Re: smoothing methodology for extracting forward forward

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---------------------- Forwarded by Vince J Kaminski/HOU/ECT on 11/17/2000=
=20
05:01 PM ---------------------------

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??????????????