Volatility smile from a quote board
Put in the bid and ask for a strip of strikes and the tool backs out an implied volatility for each side, fits a smile through them, and shows where the market disagrees with its own curve. Loaded with a worked example — overwrite it with your own board.
- Forward
- 100.33
- Level at forward
- 25.4%
- Skew
- -0.329
- Curvature
- 0.675
- Fit error
- 0.86 pts
The board
IV 35.3%/ 38.3%fitted 36.3%rich / cheap +0.67
IV 32.1%/ 33.4%fitted 32.7%rich / cheap +0.10
IV 28.9%/ 30.0%fitted 29.7%rich / cheap −0.27
IV 26.1%/ 27.8%fitted 27.4%rich / cheap −0.39
IV 23.5%/ 26.7%fitted 25.5%rich / cheap −0.38
IV 25.3%/ 27.2%fitted 24.0%rich / cheap +2.25
IV 22.4%/ 23.1%fitted 22.9%rich / cheap −0.16
IV 20.3%/ 23.0%fitted 22.1%rich / cheap −0.28
1 strike priced clear of the curve. 105 call is rich by 2.25 vol points. The whole bid-ask band sits on one side of the fit, so this is not a rounding artefact — which is the beginning of a question, not the answer to one.
Method. Each side of each quote is inverted through the same Black-Scholes as the options P&L calculator, by Newton's method kept inside a bisection bracket. The curve is a quadratic in log-moneyness against the forward, σ(k) = a + b·k + c·k², fitted by least squares with each quote weighted by the inverse square of its own bid-ask width in volatility points. The three coefficients are reported above as level, skew and curvature.
A quadratic rather than SVI on purpose: five parameters fitted to eight strikes is unstable, and a curve that jumps around when you change one quote teaches nothing. Quotes that cannot imply a volatility — no bid, a crossed market, or an option so deep in the money that its price carries no vega — are named against the strike and left out of the fit rather than silently dropped.
Rich and cheap are measured against this curve, not against value. A strike flagged here is one the fit disagrees with; the fit is a three-parameter guess drawn through a handful of points, and it is wrong more often than the market is. Read it as a place to look, and note that one badly marked quote drags the curve for every other strike.
For education and analysis. Not investment advice, not a recommendation to trade, and not a substitute for your own pricing.