Valuation of Interest Rate Derivatives › The Volatility Surface for Interest Rate Options
Quantitative FinanceAll chapters Valuation of Interest Rate Derivatives › The Volatility Surface for Interest Rate OptionsOne section · Sections in this chapter8 / 13 ↓
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Just as equity options exhibit volatility smiles and surfaces, interest rate options display complex volatility patterns across both strike and expiry dimensions.
Cap Volatility Structure
Cap volatilities are typically quoted across a matrix of strikes and expiries. The at-the-money forward (ATMF) strike corresponds to the current forward swap rate for each cap tenor. Volatilities are then quoted at various strike offsets from ATMF.
Swaption Volatility Cube
Swaption volatilities form a three-dimensional structure, varying by option expiry, underlying swap tenor, and strike. This volatility cube is fundamental to pricing and risk management in the rates market.
Market makers quote swaption volatilities in matrices such as:
| Expiry \ Tenor | 2Y | 5Y | 10Y |
|---|---|---|---|
| 1M | 45.2% | 38.1% | 32.5% |
| 6M | 42.8% | 36.5% | 31.2% |
| 1Y | 40.5% | 35.2% | 30.1% |
| 5Y | 32.1% | 28.9% | 26.5% |
The pattern typically shows higher volatilities for shorter-expiry options and shorter-tenor underlyings. This reflects the mean-reversion tendency of interest rates: longer-horizon rates exhibit less percentage volatility because they're anchored by long-term expectations.
