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PFE Simulation Methodology

PFE Simulation Methodology. Dominic J Pazzula Sr. Consultant – RiskAdvisory. About RiskAdvisory.

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PFE Simulation Methodology

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  1. PFE Simulation Methodology Dominic J Pazzula Sr. Consultant – RiskAdvisory

  2. About RiskAdvisory RiskAdvisory (A Division of SAS) RiskAdvisory is a leading provider of integrated risk solutions to energy companies operating in today's volatile energy commodity markets. Founded in 1995 by accomplished energy risk professionals, the company has provided risk software solutions, management consulting and educational services to over 220 clients in the global energy sector. Headquartered in Calgary, Canada, RiskAdvisory produces software solutions that are used by a growing number of well-known energy companies. RiskAdvisory was acquired by business intelligence software leader SAS in 2003.

  3. What is PFE? • Exposure – The amount of money I would lose if a counterparty defaulted. • Future Exposure – Exposure at a future point in time. • Potential Future Exposure – Maximum exposure under normal market conditions for a future point in time.

  4. Huh? • PFE is sort of like VaR. • However, PFE deals with the positive side of the MtM distribution. • Exposure = MAX(0, MtM)

  5. Holding Period • Unlike VaR, PFE usually looks at long holding periods. • VaR is usually concerned with short term fluctuations. • Default risk is usually negligible in the short term.

  6. PFE Through Time • Why should we look at the PFE value for one point in time??? • We shouldn’t.

  7. Calculating PFE Simulate Future Market States Market States Through Time Valuation and Exposure Calculation Engine Portfolio

  8. Issues with Long Dated Simulations • Shape of the volatility forward curve • Non-normality of price distributions • Seasonality of both prices and volatility • Shifting Correlations

  9. Shape of the Forward Volatility Curve • Near months tend to be more volatile than months further out. • This can give us trouble depending on how we simulate our prices.

  10. Non-Normality of Price Distributions • Research has shown commodities price returns do not have a normal distribution. • Excess kurtosis, or “fat tails,” increases the likelihood of extreme events. • Using a normal distribution with excess kurtosis we can underestimate the tails of our distribution.

  11. Non-Normality of Price Distributions

  12. Seasonality • Commodity prices routinely show seasonal behavior. • Commodity volatilities also show seasonal behavior.

  13. Shifting Correlations • Correlations are not constant, but most models assume they are. • As correlations approach 1(-1), aR numbers for an entire portfolio will increase (decrease). • Nirvana would be a model that dynamically simulates correlations as well as prices. • Data is an issue.

  14. Three Simulation Methodologies • Modified Covariance Simulation • Model Based Simulation • PCA Simulation of Forward Curves

  15. Modified Covariance Simulation – Model Definition • Price returns are assumed to be normally distributed. • Variance and Correlations are calculated based on static prices. • Variances are updated using market observed implied volatilities.

  16. Modified Covariance Simulation – Pros • Volatility curve issues are handled by using the implied volatilities. • Simple, easy to implement, and can be explained to management and auditors.

  17. Modified Covariance Simulation – Cons • The model relies on normality assumptions that we know do not hold. • Data for implied volatilities may be stale or non-existent.

  18. Model Based Simulation – Model Definition • Static prices are modeled using econometric techniques. • SAS Whitepaper available at: http://www.riskadvisory.com/pdfs/sasriskdimensionsriskfactor.pdf

  19. Model Based Simulation – Pros • No normality assumptions. • Modeler has full control over how the prices are simulated. • Can closely match simulated values to observed distributions.

  20. Model Based Simulation – Cons • The modeler’s job is a big one. • What worked last month may not work this month. • Automated fitting processes have to be concerned with model convergence.

  21. PCA Simulation of Forward Curves – Model Definition • Forward curve is simulated relative prices and volatilities. • Principal Component Analysis (PCA) is used to reduce the dimensionality of the simulation. • PCA components are modeled using a covariance simulation.

  22. PCA Simulation of Forward Curves – Pros • Forward volatility curve is taken into account. • Simulated variables are minimized.

  23. PCA Simulation of Forward Curves – Cons • PCA still assumes underlying normality of points along the forward curve. • Business logic must be implemented to insure the correct volatilities and prices are aligned for each step in the simulation.

  24. Final Thoughts • PFE models need to capture realistic market movements. • PFE models have to be explainable. • PFE models have to be implemented and maintained. • PFE modeling is a balancing act between these three issues.

  25. Questions? Dominic Pazzula – dominic.pazzula@sas.com

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