a-2151898-1-ignatieva_trueck_abstract

MODELING SPOT PRICE DEPENDENCE IN THE
AUSTRALIAN ELECTRICITY MARKETS
Katja Ignatieva, Macquarie University Sydney, Australia and Goethe University Frankfurt, Germany,
Phone: +61405994244, e-mail: or
Stefan Trueck, Macquarie University Sydney, Australia
Phone: +61 2 9850 8483, e-mail:

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.