |
| 2.1 | 32.4% | 32.3% | 33.3% |
| 3.1 | 31.2% | 30.9% | 32.0% |
| 7.1 | 34.1% | 33.2% | 34.1% |
| 14.1 | 35.3% | 34.2% | 34.9% |
| 21.1 | 35.6% | 34.2% | 34.6% |
| 28.1 | 35.9% | 34.4% | 34.7% |
| 56.1 | 37.9% | 36.3% | 36.5% |
| 84.1 | 38.6% | 37.0% | 37.3% |
Common mistakes
- Comparing the same strike across expiries as if it were the same option.
- Assuming the surface moves in parallel: the short end and the wings usually move far more than the long-dated money.
- Treating one odd point as an opportunity before checking for an event inside that expiry, or a wide bid-ask behind its IV.
- Pricing a multi-expiry strategy off one IV, when each leg sits on its own point of the surface.
Where this shows up on BOSS
Educational content, not investment advice. See the disclaimer.