re : fyi : uk var issues 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 olmm 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 ol . 8 mm .
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 ol 0 . 405 mm o 3 . 180 mm
0 . 1 ol 0 . 134 mm o 3 . 197 mm
0 . 2 ol 0 . 270 mm o 3 . 185 mm
0 . 3 ol 0 . 030 mm o 3 . 245 mm
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
re : fyi : uk var issues
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 olmm 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 ol . 8 mm .
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 ol 0 . 405 mm o 3 . 180 mm
0 . 1 ol 0 . 134 mm o 3 . 197 mm
0 . 2 ol 0 . 270 mm o 3 . 185 mm
0 . 3 ol 0 . 030 mm o 3 . 245 mm
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