Selecting Swaption Volatility by Expiry, Tenor, and Strike

Summary

The document explains how to identify the volatility for a swaption using a volatility surface. The relevant coordinates include the option expiry and the tenor of the underlying swap; strike is a further dimension when the data includes a smile or cube. For the example of a right to pay a fixed rate in a future swap, the quoted rate alone does not determine the volatility: one must also know the expiry and swap tenor, and establish whether the requested strike is at the money or off-market.

If only an expiry-and-tenor surface is available, it generally supplies at-the-money volatility rather than the volatility for an arbitrary strike. For an off-market strike, the answer suggests fitting SABR parameters to available strike data, or using a cap surface together with at-the-money swaption volatility through a cap-lifting method. It gives no worked calculation or comparison of methods, so implementation choices and model assumptions remain unspecified.

Key ideas

• Swaption volatility can depend on option expiry, swap tenor, and strike.
• A surface indexed only by expiry and tenor usually provides at-the-money volatility.
• An off-market strike requires strike-sensitive volatility information or an estimation method.
• SABR smile fitting and lifting from caps are proposed ways to obtain additional strike volatilities.

Tags

# Swaption Vol surface


# Swaption Vol surface












¿How can I get the implied vol from a swaption when I have a vol surface with the maturity of the option and the tenor of the swap? For example I want to know what is the volatility for a swaption that gives the holder the right to pay 6.2% in a 3-year swap starting in 5 years.

## Answer by David Duarte (score 1)

https://quant.stackexchange.com/a/51162

Swaption vol can have 3 dimensions: option expiry, underlying tenor and strike.

In your example, if nothing is said, then it's probably ATM (at the money) volatility which means it's the vol for a Swaption with a strike equal to the forward of the underlying.

So if you only have a surface, and not a cube, you probably don't have exactly the information you need.

If you do have vol data for multiple strikes, even if you don't have the 6.2% strike, you could fit SABR parameters to the smile to determine the vol for the strike you need.

Alternatively, if you have a cap surface and a Swaption ATM surface, you could also build other Swaption strike vols with a method called lifting from caps.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.