Pricing Power Derivatives: A Two-Factor Jump-Diffusion Approach

We propose a two-factor jump-diffusion model with seasonality for the valuation of electricity future contracts. The model we propose is an extension of Schwartz and Smith (Management Science, 2000) long-term / short-term model. One of the main contributions of the paper is the inclusion of a jump component, with a non-constant intensity process (probability of occurrence of jumps), in the short-term factor. We model the stochastic behaviour of the underlying (unobservable) state variables by Affine Diffusions (AD) and Affine Jump Diffusions (AJD). We obtain closed form formulas for the price of futures contracts using the results by Duffie, Pan and Singleton (Econometrica, 2000). We provide empirical evidence on the observed seasonality in risk premium, that has been documented in the PJM market. This paper also complements the results provided by the equilibrium model of Bessembinder and Lemmon (Journal of Finance, 2002), and provides an easy methodology to extract risk-neutral parameters from forward data.

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