Re: [Quantlib-dev] FW: SABR regression

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Hi Peter,
I tested your modifications and they work properly. The results are in line with the ones obtained using QL 1.2.
Anyway, the details (forward and time to expiry) are written in the excel file attached in the previous email.

time

fwd

0.1342

1.1075%

0.3833

1.1025%

Thank you very much for your help.

Paolo

Paolo Mazzocchi
Deloitte Consulting Srl
consulente di
FINANCIAL ENGINEERING - Banca IMI
Tel: 02-72615029  Int: 35029
pao...@es...<mailto:pao...@es...>

From: Peter Caspers [mailto:pca...@gm...]
Sent: Monday, November 17, 2014 7:00 PM
To: Ferdinando M. Ametrano
Cc: maz...@li...; QuantLib Mailing Lists; maddalena zanzi
Subject: Re: [Quantlib-dev] FW: SABR regression

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 <pca...@gm...<mailto:pca...@gm...>> 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 <na...@am...<mailto:na...@am...>> 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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