A volatility surface brings together two views: skew across strikes and term structure across expirations. Each point is an IV inferred from an option quote under a chosen model. A surface is a way of organizing prices; it is not a directly observed physical law of future returns.
Read an illustrative surface
| Strike | 30 days | 60 days | 90 days |
|---|---|---|---|
| $90 | 34 | 31 | 29 |
| $100 | 28 | 26 | 25 |
| $110 | 26 | 25 | 24 |
Read down the 30-day column: IV falls from 34% at strike $90 to 26% at $110, a downward strike skew in this sample. Read across the $100 row: 28%, 26%, 25% is a downward term structure. These two observations coexist. Neither implies that the $90 put must be a profitable sale.
Coordinates matter
Fixed strike, strike divided by forward price and delta are different horizontal coordinates. When spot changes, the same $100 strike moves to a different moneyness. A rule that holds IV fixed at each strike can produce different prices and Greeks from a rule that moves the smile with spot or delta.
Record whether IV is derived from calls, puts or a combined convention, and whether the pricing model supports dividends and early exercise appropriately. An American-option IV fitted with a simplified European formula may absorb model error into the volatility number.
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Shock the parts separately
A parallel three-point IV rise adds three to every cell. A skew steepening could instead raise the $90 row values by five points while leaving the $110 values unchanged. An event shock might affect the 30-day maturity most. These are different scenarios even if an average volatility statistic barely changes.
Suppose a position has +$80 vega per point in the 30-day expiry and −$50 in the 60-day expiry. A parallel two-point rise approximates +$60. If only the 30-day expiry falls four points, the same vega snapshot approximates −$320. One net-vega number conceals the difference.
Clean quotes before fitting
Exclude or investigate stale, crossed and implausible quotes. Use bid/ask IV ranges to express uncertainty when a midpoint is unreliable. Interpolation should avoid impossible option-price relationships across strikes and maturities; smoothness alone does not make a fitted surface arbitrage-consistent.
For a large stress, reprice each leg with its new coordinates and remaining life. A local sensitivity map can guide which shocks to examine, but a single Greek cannot replace the full contract valuation, exercise terms and execution costs.
