![Page 1: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/1.jpg)
Book Review: Chapter 6 ’Spot Price Models and Pricing Standard
Instruments’Anatoliy SwishchukDept of Math & Stat, U of C‘Lunch at the Lab’ TalkJanuary 31st, 2007
![Page 2: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/2.jpg)
Outline
Intro Single Factor Models Two Factor Models Three Factor Models Choosing a Spot Price Model
![Page 3: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/3.jpg)
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
(Lance’s Talk)
![Page 4: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/4.jpg)
Single Factor Models
Futures and Forward PricingOption PricingThe Schwartz Single Factor
Model (Futures/Forward, Option Pricing)
![Page 5: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/5.jpg)
Single Factor Models: SDE vs PDE
![Page 6: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/6.jpg)
Futures and Forward Pricing (Black, 1976)
![Page 7: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/7.jpg)
Volatilities (FP)=Volatility SP
![Page 8: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/8.jpg)
Option Pricing (Black, 1976): European Futures Option
![Page 9: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/9.jpg)
The Schwartz Single Factor Model (1997)
Mean-Reverting Positive S Alpha-mean reverting
rate Mu-long term level Lambda-market price of
energy risk
![Page 10: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/10.jpg)
The Schwartz Single Factor Model (x=ln S): SDE and PDE
![Page 11: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/11.jpg)
Futures and Forward Pricing (Schwartz SF Model)
![Page 12: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/12.jpg)
Futures and Forward Pricing (Schwartz SF Model): long maturity level and volatility
![Page 13: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/13.jpg)
Futures Prices and Their Volatility (Schwartz SF Model):
![Page 14: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/14.jpg)
European Call Option Pricing (Schwartz SFM): Clewlow, Strickland (1999)
![Page 15: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/15.jpg)
European Call Option Pricing (Schwartz SFM): Clewlow, Strickland (1999): s=T
![Page 16: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/16.jpg)
European Call Option Pricing (Schwartz SFM)
![Page 17: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/17.jpg)
Comparison: Option Prices in the Black and Schwartz SFM
![Page 18: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/18.jpg)
Two Factor Models (Stochastic Convenience Yield)
Gibson & Schwartz (1990)
Schwartz (1997)
Pilipovich (1997)
Hillard & Reis (1998)
![Page 19: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/19.jpg)
Two Factor Models (Stochastic Convenience Yield): PDE
![Page 20: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/20.jpg)
Two Factor Models (Stochastic Convenience Yield): Futures/Forward Pricing (Schwartz(1997))
![Page 21: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/21.jpg)
Two Factor Models (Stochastic Convenience Yield): Futures/Forward Pricing ( HR (1998))
![Page 22: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/22.jpg)
Two Factor Models (Stochastic Convenience Yield): Futures Pricing (Schwartz(1997))
![Page 23: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/23.jpg)
Two Factor Models (Stochastic Convenience Yield): Volatility of Futures Pricing (Schwartz(1997)&HR(1998))
![Page 24: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/24.jpg)
Two Factor Models (Stochastic Convenience Yield): Volatility (Schwartz(1997))
![Page 25: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/25.jpg)
Two Factor Models: Option Pricing (Clewlow & Strickland (1999))
![Page 26: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/26.jpg)
The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor)
![Page 27: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/27.jpg)
The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor, convenience yield)
![Page 28: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/28.jpg)
The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor):Shadow Spot Price vs Futures Price
![Page 29: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/29.jpg)
The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor):Shadow Spot Price vs Futures Price
![Page 30: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/30.jpg)
Three Factor Models
Schwartz (1997): extension of his TFM (Vasicek short term rate r)
Hillard & Reis (1998): interest rate follows HJM (1992) model
![Page 31: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/31.jpg)
Three Factor Models: Schwartz (1997)
![Page 32: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/32.jpg)
Three Factor Models: HR (1998)
![Page 33: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/33.jpg)
Three Factor Models PDE: Schwartz (1997) &HR (1998)
![Page 34: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/34.jpg)
Futures/Forward Pricing: (Three Factor Models, Schwartz (1997))
![Page 35: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/35.jpg)
Futures/Forward Pricing: (Three Factor Models, HR (1998))
![Page 36: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/36.jpg)
Volatility of the Futures Prices (S&HR)
![Page 37: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/37.jpg)
TFM: Option Pricing (Milstein & Schwartz (1998))
![Page 38: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/38.jpg)
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
![Page 39: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/39.jpg)
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 it’s not consistent with the attenuation of the jumps in the case of simple mean reversion
![Page 40: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/40.jpg)
Summary
![Page 41: 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](https://reader034.vdocument.in/reader034/viewer/2022051717/5a4d1b5a7f8b9ab0599aab6a/html5/thumbnails/41.jpg)
The End
Thank You for Your Attention!