Estimating Mid-Curve Swaption Volatility from Spot Swaps
Summary
A mid-curve swaption expires before its underlying swap begins, so its implied volatility cannot be read directly from the ordinary swaption volatility surface. The document describes a way market makers can estimate it by treating the forward-starting swap as a combination of spot-starting swaps.
For an option expiring in one year into a swap starting five years later and ending ten years later, the suggested inputs are the one-year volatilities of the five-year and ten-year spot swaps, together with their correlation over the option period. These inputs are used to derive the volatility of the forward swap. The explanation offers no formula, calibration details, or numerical example, and it does not establish that this approach is the only market convention; the resulting estimate depends on the volatility and correlation assumptions.
Key ideas
- A mid-curve swaption expires before its underlying swap starts.
- Its volatility is not directly available from the regular swaption surface.
- One estimation approach combines spot-swap volatilities with the correlation between those swaps.
- The estimate depends on the selected volatility and correlation inputs.
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Full text
# volatility of a mid curve option # volatility of a mid curve option Question: When checking the volatility surface for, let's say, a swaption, where the the option expires in 1Y and the underlying starts in 1Y and ends in 5Y, one would check the volatility surface for the quoted volatilities and pick the volatility from Exp. 1Yx5Y ; What happens to the volatility of a mid curve option? how do you relate/ interpolate the volatility in this case? let's say the option expires in 1Y, and the asset starts in 6Y and ends in 5Y after start? where on the volatility surface should the volatility of a mid curve option be situated? Or in other words howw do you get the volatility for the 6Y fwd 5Y swap for an option that expires in 1Y ? ## Answer by dm63 (score 11, accepted) https://quant.stackexchange.com/a/29767 A swaption in which the underlying swap starts at a date materially after the expiration date is called a midcurve swaption. The implied volatilities of these can not be obtained from the regular swaption surface. Market makers calculate implied volatilities for midcurves in a number of ways. One popular method is to compute the volatility of the forward swap using the volatilities of two spot starting swaps, and the correlation between them. For example , consider a midcurve option expiring in 1 year into a swap which starts 5 years later and ends 10 years later. The correct volatility can be computed from the 1yrx5yr volatility, the 1yrx10yr volatility , and the correlation between 5yr and 10 yr swaps for the next year.
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