Message-ID: <32004814.1075857053921.JavaMail.evans@thyme> Date: Wed, 6 Dec 2000 06:39:00 -0800 (PST) From: tanya.tamarchenko@enron.com To: wenyao.jia@enron.com Subject: Re: smoothing methodology for extracting forward forward volatilities Cc: naveen.andrews@enron.com, vince.kaminski@enron.com, debbie.brackett@enron.com, rabi.de@enron.com, jaesoo.lew@enron.com Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Bcc: naveen.andrews@enron.com, vince.kaminski@enron.com, debbie.brackett@enron.com, rabi.de@enron.com, jaesoo.lew@enron.com X-From: Tanya Tamarchenko X-To: Wenyao Jia X-cc: Naveen Andrews, Vince J Kaminski, Debbie R Brackett, Rabi De, Jaesoo Lew X-bcc: X-Folder: \Vincent_Kaminski_Jun2001_9\Notes Folders\Notes inbox X-Origin: Kaminski-V X-FileName: vkamins.nsf Winston, here is a document related to smoothing methodology for FF vols calculation. I am sending you also a spreadsheet prototype model with examples for gas and power. Fitting in the spreadsheet is done with "Solver". I'll figure out how to implement minimization in the code. Thank you, Tanya. Tanya Tamarchenko 11/17/2000 02:59 PM To: Naveen Andrews/Corp/Enron@ENRON, Alex Huang/Corp/Enron@ENRON cc: Vince J Kaminski/HOU/ECT@ECT, Vasant Shanbhogue/HOU/ECT@ECT, Vladimir Gorny/HOU/ECT@ECT Subject: Re: smoothing methodology for extracting forward forward volatilities Following up on our discussions I implemented one method for creating forward forward curve from implied vol curve. I sorted out 12 forward curves from an original forward vol curve, each of 12 curves corresponding to certain month. Then I fitted each of 12 curves with a function: y=a+A/power(x+b, beta) I figured out that when beta is from (0, .5) the above function is suitable for performing 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 some combinations of parameters a, A, b, beta for which above equality holds). 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 try this for power as well. Any comments?