Topic · Derivatives & Volatility
← All topicsVolatility Modelling
28 articles · 5 checkpoints · 16 deeper reads · 7 reference notes
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Every option on the same stock implies a different volatility depending on its strike and its expiry. Plotted together across both axes at once, those numbers form a landscape, not a single figure, the implied volatility surface.
Local volatility gets every vanilla price right and the dynamics wrong. Stochastic volatility gets the dynamics right and the prices slightly wrong. LSV bolts a correction factor onto a stochastic volatility engine so it does both, and the correction factor has a formula.
Measured volatility paths are far jaggier than any standard model allows. Treating the roughness as a parameter, and finding it sits near 0.1 instead of the textbook 0.5, explains the one thing classical stochastic volatility could never get right: why short-dated skew explodes.
A volatility smile is basically two straight lines joined by a rounded elbow. SVI is the five-parameter hyperbola that says exactly that, which is why it fits a whole expiry of option quotes with five numbers and stays sane where there are no quotes at all.
The grid of option prices already knows what volatility has to be at every price level and every future date. Dupire's formula pulls it out with a single division: how fast a call gains value when you push its expiry further out, divided by how sharply prices bend across strikes.
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