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We propose two different two-factor jump-diffusion model with seasonality for the valuation of electricity futures contracts. The models we propose are extensions of Schwartz and Smith (2000) and Lucia and Schwartz (2001), and both of them are special cases of our model. The model we propose is a two-factor jumpdiffusion model with seasonality. The two diffusive factors resemble the long-term short-term model proposed among others by Schwartz and Smith (200). One of the extensions is the possibility for the long-term factor to be a mean-reverting process. Another major extension is the inclusion of a jump term in the model and we also allow the intensity process (probability of jumps) to be non-constant. The model also includes as in Lucia and Schwartz (2001) a deterministic seasonal factor.
We model the stochastic behavio ur of the underlying (unobservable) state variables by Affine Diffusions (AD) and Affine Jump Diffusions (AJD). In that way we are able to exploit the recent transform analysis of Duffie, Pan and Singleton (2000), and Chacko and Das (2002) and we obtain closed form formulas, for the price of futures contracts.
Electricity prices are known to be very volatile and subject to frequent jumps due to system breakdown, demand shocks, and inelastic supply. As many international electricity markets are in some state of deregulation, more and more participants in these markets are exposed to these stylised facts. Appropraite pricing, portfolio, and risk management models should incorporate these facts. Authors have introduced stochastic jump processes to deal with the jumps, but we argue and show that this specification might lead to problems with identifying the true mean -reversion within the process. Instead, we propose using a regime jump model that disentangles mean-reversion from jump behaviour. This model resembles more closely the true price path of electricity prices.