Energy Price Forecasts and Confidence Intervals

1. Energy Price Forecastsand Confidence Intervals George Washington University Research Program in Forecasting and Federal Forecasters Consortium February 18, 2010 Tancred Lidderdale

2. Short-Term Energy Outlook published monthly

3. Factors that influence crude oil prices • Crude oil price forecast error • NYMEX options market implied volatilities and price forecast confidence intervals • EIA Short-Term Energy Outlook price volatility and forecast uncertainty web products

4. Oil prices relate to many uncertain factors Non-OPEC supply growth Inventories Global economic growth OPEC production decisions Global Oil Prices Spare production capacity Speculation, hedging, investment Geo-political risks Exchange rates and Inflation Weather

5. Geopolitical and economic events have driven large movements in world oil prices Real (Dec 2009) dollars per barrel Source: EIA

6. EIA’s central forecast of oil prices remains near the stated preference of the king of Saudi Arabia Dollars per barrel History Projections EIA central forecast Source: EIA Short Term Energy Outlook, Jan. 2010; PIRA

7. EIA expects monthly average oil prices to rise modestly through 2011, but options market valuations indicate a high degree of uncertainty Dollars per barrel History Projections $85 EIA central forecast 95% NYMEX futures price confidence interval

8. WTI Spot Price Forecast Error6-month-out Forecast Forecast error (forecast – actual), dollars per barrel Note: Based on forecasts published from January 2003 through June 2009.

9. WTI Spot Price Forecast Error6-month-out Forecast Mean Absolute Percent Error EIA 28.5% Consultant A 30.4% Consultant B 25.9% NYMEX 25.1% Note: Based on forecast published from January 2003 through June 2009. Source: EIA calculations.

10. WTI Spot Price Forecast Error Note: Based on forecast published from January 2003 through June 2009.

11. Price forecast uncertainty can be derived from the futures options markets

12. Deutsche Bank reports implied volatilities

13. How Are Expected Future Price Volatilities Derived? • Two alternative methods for parameterizing distribution: • Historical • Forward-looking • Alternative Historical Procedures: • Based on past price forecast error • Based on past price volatility • Based on an econometric model of prices • Forward-looking and Market-based Procedure: • Based on implied volatility derived from a commodity pricing model that uses NYMEX options on commodity futures contracts. • We selected the NYMEX implied volatility as the best available. Academic studies generally confirm implied volatility as the best predictor of realized price volatility. However, there is ongoing research that we will follow closely.

14. What is Implied Volatility? • Volatility can easily be measured using past prices of the asset • Implied volatility of an option contract is the volatility implied by the option’s market premium based on an option pricing model. • This forward-looking estimate of volatility comes from pooling expectations of those who are trading in the market.

15. How Are NYMEX Implied Volatilities Calculated? • We use at- and near-the-money implied volatilities published by the NYMEX, which inverts Fischer Black’s commodity option pricing model (1976) to solve for the implied volatility that equates the model’s value with the option premium observed in the market • Black’s model makes strong assumptions that continue to be debated, among them: • log returns are normally distributed, so prices are log-normally distributed and follow a geometric Brownian motion, also known as a geometric Weiner process • constant mean and variance • transaction costs are de minimus • a riskless portfolio consisting of options and the underlying asset can be continuously rebalanced to return the risk-free rate • investor decisions ignore tax effects

16. The Assumptions of EIA’s Model • In our notation fk = Current price of kth-nearbyfutures contract = Mean logarithmic return sk = Current implied volatility of kth-nearby option dt = Infinitesimal change in time (∆t, as ∆t → 0) tk = Time to expiry of kth contract (% of 252-day year) za/2 = Standardized normal value for a level of confidence • Model assumptions: • log returns of futures are normally distributed, and can be represented by the following equation: • this means prices follow a geometric Brownian motion (GBM) and are log-normally distributed

17. Deriving the Confidence Intervals from Black’s Model • Transform the equation • Then take the expectation for returns • The expected value is treated as an equality, and, in the standard formulation, the expected value is scaled to expiry so that

18. The Standard Confidence Interval for Futures • Setting , consistent with the standard martingale assumption [cf, Ogawa (1988)] yields: • Under the standard formulation, the lower and upper limits of the confidence interval for prices are: • The confidence interval limits for prices are consistent with the lognormal distribution, and take the form used in most applications – e.g., Federal Reserve Board presentations.

19. The Revised Limits of the Confidence Intervals • With this imposed correction for the drift in the sigma-squared term, the lower and upper limits of the confidence interval (for price) take the following form: • Imposing a correction factor is consistent with the literature – cf, Newell and Pizer (2003). • Methodology was reviewed by academics, practitioners and Fed economists, and deemed reasonable. • One reviewer suggested a “richer” approach with “mean reversion, seasonality, jumps, and even regime shifts” in modeling the distribution • Another suggested exploring risk-neutral density models, a la Melick and Thomas (1992) and Jackwerth (2004).

20. Options premiums are reported for a wide range of strike prices Option Premiums, April 2009 (1-month) contract Option Premiums, Sept. 2010 (18-month) contract

21. Consequently, reported implied volatility depends on the strike price chosen Question 2. Which strike price (or prices) do we use to track implied volatility Implied Volatility, April 2009 (1-month) contract Implied Volatility, Sept. 2010 (18-month) contract

22. Begin With NYMEX Price Path

23. Calculate Confidence Limits for Each Monthfor Any Given Confidence Level Monthly averages are discrete observations rather than a continuous time series

24. Present as Continuous Lines for Visual Convenience

25. Future Research • Do implied volatilities continue to perform as the best predictors of realized price volatility? [cf, Szakmary, et al (2003) and Duffie and Gray (1995)] • Are prices log-normally distributed or more leptokurtic (“fat-tailed”)? [cf, Jackwerth (2004)] • Are there better alternatives to the Black model specific to energy commodities – e.g., risk-neutral density and model-free methods? [cf Melick and Thomas (1992) and Jackwerth (2004)] • Can elasticity models add explanatory power to implied volatility models – i.e., are we able to demonstrate the “shock” needed to affect price and volatility expectations [cf, Hamilton (2009a, b)]

26. Future Research • Are implied volatilities of exchange- and non-exchange-traded commodities markedly different? Do trading markets increase or decrease volatility? • Is there a relationship between money flows and/or open interest on implied volatility during and across calendar months? • Does open interest provide additional insight into understanding market volatility? This would require a collaboration with the CFTC on studies of participation in options markets.

27. New Monthly STEO Crude Oil and Natural Gas Price Uncertainty Web Page

28. Crude Oil Price confidence intervals

29. Confidence limits can be customized in Excel spreadsheet