MODELING SPOT PRICE DEPENDENCE IN THE AUSTRALIAN ELECTRICITY MARKETS Katja Ignatieva, Macquarie University Sydney, Australia and Goethe University Frankfurt, Germany, Phone: +61405994244, e-mail: katja.ignatieva@mq.edu.au or ignatieva@finance.uni-frankfurt.de Stefan Trueck, Macquarie University Sydney, Australia Phone: +61 9850 8483, e-mail: Stefan.trueck@mq.edu.au Overview We examine the dependence structure of spot electricity prices among regional electricity markets in the Australian National Electricity Market (NEM) Our analysis is based on a GARCH approach to model the timevarying volatility of the marginal price series in the considered regions in combination with copulae to capture the dependence structure between the different markets We apply different copula models including both one parametric and copula mixture models We find a positive dependence structure between the prices from all of the considered markets, while the strongest dependence is usually exhibited between markets that are well connected via interconnector transmission lines Regarding the nature of dependence, among the one-parametric copulas, the Student-t copula outperforms all other one-parametric approaches On the other hand, the overall best results are obtained using mixture models due to their ability of also capturing asymmetric dependence in the tails of the distribution Overall, we find significant tail dependence between Australian wholesale electricity prices, indicating that especially extreme price observations like for example spikes may happen jointly in the regional markets Our results are important for the risk management and hedging of market participants, in particular for those operating in several regional markets simultaneously Methods We focus on the dependence between regional prices and provide a pioneer study on the use of copulae for capturing this dependence structure In the first step, we aim to describes the price behavior of each of the regional electricity markets When dealing with a single electricity market, one should take into account certain characteristics and stylized facts of the data In particular, electricity is a non-storable good and the spot prices experience mean reversion, seasonality, price spikes etc Therefore, prior to modeling the distribution of the prices, we need to employ an appropriate model to capture these characteristics We choose wavelets or recursive filter techniques to remove seasonalities from the data Alternatively, one could employ regimeswitching or jump diffusion model to account for spikes and mean reversion Furthermore, electricity prices experience heavy tails and excess kurtosis which cannot be captured by the normal distribution Therefore, some alternative distributions have to be investigated We consider a class of the Symmetric Generalized Hyperbolic (SGH) Distributions and choose AR(1)-GARCH(1,1) model with innovations coming from the SGH family, including Student-t In the second step, after capturing each of the marginals, the regional markets, we study the dependence between the markets using multivariate copulae Copulae allow to separate the study of univariate marginals from the study of dependency The usage of combining a model with time-varying volatility with the copula approach is motivated by the fact that the dependence between regional electricity markets is not constant but may vary over time Results In our study we combine a GARCH model to capture the time-varying volatility in the regional markets with a copula model to capture the dependence structure between the markets Applying different copula models including both one-parametric and copula mixture models, we find a positive dependence structure between prices from all of the considered markets: New South Wales, Queensland, South Australia, Tasmania and Victoria.We find that the strongest dependence is exhibited between markets that are well connected via interconnector transmission lines such as New South Wales and Queensland; New South Wales and Victoria and South Australia and Victoria On the other hand we find significantly less dependence between markets that are not directly interconnected such as Queensland and South Australia or New South Wales, Queensland and South Australia with Tasmania Regarding the nature of dependence, among the one-parametric copulas, the Student-t copula outperforms all other one-parametric approaches indicating some degree of symmetric tail dependence On the other hand, the overall best results are obtained using mixture models due to their ability of also capturing asymmetric dependence in the tails of the distribution Hereby, particularly good results are obtained for a mixture of the Gumbel and survival Gumbel copula Overall, we find significant tail dependence between Australian wholesale electricity prices, indicating that especially extreme price observations like for example spikes may happen jointly in the regional markets Conclusions The dependence structure between regional electricity prices cannot be appropriately modeled by a multivariate normal or even by a multivariate GARCH approach, but should be modeled using non-linear measures of dependence Our results provide important insights with respect to the development of risk management and hedging strategies for market participants, in particular for those operating in several of the considered regional markets For managing the risk of extreme prices occurring simultaneously in different markets, a copula model with the ability to also capture the tail dependence between the prices in different regional markets should be applied The performance of copula models in risk management for multivariate electricity prices should further be investigated in future work References An introduction into copulae can be found in Nelsen, R., 1998 ”An Introduction to Copulas” Springer-Verlag and Joe, H., 1997 “Multivariate Models and Dependence Concepts” Chapman & Hall To our best knowledge, only a limited number of studies have concentrated on the dependence or a multivariate analysis of different regional electricity markets, see e.g., Worthington, A.C and Higgs, H., 2005 “Transmission of prices and price volatility in Australian electricity spot markets: A multivariate Garch analysis”, Energy Economics 27(2), 337-350; Higgs, H., 2009 “Modeling price and volatility inter-relationships in the Australian wholesale spot electricity markets”, Energy Economics 31(5), 748-756 So far, none of the studies has applied copulae to model the dependence structure between different regional electricity markets On the other hand, copulae have been extensively used in other financial markets when modeling dependencies between the single stocks in a portfolio, FX rates, or studying the dependencies between international stock markets, see e.g Embrechts, P., Lindskog, F., McNeil, A., 2001 “Modeling dependence with copulas and applications to risk management”, working paper, ETH Zuerich; Breymann, W., Dias, A., Embrechts, P., 2003 “Dependence structures for multivariate high frequency data in finance”, Quantitative Finance 3, 1-14; Dias, A., Embrechts, P., 2008 “Modeling exchange rate dependence at diffrent time horizons”, working paper; Embrechts, P., McNeil, A., Straumann, D., 2001 “Correlation and dependency in risk management: Properties and pitfalls”; Ignatieva, K., Platen, E., 2010 “Modeling co-movements and tail dependency in the international stock market via copulae”, Asia-Pacific Financial Markets 17(3), 261-302 For discussion on wavelets or recursive filter techniques used to remove seasonalities from the data, refer to Weron, R., 2006 “Modeling and forecasting loads and prices in deregulated electricity markets” For alternative methods such as regime-switching or jump-diffusion model used to account for spikes and mean reversion, see e.g Bierbrauer, M., Menn, C., Rachev, S., Trueck, S., 2007 “Spot and derivative pricing in the EEX power market”, Journal of Banking & Finance 31, 3462-3485; Kanamura, T., Ohashi, K., 2008 “On transition probabilities of regime switching in electricity prices”, Energy Economics 30, 1158-1172; Janczura, J.,Weron, R., 2010 “An empirical comparison of alternate regime-switching models for electricity spot prices” MPRA working paper Modeling univariate marginals using GARCH process is discussed in Higgs, H., Worthington, A., 2008 “Stochastic price modeling of high volatility, mean reverting, spike-prone commodities: The Australian wholesale spot electricity market”, Energy Economics 30, 3172-3185 The study of the class of Symmetric Generalized Hyporbolic Distributions used to fit univariate marginals can found in Platen, E., Rendek, R., 2008 “Empirical evidence on Student-t log-returns of diversified world stock indices”, Journal of Statistical Theory and Practice 2, 233-251; Wenbo, H., Kercheval, A., 2008 “Risk management with generalized hyperbolic distributions”, working paper