Volatility Smile¶
The volatility smile is the U-shaped curve produced when implied volatility is plotted against strike price for options sharing the same underlying and expiration date. At-the-money strikes sit at the bottom of the curve, while deep out-of-the-money and deep in-the-money strikes show progressively higher implied volatilities. The pattern contradicts the constant-volatility assumption of the Black-Scholes model, revealing that markets price the probability of extreme moves higher than a lognormal distribution predicts.
HOW IT WORKS¶
The smile is an empirical pattern extracted from live option prices rather than a formula. For a fixed underlying and expiration, Black-Scholes is inverted at each strike to solve for the implied volatility that reproduces the market price; plotting those values against strike or moneyness (K/S) produces the curve. A standard quantitative summary is the 25-delta smile steepness metric:
Smile steepness = IV(25Δ put) + IV(25Δ call) − 2 × IV(50Δ)
A positive result confirms a smile; asymmetry between the two wings is the volatility skew. Equity index options typically show a "smirk" — a tilted smile where the put wing is far steeper than the call wing — because crash protection is persistently bid by institutional hedgers. Short-dated smiles are substantially steeper than long-dated ones, so comparisons across expirations require care.
IN TAPEBOARD¶
The Tapeboard options chain displays implied volatility alongside each strike, letting you visualize the smile directly from the live quote grid. Use the IV Chart panel to plot the full smile curve for any expiration; toggle between strike and moneyness (K/S) on the x-axis to normalize across underlyings. The 25-delta skew metric is surfaced in the Volatility Summary widget, updated in real time, so you can monitor smile steepness and wing asymmetry without manual calculation. When comparing expirations, load multiple curves into the Vol Surface view to see how the smile shape shifts across the term structure.