Book Review: Chapter 6 Spot Price Models and Pricing Standard Instruments

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Book Review Chapter 6 Spot Price Models and
Pricing Standard Instruments

• Anatoliy Swishchuk
• Dept of Math Stat, U of C
• Lunch at the Lab Talk
• January 31st, 2007

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Outline

• Intro
• Single Factor Models
• Two Factor Models
• Three Factor Models
• Choosing a Spot Price Model

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Intro

• Models for Pricing Energy Derivatives
• Formulated in Terms of the Spot Energy Price
• Derivatives Futures/Forwards, European Options
• Range from 1 factor Black (1976) model to a
  three-factor model with stochastic convenience
  yield and stochastic term structure of interest
  rate
• Comments seasonal factors
• Volatility Smile Numerical Techniques Chapter
  7 (Lances Talk)

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Single Factor Models

• Futures and Forward Pricing
• Option Pricing
• The Schwartz Single Factor Model
  (Futures/Forward, Option Pricing)

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Single Factor Models SDE vs PDE
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Futures and Forward Pricing (Black, 1976)
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Volatilities (FP)Volatility SP
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Option Pricing (Black, 1976) European Futures
Option
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The Schwartz Single Factor Model (1997)

• Mean-Reverting
• Positive S
• Alpha-mean reverting rate
• Mu-long term level
• Lambda-market price of energy risk

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The Schwartz Single Factor Model (xln S) SDE
and PDE
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Futures and Forward Pricing (Schwartz SF Model)
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Futures and Forward Pricing (Schwartz SF Model)
long maturity level and volatility
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Futures Prices and Their Volatility (Schwartz SF
Model)
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European Call Option Pricing (Schwartz SFM)
Clewlow, Strickland (1999)
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European Call Option Pricing (Schwartz SFM)
Clewlow, Strickland (1999) sT
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European Call Option Pricing (Schwartz SFM)
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Comparison Option Prices in the Black and
Schwartz SFM
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Two Factor Models (Stochastic Convenience Yield)
Gibson Schwartz (1990) Schwartz
(1997) Pilipovich (1997) Hillard Reis (1998)
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Two Factor Models (Stochastic Convenience Yield)
PDE
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Two Factor Models (Stochastic Convenience Yield)
Futures/Forward Pricing (Schwartz(1997))
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Two Factor Models (Stochastic Convenience Yield)
Futures/Forward Pricing ( HR (1998))
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Two Factor Models (Stochastic Convenience Yield)
Futures Pricing (Schwartz(1997))
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Two Factor Models (Stochastic Convenience Yield)
Volatility of Futures Pricing (Schwartz(1997)HR(1
998))
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Two Factor Models (Stochastic Convenience Yield)
Volatility (Schwartz(1997))
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Two Factor Models Option Pricing (Clewlow
Strickland (1999))
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The Schwartz 1 Factor Approximation Rate of
Change in the Futures Prices (Two Factor vs One
Factor)
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The Schwartz 1 Factor Approximation Rate of
Change in the Futures Prices (Two Factor vs One
Factor, convenience yield)
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The Schwartz 1 Factor Approximation Rate of
Change in the Futures Prices (Two Factor vs One
Factor)Shadow Spot Price vs Futures Price
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The Schwartz 1 Factor Approximation Rate of
Change in the Futures Prices (Two Factor vs One
Factor)Shadow Spot Price vs Futures Price
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Three Factor Models

• Schwartz (1997) extension of his TFM (Vasicek
  short term rate r)
• Hillard Reis (1998) interest rate follows HJM
  (1992) model

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Three Factor Models Schwartz (1997)
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Three Factor Models HR (1998)
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Three Factor Models PDE Schwartz (1997) HR
(1998)
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Futures/Forward Pricing (Three Factor Models,
Schwartz (1997))
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Futures/Forward Pricing (Three Factor Models, HR
(1998))
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Volatility of the Futures Prices (SHR)
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TFM Option Pricing (Milstein Schwartz (1998))
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Choosing a Spot Price Model

• For Short Maturity Options on Long Maturity
  Forward Contract Black Model could be used
• For Short Maturity Options on Short Maturity
  Forward Contract Schwartz One Factor Model could
  be used
• Large and Diverse Portfolio of Energy Contracts
  Two Factor Stochastic Convenience Yield Model is
  good

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Choosing a Spot Price Model II

• Not Necessary to Use Three Factor Model
  Stochastic Interest Rate has a relatively minor
  impact on Energy Derivatives Prices
• Jumps?-loss of the simple analytical solutions
  and numerical techniques
• HR-presented a quasi-analytical solution for
  standard options under 3FM with jumps but its
  not consistent with the attenuation of the jumps
  in the case of simple mean reversion

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Summary
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The End

• Thank You for Your Attention!