Value at Risk An Introduction To Its Use In An Energy Trading Company Krishan Sabharwal Manager, Risk & Analytics BP Energ...
4 Who We Are BP. Amoco, ARCO, and Castrol have come together to create one of the largest energy companies on the planet.
Global Presence
8 <ul><li>we’re the largest gas and oil producer in North America </li></ul><ul><li>we’re fuel for travelers at 1400 airpo...
Top North American Marketers by Volume (Bcf/d) Source: Gas Daily Note: Duke, AEP and Dynegy are no longer reporting volume...
Value at Risk <ul><li>“ Value at risk (VaR) is an attempt to provide a single number for senior management summarizing the...
Typical Energy Trading Risk Factors <ul><li>Natural gas futures prices </li></ul><ul><li>Natural gas basis (Delivery locat...
Definitions of Volatility
VaR Methodologies <ul><li>Analytic (Variance-Covariance) </li></ul><ul><ul><li>RiskMetrics </li></ul></ul><ul><li>Monte Ca...
Analytic VaR <ul><li>Benefits: </li></ul><ul><ul><li>Fast </li></ul></ul><ul><ul><li>Relatively easy to understand </li></...
The Analytic VaR “Bible”
Analytic VaR Example
Analytic VaR Example Cont.
Analytic VaR Example Cont.
Analytic VaR Matrix Math
Monte Carlo VaR <ul><li>Benefits: </li></ul><ul><ul><li>Handles non-linear (option) portfolios well via full portfolio val...
Monte Carlo VaR Technique <ul><li>Methodology: </li></ul><ul><ul><li>Estimate volatility of each underlying risk factor in...
Monte Carlo based VaR
Historical Simulation <ul><li>Benefits: </li></ul><ul><ul><li>No volatility or correlation data required </li></ul></ul><u...
Historical Simulation Cont. <ul><li>Which Time period would you select? </li></ul>Historic Henry Hub Gas Volatility & Pric...
Historical Simulation Cont. <ul><li>Methodology: </li></ul><ul><ul><li>Select historic dataset as a proxy for the future <...
Stress Testing <ul><li>Benefits: </li></ul><ul><ul><li>Same as historical simulation, generally </li></ul></ul><ul><ul><li...
Principal Components Analysis w/ MC Simulation <ul><li>Benefits: </li></ul><ul><ul><li>Handles highly correlated datasets ...
Principal Components Analysis w/ MC Simulation Cont. <ul><li>Good fit for BP Energy’s natural gas position </li></ul><ul><...
Principal Components Analysis w/ MC Simulation Cont. <ul><li>Methodology: </li></ul><ul><ul><li>Extract principal componen...
Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA underlying dataset:
Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA results:
Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA results:
Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA results:
 
 
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bp Value at Risk An Introduction To Its Use In An Energy ...

  1. 1. Value at Risk An Introduction To Its Use In An Energy Trading Company Krishan Sabharwal Manager, Risk & Analytics BP Energy Company November 7 th , 2003
  2. 2. 4 Who We Are BP. Amoco, ARCO, and Castrol have come together to create one of the largest energy companies on the planet.
  3. 3. Global Presence
  4. 4. 8 <ul><li>we’re the largest gas and oil producer in North America </li></ul><ul><li>we’re fuel for travelers at 1400 airports in 87 countries </li></ul><ul><li>we are among the most profitable petrochemical producers in the world </li></ul><ul><li>we’re the largest marketer of raw materials used to make CD boxes, insulation and other everyday products </li></ul><ul><li>we are the leading solar producer in the world </li></ul>Performance Capital Employed* $63 Billion * Excludes liabilities for current and deferred taxation of $4 billion for total capital employed of $59 billion
  5. 5. Top North American Marketers by Volume (Bcf/d) Source: Gas Daily Note: Duke, AEP and Dynegy are no longer reporting volumes; El Paso did not respond to queries 2.8 3.5 Oneok 9 10.5 4.0 Reliant 7 4.6 8.8 ConocoPhillips 5 9.5 9.5 Sempra 4 5.4 3.5 Williams 10 2.2 3.5 Nexen 8 3.8 4.2 Cinergy 6 9.2 9.9 Coral 3 21.4 12.6 Mirant 2 14.9 20.1 BP 1 1Q02 1Q03 Company Rank
  6. 6. Value at Risk <ul><li>“ Value at risk (VaR) is an attempt to provide a single number for senior management summarizing the total risk in a portfolio of financial assets.” – Hull </li></ul><ul><li>JP Morgan’s 4:15 report to senior management </li></ul><ul><li>Usually takes the form of “We are X percent certain that we will not lose more than V dollars in the next N days.” </li></ul><ul><ul><li>X typically 95 – 99% </li></ul></ul><ul><ul><li>N typically 1 day </li></ul></ul><ul><ul><li>V typically very large, depending on X and N! </li></ul></ul>
  7. 7. Typical Energy Trading Risk Factors <ul><li>Natural gas futures prices </li></ul><ul><li>Natural gas basis (Delivery location price – Futures Price) </li></ul><ul><li>Electricity forward market prices </li></ul><ul><li>Crude oil futures prices </li></ul><ul><li>Crude products (gasoline, diesel, etc.) prices </li></ul><ul><li>Coal prices </li></ul><ul><li>Emission credit prices </li></ul><ul><li>Interest rates </li></ul><ul><li>Etc. </li></ul><ul><li>Green = Typical BP Energy (Houston) exposures </li></ul>
  8. 8. Definitions of Volatility
  9. 9. VaR Methodologies <ul><li>Analytic (Variance-Covariance) </li></ul><ul><ul><li>RiskMetrics </li></ul></ul><ul><li>Monte Carlo Simulation </li></ul><ul><li>Historical Simulation </li></ul><ul><li>Stress Testing </li></ul><ul><li>Principal Components Analysis (w/ MC Simulation) </li></ul>
  10. 10. Analytic VaR <ul><li>Benefits: </li></ul><ul><ul><li>Fast </li></ul></ul><ul><ul><li>Relatively easy to understand </li></ul></ul><ul><ul><li>Allows for VaR “Greeks” (VaRdelta, Component VaR) </li></ul></ul><ul><li>Weaknesses </li></ul><ul><ul><li>Doesn’t handle non-linear (option) portfolios well </li></ul></ul><ul><ul><li>Highly correlated market exposures can lead to dysfunctional statistics </li></ul></ul><ul><ul><li>Exposure “bucketing” typical to keep dataset manageable </li></ul></ul><ul><ul><li>Assumes returns are normally distributed </li></ul></ul>
  11. 11. The Analytic VaR “Bible”
  12. 12. Analytic VaR Example
  13. 13. Analytic VaR Example Cont.
  14. 14. Analytic VaR Example Cont.
  15. 15. Analytic VaR Matrix Math
  16. 16. Monte Carlo VaR <ul><li>Benefits: </li></ul><ul><ul><li>Handles non-linear (option) portfolios well via full portfolio valuation </li></ul></ul><ul><ul><li>Highly correlated market exposures not a problem </li></ul></ul><ul><ul><li>Relatively easy to understand </li></ul></ul><ul><li>Weaknesses </li></ul><ul><ul><li>Doesn’t allow for VaR “Greeks” (VaRdelta, Component VaR) </li></ul></ul><ul><ul><li>Generally slower than closed-form techniques </li></ul></ul><ul><ul><li>May require high number of iterations to achieve confidence in results </li></ul></ul><ul><ul><li>May still require “bucketing” </li></ul></ul><ul><ul><li>Normal return distribution assumption (typically) </li></ul></ul><ul><ul><li>The “Monte Carlo” effect! </li></ul></ul>
  17. 17. Monte Carlo VaR Technique <ul><li>Methodology: </li></ul><ul><ul><li>Estimate volatility of each underlying risk factor in BP Energy’s portfolio: </li></ul></ul><ul><ul><ul><li>Nymex natural gas futures contracts </li></ul></ul></ul><ul><ul><ul><li>Basis (physical delivery location – Nymex) </li></ul></ul></ul><ul><ul><ul><li>Electricity forward contracts </li></ul></ul></ul><ul><ul><li>Estimate the correlation of the risk factors: </li></ul></ul><ul><ul><ul><li>Intracommodity (June ’02 Nymex gas to July ’02 Nymex gas) </li></ul></ul></ul><ul><ul><ul><li>Cross Commodity (June ’02 Nymex gas to June ’02 Cinergy electricity) </li></ul></ul></ul><ul><ul><ul><li>Hybrid (June ’02 Nymex gas to June ’02 Chicago Citygate gas) </li></ul></ul></ul><ul><ul><li>Simulate all risk factors & revalue the portfolio for each iteration </li></ul></ul>
  18. 18. Monte Carlo based VaR
  19. 19. Historical Simulation <ul><li>Benefits: </li></ul><ul><ul><li>No volatility or correlation data required </li></ul></ul><ul><ul><li>Intuitive – “grounded in reality” </li></ul></ul><ul><ul><li>Fast </li></ul></ul><ul><ul><li>Handles non-linear (option) portfolios well via full portfolio valuation </li></ul></ul><ul><ul><li>Actual return distribution used vs. Normal assumption </li></ul></ul><ul><li>Weaknesses: </li></ul><ul><ul><li>“ Past returns are not indicative of future results” </li></ul></ul><ul><ul><li>VaR is a function of historical time period selection – subjective! </li></ul></ul><ul><ul><li>May be limited historical data for certain commodities </li></ul></ul>
  20. 20. Historical Simulation Cont. <ul><li>Which Time period would you select? </li></ul>Historic Henry Hub Gas Volatility & Price Levels (1/1/95 - 12/31/01) 0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 200% 01/03/95 07/22/95 02/07/96 08/25/96 03/13/97 09/29/97 04/17/98 11/03/98 05/22/99 12/08/99 06/25/00 01/11/01 07/30/01 20-day Moving Annualized Volatility $- $1 $2 $3 $4 $5 $6 $7 $8 $9 $10 Price ($/MMbtu) Prompt NYMEX Volatility Prompt NYMEX Price
  21. 21. Historical Simulation Cont. <ul><li>Methodology: </li></ul><ul><ul><li>Select historic dataset as a proxy for the future </li></ul></ul><ul><ul><li>Subject existing portfolio to historic data return distribution, revaluing the portfolio at each step </li></ul></ul><ul><ul><li>As with MC simulation – find the loss at your confidence level from the resultant P/L distribution </li></ul></ul>
  22. 22. Stress Testing <ul><li>Benefits: </li></ul><ul><ul><li>Same as historical simulation, generally </li></ul></ul><ul><ul><li>Allows management to specify a price environment to stress the portfolio </li></ul></ul><ul><li>Weaknesses: </li></ul><ul><ul><li>Allows management to specify a price environment to stress the portfolio </li></ul></ul><ul><ul><li>“ Grounded in reality” is a matter of perception </li></ul></ul>
  23. 23. Principal Components Analysis w/ MC Simulation <ul><li>Benefits: </li></ul><ul><ul><li>Handles highly correlated datasets very well </li></ul></ul><ul><ul><li>Reduces the number of simulated underlying risk factors </li></ul></ul><ul><ul><li>Full portfolio valuation – handles non-linear (options) instruments well </li></ul></ul><ul><li>Weaknesses: </li></ul><ul><ul><li>Not as fast as analytic approach </li></ul></ul><ul><ul><li>Can’t develop VaR “Greeks” </li></ul></ul><ul><ul><li>“ Black Box” effect </li></ul></ul>
  24. 24. Principal Components Analysis w/ MC Simulation Cont. <ul><li>Good fit for BP Energy’s natural gas position </li></ul><ul><ul><li>63 natural gas delivery locations in North America </li></ul></ul><ul><ul><ul><li>Majority of trading activity in first 13 months or so. </li></ul></ul></ul><ul><ul><ul><li>Analytic or MC Correlation matrix = 819 x 819 = 670,761 elements – very highly correlated – a statistical nightmare! </li></ul></ul></ul><ul><ul><li>Embedded optionality in many positions </li></ul></ul><ul><ul><ul><li>Requires a full portfolio valuation approach to capture the “Greeks” </li></ul></ul></ul>
  25. 25. Principal Components Analysis w/ MC Simulation Cont. <ul><li>Methodology: </li></ul><ul><ul><li>Extract principal components, or independent normally distributed return factors, from historic dataset </li></ul></ul><ul><ul><li>Simulate the the principal components to generate forward curve changes </li></ul></ul><ul><ul><li>Revalue the portfolio under each iteration of forward curve change </li></ul></ul><ul><ul><li>As with MC simulation – find the loss at your confidence level from the resultant P/L distribution </li></ul></ul>
  26. 26. Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA underlying dataset:
  27. 27. Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA results:
  28. 28. Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA results:
  29. 29. Principal Components Analysis w/ MC Simulation Cont. Natural Gas PCA results:
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