1. Hedging and Calculus at PG&E: Diablo Valley College Field Trip Chuck Riedhauser April 15, 2008

2. 2 Overview PG&E procurement activities Valuation of power plants Hedging spread options

3. April 15, 20083 Pacific Gas and Electric Combined gas and electric utility in northern and central California Natural Gas –4 million customer accounts –850 bcf (billion cubic feet) Electric –5 million customer accounts –86,000 GWh (gigawatt-hours) –20,000 MW peak load

4. April 15, 20084 Electricity Procurement PG&E owned facilities produce less than half the electricity consumed in our service territory PG&E purchases most of its power from third parties –Calpine, PPM, etc. Energy Procurement division negotiates contracts, takes delivery, and schedules power –Quantitative Analysis group values all potential contracts and assists in risk management (hedging) of contracts

5. April 15, 20085 Procurement Contracts The typical contract we (PG&E) purchase is a “tolling agreement” for a gas-fired power plant –We get the ability to call on power when we need it –We pay a fee and provide the gas Costs of power are heavily tied to gas commodity prices Power prices are also random

6. April 15, 20086 Random Gas and Power Prices

7. April 15, 20087 Price Parameters Parameters describe random prices Forward prices –Expected value of random prices Volatilities –Measure of much prices fluctuate –Related to standard deviation Correlation –Measures how likely prices are to move together

8. April 15, 20088 The Valuation Problem How do we value a contract which depends on 2 random prices? Option theory! Power plant (or toll) is viewed as a “spread option” between gas and power We want to know the value of a spread option which expires in the future

9. April 15, 20089 Spread Option

10. April 15, 200810 Hedging a Power Plant What is hedging? –Reducing the unexpected changes in the value of a plant or contract Why do we hedge? –Our customers are risk averse—they don’t like unexpected price increases How do we hedge a power plant? –We enter into contracts which offset value changes in power plant –How much of these other contracts should we purchase? Look at how power plant value changes as the forward prices of gas and power change

11. April 15, 200811 Hedging a Power Plant, continued How does the value of a power plant (i.e., spread option) change for small changes in the forward prices? –Taylor series expansion of spread option value

12. April 15, 200812 Hedging a Power Plant, continued Spread option is “hedged” by acquiring other positions which have the opposite dependence on price moves First order hedge –Add positions with first order expansion Second order hedge positions have expansion

13. April 15, 200813 Hedge Ratios The partial derivatives of the option value with respect to forward prices are called “hedge ratios” Hedge ratios derived from the option value formula –Repeated application of the chain rule for derivatives gives …

14. April 15, 200814 Hedge Ratios, continued

15. April 15, 200815 Hedging Power Plants Power plants modeled as spread options –Comprehends random gas and power prices Spread option value expressed in terms of cumulative distribution function Taylor series forms basis for hedging Hedge ratios calculated by chain rule

16. Questions?