The rate vol surface is the market's summary of optionality across expiry, tenor, and strike. Unlike equity options — which have a 2D surface (expiry × strike) — rate options form a 3D cube: expiry × tenor × strike (for swaptions, with tenor being the swap length) plus a separate cap vol surface (expiry × strike for each caplet). Models that calibrate only to ATM vols are blind to the skew and smile; they systematically misprice OTM caps, swaption strangles, and CMS spread options. This lesson describes how the vol surface is structured, what shapes it takes in practice, how normal vol replaced Black vol as the standard in EUR markets, and how the SABR parametrisation provides a consistent interpolation framework across strikes.
In this lesson
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- The Swaption Vol Matrix
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- The Cap Vol Surface (Vol Cube)
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- Normal Vol and the Negative-Rate Era
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- The SABR Parametrisation
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- Calibrating Models to the Vol Surface
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- Where This Goes Next
Before you start
- Pricing Rate Options in Short-Rate Models: Trees and Closed Forms
- Smile Extensions: Displaced Diffusion, CEV, and Beyond
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