Published in: European Journal of Operational Research

Publication year: 2008
Co-Author 1: Jifang Zhuang

Co-Author 2: Ruud Egging

 

In this paper, we analyze market equilibrium models with random aspects that lead to stochastic complementarity problems. While the models presented depict energy markets, the results are believed to be applicable to more general stochastic complementarity problems. The contribution is the development of new heuristic, scenario reduction approaches that iteratively work towards solving the full, extensive form, stochastic market model. The methods are tested on three representative models and supporting numerical results are provided as well as derived mathematical bounds.

Published in: Energy Economics

Publication year: 2009

The paper examines the long-run relation and short-run dynamics between electricity prices and three fossil fuel prices – coal, natural gas and crude oil – using annual data for the U.S. for 1960–2007. The results suggest (1) a stable long-run relation between real prices for electricity and coal (2) Bi-directional long-run causality between coal and electricity prices. (3) Insignificant long-run relations between electricity and crude oil and/or natural gas prices. And (4) no evidence of asymmetries in the adjustment of electricity prices to deviations from equilibrium. A number of implications are addressed.

Published in: Journal of Banking & Finance

Publication year: 2008
Co-Author 1: Ehud I. Ronn

 

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and

commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for

all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.

 

This paper proposes a new volatility model for energy prices using the supply–demand relationship, which we call a supply and demand based volatility model. We show that the supply curve shape in the model determines the characteristics of the volatility in energy prices. It is found that the inverse Box–Cox transformation supply curve reflecting energy markets causes the inverse leverage effect, i.e., positive

correlation between energy prices and volatility.
The model is also used to show that an existing (G)ARCH-M model has the foundations on the supply–demand relationship. Additionally, we conduct the empirical studies analyzing the volatility in the U.S. natural gas prices.

Keywords: wholesale spot electricity market, multivariate GARCH
Published in: Energy Economics
Publication year: 2009

This paper examines the inter-relationships of wholesale spot electricity prices among the four regional electricity markets in the Australian National Electricity Market (NEM): namely, New South Wales, Queensland, South Australia and Victoria using the constant conditional correlation and Tse and Tsui's (Tse, Y.K., Tsui, A.K.C., 2002. A multivariate generalised autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20 (3), 351–362.) and Engle's (Engle, R.,2002. Dynamic conditional correlation: a sample class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20 (3), 339–350.) dynamic conditional

correlation multivariate GARCH models. Tse and Tsui's (Tse, Y.K., Tsui, A.K.C., 2002. A multivariate generalised autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20 (3), 351–362.) dynamic conditional correlation multivariate GARCH model which takes

account of the Student t specification produces the best results. At the univariate GARCH(1,1) level, the mean equations indicate the presence of positive own mean spillovers in all fourmarkets and little evidence of mean spillovers from the other lagged markets. In the dynamic conditional correlation equation, the highest

conditional correlations are evident between the well-connected markets indicating the presence of strong interdependence between these markets with weaker interdependence between the not so wellinterconnected markets.

It is commonly known that wholesale spot electricity markets exhibit

high price volatility, strong mean-reversion and frequent extreme

price spikes. This paper employs a basic stochastic model, a mean-reverting

model and a regime-switching model to capture these

features in the Australian national electricity market (NEM),

comprising the interconnected markets of New South Wales,

Queensland, South Australia and Victoria. Daily spot prices from 1

January 1999 to 31 December 2004 are employed. The results show

that the regime-switching model outperforms the basic stochastic and

mean-reverting models. Electricity prices are also found to exhibit

stronger mean-reversion after a price spike than in the normal period,

and price volatility is more than fourteen times higher in spike periods

than in normal periods. The probability of a spike on any given day

ranges between 5.16% in NSW and 9.44% in Victoria.

 

Keywords:
Published in: Studies in non-linear dynamics & econometrics
Publication year: 2006

Due to its non-storable nature, electricity is a commodity with probably the most volatile spot prices, exemplified by occasional spikes. Appropriate pricing, portfolio, and risk management models have to incorporate these characteristics, and the spikes in particular. We investigate the nature of power spikes in a number of different markets. We test what time-series model is best able to capture the dynamics of these disruptive spot prices. We use regime-switching models to infer whether the price spikes should be treated as abnormal and independent deviations from the ‘normal’ price dynamics or whether they form an integral part of the price process. We test the time-series models on day-ahead markets in Europe and the US. We find that regime-switch models are better able to capture the market dynamics than a GARCH(1,1) or Poisson jump model. We also find clear differences between the markets and attribute part of the differences to the share of hydro-power in the total supply stack: hydro-power serves as an indirect means to store electricity, which has a dampening effect on spikes.

Keywords:
Published in: Energy Risk
Publication year: 2004

Aurelian Tröndle presents a general framework for modelling prices of storable and non-storable energy assets, which sheds light on different market fundamentals, and shows how energy market volatility is seasonal and anything but stable.The model shows the stochastic properties of the underlying processes of price evolution

Keywords: weather derivatives
Published in: Weather
Publication year: 2004
Co-Author 1: Jeremy Penzer

The analysis of historical meterological data is vital for structuring weather derivatives. But how should weather traders deal with the trends that may exists in the data?