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Enron Mail |
---------------------- Forwarded by Lon Draper/CAL/ECT on 05/23/2001 05:16 PM --------------------------- From: Paulo Issler/ENRON@enronXgate on 05/22/2001 01:39 PM To: Lon Draper/CAL/ECT@ECT cc: Stinson Gibner/ENRON@enronXgate, Claudio Ribeiro/ENRON@enronXgate Subject: Quanto Swap Lon: Please find attached a spreadsheet and a presentation we put together for the Weather Desk on the quanto swap valuaion and hedging. We concluded that the swap pricing needs an extra term to account for the correlation between forward gas price returns and HDDs. This extra term results from the product of the mentioned correlation, gas daily volatility, HDD standard deviation, and the time period when gas forward prices and HDDs are correlated. The case in question prices a quanto swap for a particular day of the season. On the presentation, the valuation formula presents the pricing in terms of blended correlation. The SQRT of the time to valuation will vanish when the expression of the blended correlation is substituted. The spreadsheet shows the making to market of such contract as well as the dynamic hedging that is necessary when the forecast HDD starts changing. Note that the hedging demands a fairly steady position in HDDs and that your gas position poses significant changes when you get into the correlated period. In your particular case the pricing formula follows the same basic stucture and principles. The parameters, however, have a different meaning. The difference comes from the fact that you are paying the HDD differencial in month "j-1" with gas "currency" of month "j". The formula becomes: Vt = DF * TS * [ Ptj * [ [Dtj-1 - Kj-1] + SIGd * SIGp2 * RHO * SQRT(T-T1) ] ] Where: Vt = value of the quanto swap today. Ptj = forward gas price for month j Dtj-1 = expected total accumulated HDDs for the month j-1 Kj-1 = strike of the swap for month j-1 (may be equat Dtj-1) SIGd = standard deviation of accumulated HDDs for month j-1 SIGp2 = gas volatility when contract is prompt month (period when HDDs and gas prices are correlated). RHO = correlation between forward contract and acumulated HDDs for month j-1. (T-T1) = time in years when HDDs and gas prices are correlated. TS = Ticket Size or volumetric factor (expressed in MMBTUs/HDDs) DF = discount factor - the swap settles at the end of month j-1. Finally, I appolagize for having my write-up in an e-mail. Please do not hesitate to call me with your questions. Paulo Issler x 56274
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