SABR model calibration

alanxyz · June 7th, 2007, 8:09 am

Allow for my ignorance.I am trying to calibrate SABR model to FTSE100 index options data of 282 prices. It is the solver in excel that I use. However the solver returns with #NUM! error for several of the 'model implied volatility' cells. I checked the calculation and found that the 'square root' part of the SABR formula for impvol is complex for these cells. What can I do?Thanks.

allenkat · March 19th, 2010, 3:58 pm

A comment about alaxyz's problem: I had some complex number issues too, but that was when rho = 1 or -1...My problem is that I fix the smile and skew 1st by calibrating volvol and rho, but when I change alpha, the smile changes slope. According to Hagan, Alpha should only effect the height of the smile.. any ideas?TY

Alan · March 19th, 2010, 4:28 pm

Welcome to the thread reserved exclusively for allens or alans.Reminds me of a movie in which all the girls were called Heather The SABR parameter alpha x S^(beta-1) should calibrate very closely to the atm implied vol of your shortest maturity options:This is evident from writing the sde asdS = [sig(t) S^(beta-1)] S dB(t)=> alpha S^(beta-1) ~ sig_imp(atm, close-to-expration),where S is the underlying price. If not, suspect you have an error. So, you shouldn't try to impose an alpha, but instead let it float and confirm the above.

Cuchulainn · March 19th, 2010, 7:06 pm

QuoteOriginally posted by: AlanWelcome to the thread reserved exclusively for allens or alans.Sorry to butt in, Alans, but you must see this..In the 70's Alan Whicher was everywhere. Now duck for cover.

Alan · March 19th, 2010, 11:16 pm

Somehow, I didn't know that Alan, but Monty Python makes me laugh even when I don't have a clue.

allenkat · March 20th, 2010, 1:05 am

Thanks Alan,I actually don't have any ATM data..I use day settlements. I am trying to find a model that best simulates futures contracts on NYMEX NG. So trying to fit the smile has not worked out...I did find a paper on "illiquid ..." in which the calibration is done through data saries..I am going to try the Heston model next, unless you have another model in mind.Thank you again!

Alan · March 20th, 2010, 8:46 pm

Well, simulating NG sounds like a completely different problem. If it was my problem,I would talk to experienced traders about what kinds of repetitive events really move themarket. Is it inventory reports, or what? You can model that. Study the time series --what are the important properties? Study the option chains.In the end, I doubt a simple time-homogeneous model like SABR or Heston is going to cut it.