Modeling electricity spot prices: combining mean reversion, spikes, and stochastic volatility

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractStarting with the liberalization of electricity trading, this market grew rapidly over the last decade. However, while spot and future markets are rather liquid nowadays, option trading is still limited. One of the potential reasons for this is that the spot price process of electricity is still puzzling researchers and practitioners. In this paper, we propose an approach to model spot prices that combines mean-reversion, spikes and stochastic volatility. Thereby we use different mean-reversion rates for "normal" and "extreme" (spike) periods. Another feature of the model is its ability to capture correlation structures of electricity price spikes. Furthermore, all model parameters can easily be estimated with help of historical data. Consequently, we argue that this model does not only extend academic literature on electricity spot price modeling, but is also suitable for practical purposes, e.g. as underlying price model for option pricing. List of SymbolsSeasonality function value at time t Φ(·)Normal distribution function Sigma Correlation matrix Ω Probability space α x Mean-reversion rate of the "normal" diffusion process α yMean-reversion rate of the "extreme" spike process α zMean-reversion rate of the unseparated process γ Regression coeffienct ε(t)Daily changes of Z(t) not caused by mean-reversion λ Spot price at time t T Time horizion X(t) "Normal" diffusion process at time t Y(t) "Extreme" spike process at time t at time t Z(t)Unseparated stochastic process at time t dB(t) Independent Increments of the Brownian motion dI(t) Independent Increments of the compound Poisson process m(t)Moving average filter at time t sea(t)Yearly seasonality at time t w(t mod 7)Weekly seasonality at time t ii 1 INTRODUCTION

Predictability of price movements in deregulated electricity markets

“…The values of prices can vary by a factor of 100 over a time scale of just several hours. These dramatic changes tend to occur in a seemingly spontaneous fashion which is sometimes erroneously interpreted as a signature of a random uncorrelated process (see for example [15]). A more detailed mathematical analysis reveals nontrivial auto-correlations in these sudden price jumps [16,17,18,19] which indicate a possibility of prediction of electricity price movements based on the information on their historic evolution [7].…”

The affine styled-facts price dynamics for the natural gas: evidence from daily returns and option prices

“…The large value of jump intensity makes fatter-tail of distribution (see, Matsuda 2004;Gatheral 2006). Third, compound Poisson jump diffusion model is quite common and is used not only in the financial market but also in the commodity market (Chang et al 2007;Chevallier and Ielpo 2013;Wilmot and Mason 2013;Schmitz et al 2014;Mayer et al 2015;Diewald et al 2015;Xiao et al 2015) because of the analytic tractability of their solutions. The explicit analyticity of the derivatives' model generated under this process allows for more proper calibrations and analyses of the styled-facts contained in the market prices.…”

“…g t in Eq. (1) denotes deterministic seasonal function modified from Lucia and Schwartz's (2002), Weron (2006) and Mayer et al (2015) as follows:…”

“…1 Wong and Lo (2009) model MR under the stochastic volatility process. Weron (2006) and Mayer et al (2015) look at seasonality. Pillay and O'Hara (2011) discuss MRSV model with jump risk.…”

Modeling Long-term Seasonality and Spikes of the Spot Electricity Prices in Turkey

“…where a certain percentage of the highest (and/or lowest) prices, e.g., the upper 1% of prices are classified as outliers (see Mayer et al, 2012); 3Fixed price change thresholds where price increments or price returns exceeding some threshold are classified as outliers (Bierbrauer et al, 2004); (4) Variable price change thresholds, more commonly known as the "recursive filter" technique, where prices corresponding to the price increments (or returns) exceeding three standard deviations of all returns are removed one by one in an iterative procedure (c.f. Weron, 2006); (5) Wavelet filtering where the signal (the price series) is first decomposed using the wavelet transform, then reconstructed up to a certain level of detail (c.f.…”