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Enron Mail |
Vince,
UK VAR breached the limit last week. UK traders asked us to review the correlations across UK gas and power as well as the correlations across EFA slots. We did part of the work last week. Now we'll update the correlations based on historical prices. Tanya. Richard Lewis 10/08/2000 07:31 AM To: Tanya Tamarchenko/HOU/ECT@ECT cc: Oliver Gaylard/LON/ECT@ECT, James New/LON/ECT@ECT, Steven Leppard/LON/ECT@ECT, Rudy Dautel/HOU/ECT@ECT, Kirstee Hewitt/LON/ECT@ECT, Naveen Andrews/Corp/Enron@ENRON, David Port/Market Risk/Corp/Enron@ENRON, Ted Murphy/HOU/ECT@ECT, Simon Hastings/LON/ECT@ECT, Paul D'Arcy/LON/ECT@ECT, Amir Ghodsian/LON/ECT@ECT Subject: Re: VaR correlation scenarios Thanks Tanya, these are interesting results. I am on vacation next week, so here are my current thoughts. I am contactable on my mobile if necessary. Gas to power correlations I see your point about gas to power correlation only affecting VAR for the combined gas and power portfolio, and this raises an interesting point: At a conservative 30% long term correlation, combined VAR is o1mm less than previously expected - so how does this affect the limit breach? Strictly speaking, we are still over our UK power limit, but the limit was set when we were assuming no gas power correlation and therefore a higher portfolio VAR. A suggested way forward given the importance of the spread options to the UK Gas and Power books- can we allocate to the gas and power books a share of the reduction in portfolio VAR - ie [Reduction = Portfolio VAR - sum(Power VAR + Gas VAR)]? Also, if I understand your mail correctly, Matrix 1 implies 55% gas power correlation is consistent with our correlation curves, and this reduces total VAR by o1.8mm. EFA slot correlations The issue of whether our existing EFA to EFA correlation matrix is correct is a separate issue. I don't understand where the Matrix 2 EFA to EFA correlations come from, but I am happy for you to run some historical correlations from the forward curves (use the first 2 years, I would suggest). Our original matrix was based on historicals, but the analysis is worth doing again. Your matrix 2 results certainly indicate how important these correlations are. Closing thoughts Friday's trading left us longer so I would not expect a limit breach on Monday. We are still reviewing the shape of the long term curve, and I'd like to wait until both Simon Hastings and I are back in the office (Monday week) before finalising this. Regards Richard Tanya Tamarchenko 06/10/2000 22:59 To: Oliver Gaylard/LON/ECT@ECT, Richard Lewis/LON/ECT@ECT, James New/LON/ECT@ECT, Steven Leppard/LON/ECT@ECT, Rudy Dautel/HOU/ECT@ECT, Kirstee Hewitt/LON/ECT@ECT, Naveen Andrews/Corp/Enron@ENRON, David Port/Market Risk/Corp/Enron@ENRON, Ted Murphy/HOU/ECT@ECT cc: Subject: Re: VaR correlation scenarios Everybody, Oliver sent us the VAR number for different correlations for UK-Power portfolio separately from UK-Gas portfolio. First, if VAR is calculated accurately the correlation between Power and Gas curves should not affect VAR number for Power and VAR number for Gas, only the aggregate number will be affected. The changes you see are due to the fact that we use Monte-Carlo simulation method, which accuracy depends on the number of simulations. Even if we don't change the correlations but use different realizations of random numbers, we get slightly different result from the model. So: to see the effect of using different correlations between Gas and Power we should look at the aggregate number. I calculated weighted correlations based on 2 curves I got from Paul. As the weights along the term structure I used the product of price, position and volatility for each time bucket for Gas and each of EFA slots. The results are shown below: Inserting these numbers into the original correlation matrix produced negatively definite correlation matrix, which brakes VAR engine. Correlation matrix for any set of random variables is non-negative by definition, and remains non-negatively definite if calculated properly based on any historical data. Here, according to our phone discussion, we started experimenting with correlations, assuming the same correlation for each EFA slot and ET Elec versus Gas. I am sending you the spreadsheet which summaries the results. In addition to the aggregate VAR numbers for the runs Oliver did, you can see the VAR numbers based on correlation Matrix 1 and Matrix 2. In Matrix 1 the correlations across EFA slots are identical to these in original matrix. I obtained this matrix by trial and error. Matrix 2 is produces by Naveen using Finger's algorithm, it differs from original matrix across EFA slots as well as in Power versus Gas correlations and gives higher VAR than matrix 1 does. Concluding: we will look at the historical forward prices and try to calculate historical correlations from them. Tanya. Oliver Gaylard 10/06/2000 01:50 PM To: Richard Lewis/LON/ECT@ECT, James New/LON/ECT@ECT, Steven Leppard/LON/ECT@ECT, Rudy Dautel/HOU/ECT@ECT, Kirstee Hewitt/LON/ECT@ECT, Naveen Andrews/Corp/Enron@ENRON, Tanya Tamarchenko/HOU/ECT@ECT, David Port/Market Risk/Corp/Enron@ENRON cc: Subject: VaR correlation scenarios The results were as follows when changing the gas/power correlations: Correlation VaR-UK Power book VaR- UK Gas book 0.0 o10.405MM o3.180MM 0.1 o10.134MM o3.197MM 0.2 o10.270MM o3.185MM 0.3 o10.030MM o3.245MM 0.4 Cholesky decomposition failed (Not positive definite) 0.5 Cholesky decomposition failed (Not positive definite) 0.6 Cholesky decomposition failed (Not positive definite) 0.7 Cholesky decomposition failed (Not positive definite) 0.8 Cholesky decomposition failed (Not positive definite) 0.9 Cholesky decomposition failed (Not positive definite) 1.0 Cholesky decomposition failed (Not positive definite) Peaks and off peaks were treated the same to avoid violating the matrix's integrity. Interesting to note that for a higher correlation of 0.2 the power VaR increases which is counter to intuition. This implies that we need to look into how the correlations are being applied within the model. Once we can derive single correlations from the term structure, is the next action to understand how they are being applied and whether the model captures the P+L volatility in the spread option deals. From 0.4 onwards the VaR calculation failed. Oliver
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