What is the volatility hump for the 3m LIBOR cap vol and what are its causes?

Advaita · November 13th, 2006, 5:16 pm

Thanks,

NorthernJohn · November 13th, 2006, 9:35 pm

That is quite an open ended question.If you umean the fact that vol starts off small, grows, then falls again, as you look at it plotted against time, then...Next weeks's 3 month Libor is reasonably well known. The Libor in 2 years is less well known, so has a higher vol. The variance keeps increasing, but rates are bounded, a bit. We do not see 3m libor in 50 years as being likely to be above 10%, or below zero, so variance does not drow so quickly. Variance is vol^2 . t, so, as t keeps increasing, and variance starts being bounded, vol must drop.

Advaita · November 14th, 2006, 7:34 pm

Great! I understand now. Thanks.I suppose I can use the same logic to the SWAP RATE to understand why there is a similar hump for a given tenor (or a given forward rate) as we increase the maturity.

NorthernJohn · November 14th, 2006, 9:39 pm

Indeed you can. Swap is a set of correlated resets, so the vol of the string of them is a function of the Libor vols and their correlations.

hli829 · January 5th, 2007, 2:02 pm

Rebonato (1999) has a good explanation on the location of the hump issue.

hli829 · January 5th, 2007, 2:02 pm

Rebonato (1999) has a good explanation on the location of the hump issue.

Advaita · January 18th, 2007, 11:33 pm

hli could you elaborate on it quickly please?