Swaption volatility

A basis point is 0.01 of a percentage point, so 100 basis points is 1%. Normal volatility is a width stated directly in rate points. A normal volatility of 25 basis points means 0.25 percentage points of rate.

Lognormal volatility is a percent of the rate itself. Twenty percent of a 4% swap rate is 0.80 percentage points, about 80 basis points. That is a wider assumption than 25 basis points. The two quotes describe different widths, so the quote type has to travel with the number.

An equity volatility surface uses strike and expiration. A swaption grid uses three axes: how long until the option expires, how long the underlying swap runs, and the strike rate. The equity picture, with its own axes, is the volatility surface lesson.

Read one cell of the sketch: the row “1Y expiry” and the column “10Y tenor” is 28 basis points. That is the classroom normal volatility for an option that expires in one year and, if exercised, delivers a ten-year swap. A strike of 4% on that same expiry and tenor is a third axis. The grid drawn here does not show it.

A Black swaption price takes one volatility and returns one price. That volatility is one cell: one expiry, one tenor, one strike. A smile means the volatility changes as the strike moves away from the forward swap rate. How that smile can arise is the SABR lesson.