Re: FW: SABR regression

Posted by Peter Caspers-4 on Nov 17, 2014; 5:55pm
URL: http://quantlib.414.s1.nabble.com/Fwd-FW-SABR-regression-tp16042p16046.html

Hi Ferdinando,

I pushed a fix here (effectively it should yield the same results as the file attached earlier)

https://github.com/lballabio/quantlib/pull/170

As far as I remember the reason for the change in the transformation function (for 1.3 or 1.4 ?) were nan / inf values occuring from time to time in the calibration. This is why I replaced the parabolas by truncated parabolas with linear wings (such that the result is C^1).

If you feel that your test case is still working better in 1.2, could you please send some more details (forward, time to expiry), I'd be happy to discuss again then.

Best regards
Peter

On 17 November 2014 13:25, Peter Caspers <[hidden email]> wrote:

Hi Ferdinando,

one problem is the transformation function direct(...) which is buggy for alpha and nu. Can you try the attached version instead and see if it works better ?

I'd like to have a closer look and try on more cases before I send a PR though.

Thanks

Peter

On 17 November 2014 12:06, Ferdinando M. Ametrano <[hidden email]> wrote:

Hi Peter

SABR implementation on the current trunk has a regression compared with QuantLib 1.2.1

While trying to calibrate problematic smiles as:

strike	1.00%	1.13%	1.25%	1.38%	1.50%
vol1	23.20%	20.25%	31.21%	39.02%	50.45%
vol2	16.67%	20.20%	27.85%	32.79%	37.27%

1.2.1 was able to offer these (non-optimal but decent) solutions:

max error	rms error	end criteria	alpha	beta	nu	rho
1.79%	0.94%	StationaryPoint	0.58%	25.00%	346.03%	34.19%
0.65%	0.43%	StationaryPoint	0.62%	25.00%	193.97%	63.66%

the current trunk instead fails for the second smile with error "qlSABRInterpolationAlpha - nu must be non negative: -124.897 not allowed".

If one tries to just use the four leftmost volatilities to simplify the problem, both calibrations fail with the same error. This leads me to believe the problem is about the solver looking for a solution in the negative nu region. If this is the case it could be solved having a positive constraint for nu. Do you agree? Could you please look into it?

Please find attached a spreadsheet reproducing the error. We might even want to add a non regression test to the test suite.

thank you for your help

regards

F

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