The Price of Power - the Valuation of Power and Weather Derivatives
43 Pages Posted: 3 Mar 2002
Date Written: June 2000
Pricing contingent claims on power presents numerous challenges due to (1) the nonlinearity of power price processes, and (2) time-dependent variations in prices. We propose and implement an equilibrium model in which the spot price of power is a function of two state variables: demand (load or temperature) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 2000, the market price of risk represented as much as 50 percent of PJM power forward prices for delivery during summer months. This is plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This huge risk premium suggests that the power market is not fully integrated with the broader financial markets. The data also suggest that power forward prices overreact to current demand shocks.
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