Re: SABR global versus local fit

Posted by terry leitch on Jun 18, 2016; 2:02pm
URL: http://quantlib.414.s1.nabble.com/SABR-global-versus-local-fit-tp17538p17540.html

I was coming to that conclusion but your 2 cents accelerated it. I thought I could salvage the cube by paring down the expirations and tenors used to local choices, but it seems to still be off by about 5-10% in percent of vol points for the trials I’m running.

Did you use linear interpolation on the sabr coefficients? Do you interpolate alpha by expiry and tenor and the other coefs by strike, expiry, and tenor? Do you duration weight the interpolated vols?

I wonder what is the added benefit of using a 4 parameter stochastic model that is arb free at a finite number of times versus just using a 3 dimension interpolation on strike,expiry, and tenor.

Too bad the cube is off. It’s close but not quite.

On Jun 17, 2016, at 3:48 PM, Mike DelMedico <[hidden email]> wrote:

I would ditch the ql implementation of swaption cube, and go with local sabr fits and some robust interpolation methods.  Much more flexible in my opinion.  I ran into problems when data wasn't symmetrical, as is the case in most of the major currencies. Just my two cents.

On Jun 17, 2016 2:01 PM, "terry leitch" <[hidden email]> wrote:

I’m currently writing an interface for Rquantlib into the saber swaption module using SwaptionVolCube1. I have an end of day surface from a well known exchange that covers from 1x1 all the way to 10x30 swaptions at +/- 200bps around ATM. Due to the proprietary nature, I don’t have permission to share but will try to seek it so I can be more specific.

First issue is NA’s. How does quant lib handle them? The data at the front end has from 1-5 strikes with NA’s due to the low rate environment. To keep the strikes consistent across all time I need to put in values, but the fit doesn’t converge at the front end, possibly due to the interpolated values. I’ve tried several extrapolations but none produce a cube that will converge in the fit, always exceeding the max error. My current view is that I need to develop vol cubes for a given problem based on the structure of expirations. So, for a xx5 I build a shorter Does anyone have a view?

Second, how does the cube fit method weight the volatilities for swap tenors? Is it equal weighting? If it is, that would be an issue because the duration of a 1x1 is a fraction of a 1x30. I noticed most error messages in the fit involve 1Y swap tenors, is the fit weighting by duration but then failing on an absolute measure of volatility difference, a difference I might be willing to ignore due to overall magnitude?

Third, are there any examples where the normal vol option has been used?

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