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Enron Mail |
Cc: alex.huang@enron.com, vince.kaminski@enron.com, vasant.shanbhogue@enron.com,
ted.murphy@enron.com, vladimir.gorny@enron.com Mime-Version: 1.0 Content-Type: text/plain; charset=ANSI_X3.4-1968 Content-Transfer-Encoding: quoted-printable Bcc: alex.huang@enron.com, vince.kaminski@enron.com, vasant.shanbhogue@enron.com, ted.murphy@enron.com, vladimir.gorny@enron.com X-From: Tanya Tamarchenko X-To: Naveen Andrews X-cc: Alex Huang, Vince J Kaminski, Vasant Shanbhogue, Ted Murphy, Vladimir Gorny X-bcc: X-Folder: \Vincent_Kaminski_Jun2001_6\Notes Folders\All documents X-Origin: Kaminski-V X-FileName: vkamins.nsf Naveen, your function class a + b(t+c)(-1) corresponds to my beta=3D1. If we are go= ing ?to use certain class of functions we have to specify the range of para= meters?a, b, c, beta, etc. that guarantees us to be able to do out bootstra= pping ?procedure for extracting ffvol. That's what I did for the function= ?a+A*(t+B)(-beta) (see my previous e-mail below). I'll try to come up with= =20 parameter ranges for a+b*exp(-cx) as well. Tanya Naveen Andrews@ENRON 11/17/2000 04:41 PM To: Tanya Tamarchenko/HOU/ECT@ECT cc: Alex Huang/Corp/Enron@ENRON, Vince J Kaminski/HOU/ECT@ECT, Vasant=20 Shanbhogue/HOU/ECT@ECT, Ted Murphy/HOU/ECT@ECT, Vladimir Gorny/HOU/ECT@ECT= =20 Subject: Re: smoothing methodology for extracting forward forward=20 volatilities =20 Tanya, The exponentials we tried earlier (a+bexp(-cx), etc, fit well b= ut=20 gave negative numbers in the bootstrapping. I tried a + b(t+c)(-1) , a standard power law, and as the ?acco= mpanying graph shows (for the 12 months), the fits are quite good.? = In this case, the ffvols do not become negative (I believe this ?corres= ponds to your 0 beta). ? I would have preferred exp(-t) and variants (can= explain owing to ?mean-reverting vols), but the power law might be a pract= ical alternative ?(from an implementation standpoint).?Naveen??? ????Tanya = Tamarchenko@ECT?11/17/2000 02:59 PM?To: Naveen Andrews/Corp/Enron@ENRON, Al= ex Huang/Corp/Enron@ENRON?cc: Vince J Kaminski/HOU/ECT@ECT, Vasant Shanbhog= ue/HOU/ECT@ECT, Vladimir ?Gorny/HOU/ECT@ECT ??Subject: Re: smoothing method= ology for extracting forward forward ?volatilities ??Following up on our d= iscussions I implemented one method for creating forward ?forward curve?fro= m implied vol curve. ?I sorted out 12 forward curves from an original forwa= rd vol curve, each of 12 ?curves corresponding?to certain month. Then I fit= ted each of 12 curves with a function:??y=3Da+A/power(x+b, beta)??I figured= out that when beta is from (0, .5) the above function is suitable ?for per= forming our bootstrapping?routine of deriving ff vols from implied, because= :??y(x+t) * y(x+t) * (x+t) - y(x) * y(x) * tx< 0 for all x= , t.??(I have to double check on this again. Also when beta<0.5 there are s= ome ?combinations of parameters a, A, b, beta?for which above equality hold= s). Even with restriction on beta this class of ?functions represents quite= a variety of shapes.??Below you see the example of fitting as well as the = example of ff vol curve ?constructed from implied vol curve for NG.??I'll t= ry this for power as well.??Any comments???????????????
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