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