Rebonato's work on cap swaption in BGM

Nonius · Post by **Nonius** » Mon Jun 14, 2004 11:10 am

http://citeseer.ist.psu.edu/cache/papers/cs/25768/http:zSzzSzwww.rebonato.comzSzcapletswaption.pdf/linking-caplet-and-swaption.pdf

I sort of always favored affine over BGM for reasons of analytical tractability, but Rebonato claims that good numerical approximations for swaption vols as linear combos of cap vols can be done. I know this is like, so 5 years ago, but, in your collective experience, how good are these approximations in the real world.

dgn2 · Post by **dgn2** » Mon Jun 14, 2004 11:37 am

I am trying to implement this in my spare time. It looks doable over the next couple weeks. Maybe I can post my results and someone else can be the judge. I would like to hear any experience out there about use of this approximation.

Nonius · Post by **Nonius** » Mon Jun 14, 2004 11:55 am

I only have implemented the calibration component based on the assumption of "good approximation". this calibration is a semi def constaint with a quadradic objective....but, if you want to force the constraint of cap vols, then, it becomes mildly nonlinear, but I know how to do that.

I tried to do Affine twice with the Goldstein approximation, but, thus far my calibration routine is not working very well for that model. Part of this is due to my lousy programming skilz. Goldstein's approach leads to approximations by expanding to fit as many moments as you want.

dgn2 · Post by **dgn2** » Mon Jun 14, 2004 12:04 pm

Mildly nonlinear should not be a problem for Matlab....I hope .

gatarek · Post by **gatarek** » Mon Jun 14, 2004 6:01 pm

(empty post)

Nonius · Post by **Nonius** » Mon Jun 14, 2004 6:04 pm

Well, if Elan can get his sheah together and help me finish the paper, then, we'll have a general nonlinear framework.

Dude, what will it TAKE?

gatarek · Post by **gatarek** » Mon Jun 14, 2004 6:29 pm

(empty post)

Nonius · Post by **Nonius** » Mon Jun 14, 2004 6:30 pm

you gonna show up for the NoniusFest on Wed night?

Nonius · Post by **Nonius** » Sun Jun 20, 2004 7:38 am

Reply to an Existing Message

elan · Post by **elan** » Sun Jun 20, 2004 1:50 pm

Rebonato's approximation to swaption vol as a linear combination is not very accurate and should not be used. Aside from the fact that it is meant to capture the ATM vol only, it can be regarded as the zeroth order term in a crudely designed small noise expansion. Along these lines, a much better expansion is given by Kawai (the pdf file is somewhere on the net) who calculates higher order corrections to the swaption pricing function.

Nonius, this is an interesting paper, thanks!