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 31 st, 2007

2. Outline Intro Single Factor Models Two Factor Models Three Factor Models Choosing a Spot Price Model

3. 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)

4. Single Factor Models Futures and Forward Pricing Option Pricing The Schwartz Single Factor Model (Futures/Forward, Option Pricing)

5. Single Factor Models: SDE vs PDE

6. Futures and Forward Pricing (Black, 1976)

7. Volatilities (FP)=Volatility SP

8. Option Pricing (Black, 1976): European Futures Option

9. The Schwartz Single Factor Model (1997) Mean-Reverting Positive S Alpha-mean reverting rate Mu-long term level Lambda-market price of energy risk

10. The Schwartz Single Factor Model (x=ln S): SDE and PDE

11. Futures and Forward Pricing (Schwartz SF Model)

12. Futures and Forward Pricing (Schwartz SF Model): long maturity level and volatility

13. Futures Prices and Their Volatility (Schwartz SF Model):

14. European Call Option Pricing (Schwartz SFM): Clewlow, Strickland (1999)

15. European Call Option Pricing (Schwartz SFM): Clewlow, Strickland (1999): s=T

16. European Call Option Pricing (Schwartz SFM)

17. Comparison: Option Prices in the Black and Schwartz SFM

18. Two Factor Models (Stochastic Convenience Yield) Gibson & Schwartz (1990) Schwartz (1997) Pilipovich (1997) Hillard & Reis (1998)

19. Two Factor Models (Stochastic Convenience Yield): PDE

20. Two Factor Models (Stochastic Convenience Yield): Futures/Forward Pricing (Schwartz(1997))

21. Two Factor Models (Stochastic Convenience Yield): Futures/Forward Pricing ( HR (1998))

22. Two Factor Models (Stochastic Convenience Yield): Futures Pricing (Schwartz(1997))

23. Two Factor Models (Stochastic Convenience Yield): Volatility of Futures Pricing (Schwartz(1997)&HR(1998))

24. Two Factor Models (Stochastic Convenience Yield): Volatility (Schwartz(1997))

25. Two Factor Models: Option Pricing (Clewlow & Strickland (1999))

26. The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor)

27. The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor, convenience yield)

28. The Schwartz 1 Factor Approximation: Rate of Change in the Futures Prices (Two Factor vs One Factor): Shadow Spot Price vs Futures Price

30. Three Factor Models Schwartz (1997): extension of his TFM (Vasicek short term rate r) Hillard & Reis (1998): interest rate follows HJM (1992) model

31. Three Factor Models: Schwartz (1997)

32. Three Factor Models: HR (1998)

33. Three Factor Models PDE: Schwartz (1997) &HR (1998)

34. Futures/Forward Pricing: (Three Factor Models, Schwartz (1997))

35. Futures/Forward Pricing: (Three Factor Models, HR (1998))

36. Volatility of the Futures Prices (S&HR)

37. TFM: Option Pricing (Milstein & Schwartz (1998))

38. 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

39. 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

40. Summary

41. The End Thank You for Your Attention!