Book Review: Energy Derivatives: Pricing

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Book Review Energy Derivatives Pricing Risk
Management, Clewlow L., Strickland C.,
2000Chapter 4 Energy Forward Curves

• Li Xu
• Lunch at Lab Talk
• Department of Mathematics Statistics
• University of Calgary

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Outline

• Introduction
• Forward Curves in the Debt Market
• Constructing Forward Curves
• Cost of Carry Relationship
• Forward Price Bounds for Energies
• Seasonality in Prices
• Forward Curves in the Electricity Market
• Arbitrage Pricing Approach
• The Econometric Approach
• The Spot Price Modeling Approach

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Introduction

• The forward curve contains information about the
  prices an investor can lock into today for
  different times in the future.
• Forward prices are also the key inputs to many
  derivative pricing models (See Chapter 8).
• Further discussion can be found in Gabillon
  (1995), Humphreys and Shimko (1997) and Leong
  (1997).

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Market Forward Curves
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Market Forward Curves

• Backwardation futures prices lower than the spot
  prices.
• Contango futures prices higher than the spot
  prices.
• Seasonality
• These three shapes depend on the level of
  transaction costs, convenience yield, and
  seasonal changes in supply and demand.

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Forward Curves in the Debt Markets

• Forward rates are easily implied from the prices
  of bonds and spot interest rates.

• Not arbitrarily set but depend on the
  relationship between traded instruments.
• Calculated based on the observed current spot
  values not the forecasted level of future spot
  values.

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Constructing Forward Curves

• Cost of Carry Relationship
• Forward Price Bounds for Energies
• Seasonality in Prices
• Explain the three shapes of the forward curves in
  the energy market

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Cost of Carry Relationship

• Cost of carry arbitrage (stock market)
• No arbitrage opportunity
• If asset pays a continuous yield

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Forward Price Bounds for Energies

• Consider cost of storage and transportation
• Cost of carry relationship (oil market)
• Contango forward curves

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Forward Price Bounds for Energies

• Convenience yield
• Cost of carry relationship (oil market)
• Backwardation forward curves

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Seasonality in Prices

• Why?
• Has an arbitrage opportunity
• Reasons for the inefficiency of the gas forward
  market (See Leong (1997))

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Forward Curves in the Electricity Market

• Arbitrage Pricing Approach
• The Econometric Approach
• The Spot Price Modeling Approach

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Spot Price seasonality for the electricity market
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Spot Price seasonality for the electricity market
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Reasons for Seasonality

• Leong (1997) suggested the following reasons
• Non-storability of electricity
• Arbitrage relationships which depends on storing
  the energy breakdown
• Electricity is a very regional market

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Arbitrage Pricing Approach

• Link the forward electricity curve to the prices
  of the fuels used to generated the electricity
• Consider conversion process
• Heat rate efficiency of generation
• Relationship
• The shape of the two forward curves are similar
• Take into account of other costs

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The Econometric Approach

• Griswold (1997) discussed a simulation model
• Can be performed by many software packages
• Drawback just a prediction of spot hourly energy
  prices in the future

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The Spot Price Modeling Approach

• Assume the spot price is driven by stochastic
  factors and other key variables
• Similar to interest rate models (e.g. Vasicek
  model (1977) and CIR model (1985))
• Refer to Gabillion (1995) and Pilipovic (1997)

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Thank you!

• lxu_at_math.ucalgary.ca