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
Exchange rates and Inflation
Geo-political risks
Weather
5
Geopolitical and economic events have driven
large movements in world oil prices
Real (Dec 2009) dollars per barrel
Source EIA
6
EIAs central forecast of oil prices remains near
the stated preference of the king of Saudi Arabia
Dollars per barrel
Projections
History
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
Projections
History
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 options 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 Blacks commodity option pricing
  model (1976) to solve for the implied volatility
  that equates the models value with the option
  premium observed in the market
• Blacks 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 EIAs Model

• In our notation
• fk Current price of kth-nearby futures
  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 Blacks
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