Electricity futures price models: Calibration and forecasting

Abstract

A new one factor model with a random volatility parameter is presented in this paper for pricing of electricity futures contracts. It is shown that the model is more tractable than multi-factor jump diffusion models and yields an approximate closed-form pricing formula for the electricity futures prices. On real market data, it is shown that the performance of the new model compares favorably with two existing models in the literature, viz. a two factor jump diffusion model and its jump free version, i.e., a two factor linear Gaussian model, in terms of ability to predict one day ahead futures prices. Further, a multi-stage procedure is suggested and implemented for calibration of the two factor jump diffusion model, which alleviates the difficulty in calibration due to a large number of parameters and pricing formulae which involve numerical evaluation of integrals. We demonstrate the utility of our new model, as well as the utility of the calibration procedure for the existing two factor jump diffusion model, by model calibration and price forecasting experiments on three different futures price data sets from Nord pool electricity data. For the jump diffusion model, we also investigate empirically whether it performs better in terms of futures price prediction than a corresponding, jump-free linear Gaussian model. Finally, we investigate whether an explicit calibration of jump risk premium in the jump diffusion model adds value to the quality of futures price prediction. Our experiments do not yield any evidence that modelling jumps leads to a better price prediction in electricity markets.

Stochastic multifactor models in risk management of energy futures

“…Thus, we feel it is not necessary to include a jump component in the multifactor models in modeling electricity futures. Moreover, our results are consistent with the finding in Islyaev and Date (2015) that modeling jumps does not lead to a better price prediction in electricity markets.…”

“…To see if adding an additional jump component would improve the performance of the model for the electricity futures, we follow the works in Villaplana (2003) and Islyaev and Date (2015). We consider a model with a jump component, in which all else is the same as in Model 2 except that Equation (3.2) is as follows: where is a Compound Poisson process which has intensity and jump sizes .…”

“…Other studies in the literature on stochastic multifactor models without a jump component for electricity derivatives valuation includes: Burger, Klar, Muller, and Schindlmayr (2004), Cartea and Villaplana (2008), Janczura (2014), and others. Islyaev and Date (2015) investigated empirically whether multifactor jump diffusion models perform better in terms of futures price prediction than a corresponding jump‐free linear Gaussian model, and found that modeling jumps does not leads to a better price prediction in electricity markets. Similar to Islyaev and Date, we add a jump component into the stochastic four‐factor model with two complement stochastic seasonal components and compare it with the jump‐free model.…”

Electric Power Industry: Operational and Public Policy Challenges and Opportunities

“…Their results provide an important input into the debate on whether retaining the flexibility to update emission targets is beneficial despite its negative effect of causing policy uncertainty. Similarly, Drake et al (2016) show that emissions price uncertainty under cap-andtrade policy results in greater expected profit than achieved under emissions tax policy with constant emissions price, which contradicts the conventional (2002), Lucia and Schwartz (2002), Fleten and Lemming (2003), Longstaff and Wang (2004), Bunn (2004), Carmona and Coulon (2014), Islyaev and Date (2015), and Caldana et al (2017) Pricing of electricity contracts and derivatives Kwon et al (2006), Thompson (2013), Islyaev and Date (2015), and Wu and Babich (2012) Electricity trading through forward and spot markets Sen et al (2006), Kwon et al (2006), Dong and Liu (2007) Sioshansi (2002), Eydeland and Wolyniec (2003), Deng and Oren (2006), and Liu et al (2006) Open research questions…”

Influence of Fluctuations in Fossil Fuel Commodities on Electricity Markets: Evidence from Spot and Futures Markets in Europe

“…For this reason, electricity futures trading is more extensive than spot trading. There are also many studies concerning the electricity futures market (e.g., [5][6][7][8]).…”