## Abstract

This article investigates the relationship among price changes, volatility forecasts, and accurate Value-at-Risk (VaR) estimates in power markets. The authors use various GARCH(p,q) methods to model daily volatility and estimate VaR in New South Wales (NSW) and Queensland (QLD) regions. Then, they explore the relationship among price changes, and volatility forecasts and accurate VaRs for both generator and retailer sides, at 99 percent, 95 percent and 90 percent VaR confidence levels in six different out-of-sample periods. They find that forecasted volatility and accurate VaR variables tend to be statistically significant in explaining variations in power price changes. They also find that the coefficients of forecasted volatility tend to be negative. This indicates that higher forecasted volatility predicts negative price changes. Therefore, market participants in power markets, either generator or retailer, should expect a negative price change when their volatility forecast is high. Furthermore, the authors find that accurate VaR tends to lead to a decrease in price changes. This implies that well-functioning market risk management explains an unfavorable price change for the generator, but a favorable price change for the retailer in the Australian power markets.

There are few research works discussing risk measurement using Value-at-Risk (VaR) in power markets. A possible reason is that VaR is normally used in discussing standard financial assets, like stocks and bond markets. However, after financialization of commodity markets (as documented in Stoll and Whaley [2010], Tang and Xiong [2012], Basak and Pavlova [2016]), it seems that the power market can be treated like other financial instruments. Furthermore, Adams and Glück [2015] document that commodities have become increasingly important for institutional investors. Joskow and Kahn [2001] argue that spot power market is a commodity. Therefore, it is likely that market participants in the power market will use VaR analysis and trigger a new research area.

Recent investigations of VaR in power markets have been conducted by Chan and Gray [2006], Walls and Zhang [2006], Frauendorfer and Vinarski [2007], Herrera and González [2012], and Andriosopoulos and Nomikos [2012]. However, none of that work addresses the relationship among price changes, volatility forecasts, and accurate VaR in the power market. Recent works in power market volatility (Pen and Sévi [2010], Haugom et al. [2011], Ullrich [2012], Kalantzis and Milonas [2015], and Qu et al. [2016]) still do not address the question. Indeed, the question concerning that relationship is essential; otherwise, market participants could argue that there is no need to do a good job in forecasting volatility and VaR in the power market. If we could report a significant relationship between volatility forecasts, accurate VaR estimates, and price changes, then markets participant will pay more attention to the VaR estimate.

We use the GARCH (Bollerslev [1986]) VaR estimate and investigate the relationship among price changes, volatility forecasts, and accurate VaR estimates in the Australian interconnected power markets, specifically New South Wales (NSW) and Queensland (QLD). The Australian interconnected power markets are significantly more volatile than other comparable power markets, and similarly to Higgs and Worthington [2008], we use daily spot series. The characteristics of high volatility and daily series in Australian interconnected power markets are the reasons for using GARCH in volatility modelling, similar to Koopman et al. [2007] and Efimova and Serletis [2014].

The remainder of the article is organized as follows. The next section provides an overview about Australian interconnected power markets. The third section reviews relevant studies about volatility modelling and VaR in power markets. The fourth section describes the methodology. The fifth section explains the data and discusses the empirical results. The final section concludes.

## AUSTRALIAN INTERCONNECTED POWER MARKETS

Over the last twenty-five years, the Australian power market has been transformed from monopolies that existed prior to 1997 to open competition. In the late 1990s, the Australian government announced a significant structural reform by separating power generation and power transmission from power distribution and the retail supply. Therefore, as customers were free to choose their supplier, competition was introduced into the retail power market. Currently, the Australian power market, the National Electricity Market, (NEM), one of the world’s longest interconnected power systems, is interconnected through several regional networks. The price mechanism in the NEM can be explained as follows. The generators submit offers every five minutes, and the number of generators required to produce electricity is determined by the submitted offers. After that, the final price is constructed every half-hour for each of the regions by averaging the five-minute spot price. Therefore, there are 48 different half-hourly spot prices in a day for each region in the NEM.

We should note that Higgs and Worthington [2008], who find that price spikes occur more frequently in Australian power markets than in the U.S. pool (Pennsylvania—New Jersey—Maryland). Thus, the Australian interconnected power markets are considered more spike-prone and volatile than many comparable power markets and risk analysis in Australian power markets is essential. Clearly, this will contribute to the energy finance literature over time.

This article focuses on only two Australian power markets, NSW and QLD, because these regions are jurisdictions representative in Australian electricity markets for investigating macroeconomic costs associated with “Time of Use” pricing (see Nelson and Orton [2013]). Furthermore, according to Anderson et al. [2007], NSW and QLD have the two highest installed capacities; they are the only regions with more than 10,000 megawatts (MW) in the Australian power markets. We also chose to exclude South Australia (SA) and Victoria (VIC) regions because we found (in unreported results) that SA and VIC GARCH(1,2) and GARCH(2,2) estimates are explosive. Explosive GARCH estimates sometimes occur in certain markets such as the Sudanese (Ahmed and Suliman [2011]) or Ugandan (Namugaya et al. [2014]) stock exchanges. We could have used another type of GARCH model for the SA and VIC power markets, but this would have generated inconsistent comparisons since this article focuses on GARCH(p,q) models. Therefore, we will only cover the NSW and QLD power markets.

## LITERATURE REVIEW

There are a number of studies examining VaR in the power market. Most of the works tend to extend the standard VaR model. For instance, Chan and Gray [2006] incorporate weekly seasonality and autoregression in their EGARCH specification. They model the tails of the return distribution by applying the extreme value theory (EVT). Another article by Walls and Zhang [2006] uses EVT in their extended VaR model. They report that their extended VaR is more accurate in the Alberta power market. Herrera and González [2012] also extend VaR in power market by adopting EVT. Another version of extending VaR is performed by Frauendorfer and Vinarski [2007], who report the limits of the traditional VaR in the power markets. They propose a quasi-sensitivity analysis of the VaR with respect to the risk factors, price, and volatility. Andriosopoulos and Nomikos [2012] capture the dynamics of energy prices by extending a set of VaR models. However, none of these studies determines whether the forecast volatility and an accurate VaR estimate can explain price changes in power markets.

Recent works on volatility modelling in power markets do not address the relationship among price changes, volatility forecasts, and accurate VaR measures in power markets either. For instance, Haugom et al. [2011] apply market measures for the prediction of volatility in the Nord Pool electricity forward market. Kalantzis and Milonas [2015] investigate the impact of the introduction of electricity futures on the spot-price volatility of the French (Powernext) and German (EEX) electricity markets. Pen and Sévi [2010] estimate a VAR-BEKK model and find evidence of return and volatility in three different forward electricity markets. Another article by Qu et al. [2016] measures volatility and jumps in power prices by using the non-parametric realized volatility technique and the associated jump detection. Ullrich [2012] estimates realized volatility and the frequency of price spikes in eight wholesale electricity markets.

Overall, to the best of our knowledge, no study addresses the question as to whether forecast volatility and accurate VaR estimates can explain price changes. We also realize that works on electricity volatility of the present analyses from the generators’, that is, the sellers’ side. No one has discussed electricity volatility in power markets from the retailer and buyer perspectives. Indeed, analyses coming from both sides are essential because the price spike generates market risks that should be monitored and managed thoroughly. A dramatic increase (i.e., huge positive “return”) is favorable for generators in the power market, while a dramatic decrease (i.e., huge negative “return”) is favorable for retailers in the power market. We can see that a price change might be favorable for generators but unfavorable for retailers and vice versa. Therefore, we argue that a comprehensive analysis should encompass the perspectives of both generators and retailers.

## METHOD

We use the GARCH model for estimating VaR in the interconnected power markets, similar to Koopman et al. [2007] and Efimova and Serletis [2014]. According to Bollerslev [1986], the GARCH(p,q) model can be written as follow:

1where σ_{t} denotes the volatility forecast for time *t* and *y _{t}* is the realized return at time

*t*.

We compare and determine the most fitted various *p* and *q* values up to GARCH (2,2). This method follows Chinn and Coibion [2014] for dynamic GARCH in commodity markets.

A standard risk measurement VaR can be formally expressed (Hull [2007], Jorion [2007]) as follows:

2where σ denotes volatility of the return of an asset and Φ^{–1}(α) is the inverse cumulative normal distribution at α confidence level. However, He et al. [2016] find that switching from the normal distribution to Student’s *t* distribution improves the model performance in the Australian power markets data. Thus, we modify Equation (2) by using Student’s *t* distribution instead of normal distribution as follows:

where σ denotes volatility of the return of an asset and is the critical value of *t*-distribution at α confidence level and df degrees of freedom. We can see from Equation (2) and Equation (3) that a VaR estimate value largely depends on the volatility estimate. Therefore, an accurate volatility estimate implies an accurate VaR. In this article, we analyze left-tailed VaR for the generators’ side (because a negative price change means a loss for generators) and right-tailed VaR for the retailers’ side (because a positive price change means a loss for retailers).

We explore the relationship among price changes, volatility forecasts, and accurate VaR using regression Equation (4). According to Pindyck [2004], volatility is one of the explanatory variables of commodity return. Then, we modify the Pindyck [2004] model by including both forecasted volatility and a dummy variable about the accurate VaR estimate. Our model is similar to Handika and Sondi [2017] and can be expressed as follows:

4where *RET _{t}* denotes the return (i.e., price change) of a commodity at day

*t*, σ

_{t}denotes the volatility forecast for day

*t*, and DUMVAR is the dummy variable explaining the VaR performance at day

*t*: it is 1 when the forecasted volatility is accurate (i.e., the realized price change does not violate the forecasted VaR limit), and 0 otherwise.

## EMPIRICAL ANALYSIS

We obtained the half-hourly prices series of Australian power market prices in NSW and QLD regions from the AEMO website.^{1} Then, we calculated the daily price for each region by averaging the different 48 half-hour power prices. Our in-sample period runs from January 1, 2000 to December 31, 2009, and the out-of-sample period runs from January 1, 2010 to December 31, 2015 (a 10-year in-sample period and a six-year out-of-sample period). Our choice with regard to these in-sample and out-of-sample periods reflects the fact that financialization of commodity markets only started in the 2000s (Rossi [2012], Tang and Xiong [2012], Handika and Sondi [2017]). We find that 10 years is a standard time frame for empirical finance studies (Ledoit and Wolf [2008]). We also perform robustness checks in the yearly sub-sample analysis during the out-of-sample period. These yearly robustness checks follow the method from Gorton and Rouwenhorst [2006], Wong [2010], and Perignon et al. [2008], and they are similar to those used by Handika and Sondi [2017].

Exhibit 1 reports the descriptive statistics of daily price changes in the NSW and QLD power markets: the mean, standard deviation, minimum, maximum, range, and number of observations. Exhibit 1 also reports the descriptive statistics during the all-sample period (from January 1, 2000 to December 31, 2015), with the in-sample period (from January 1, 2000 to December 31, 2009) and the out-of-sample period (from January 1, 2010 to December 31, 2015).

We find that averages of daily price change are 0.03 percent for NSW and 0.01 percent for QLD during the all-sample period, 0.02 percent for NSW and negative 0.01 percent for QLD during the in-sample period and 0.05 percent for both NSW and QLD during the out-of-sample period. Overall, NSW tends to experience slightly higher average price changes than QLD. We find that the volatilities of daily price changes are 38.66 percent for NSW and 45.10 percent for QLD during the all-sample period, 45.06 percent for NSW and 47.95 percent for QLD during the in-sample period, and 24.51 percent for NSW and 39.91 percent for QLD during the out-of-sample period. Overall, NSW tends to be slightly less volatile than QLD during the in-sample period, and QLD tends to be more volatile than NSW during the out-of-sample period. We also see that the range (the difference between maximum and minimum daily price changes) tends to be higher in QLD than in the NSW during the all-sample, in-sample, and out-of-sample periods. This indicates that overall, QLD daily price changes tend to be more volatile than NSW. We find that the values of Chi-squared Jarque-Bera (X^{2} JB) test are very high (from thirty-five thousand to more than two hundred thousand) for both NSW and QLD during the all-sample, in-sample, and out-of-sample periods. This normality test indicates that the daily price changes are not normally distributed. Further analysis using skewness and kurtosis values reveals that the daily price changes tend to left-skewed leptokurtic for NSW and right-skewed leptokurtic for QLD.

The next step is estimating various GARCH(p, q) models using in-sample period data for both NSW and QLD regions. We perform the estimation for GARCH(1,1), GARCH(2,1), GARCH(1,2), and GARCH(2,2).

Exhibit 2 reports the log-likelihood values for various p and q values up to GARCH(2,2) models for both generator and retailer sides in NSW and QLD regions. Danielsson [2011] notes that the best GARCH(p, q) model is the model with the highest log-likelihood value, that is, the least negative log-likelihood value. Therefore, we can see that GARCH(2,2) is consistently the best model for both generator and retailer sides in the NSW and QLD regions.

Then, we perform the regression equation (3) to investigate the relationship among price changes, forecasted volatility, and accurate VaRs at different confidence levels (99 percent, 95 percent, and 90 percent) for both generator and retailer sides in the NSW and QLD regions during different out-of-sample periods. We classify two sub-groups of out-of-sample periods: “short” for 1-year, 2-year, and 3-year out-of-sample periods; and “long” for 4-year, 5-year, and 6-year out-of-sample periods. The regression results are reported in Exhibits 3A and 3B, Exhibits 4A and 4B, and Exhibits 5A and 5B for 99 percent VaR, 95 percent VaR, and 90 percent VaR, respectively.

According to Exhibits 3A and 3B, we find that forecasted volatility and accurate VaR estimates tend to be statistically significant in explaining variation in power price changes. This result is strong in the NSW region for all out-of-sample periods at 99 percent VaR. The forecasted volatility variable seems to not be statistically significant in the QLD region at 1-year, 2-year, 3-year, and 4-year out-of-sample periods. The coefficients’ sign for forecasted volatility tend to be negative, with the exceptions only in the QLD region for 1-, 2-, 3-, and 4-year out-of-sample periods. These results indicate that higher forecasted volatility predicts negative price change. This negative sign is consistent with the results of Pindyck [2004] for natural gas commodities. This is interesting because power and natural gas commodities share a similar property of being non-storable. In the QLD region, however, the coefficient sign for accurate VaR is negative for both generator and retailer. This means that an accurate VaR explains a decrease in price change. Recall that a decrease in price change is unfavorable for the generator, but is favorable for the retailer. Therefore, we can see that an accurate VaR leads to an unfavorable price change to the generator, but a favorable price change to the retailer in the power markets. The explanatory powers range from upper 6 percent to 20 percent. This is a relatively sensible number range if we compare it to the explanatory powers of the models in power markets (for instance, Bessembinder and Lemmon [2002], or Redl et al. [2009]).

Exhibit 4A and Exhibit 4B report the results of the regression equation (3) at 95 percent VaR. We find that forecasted volatility and accurate VaR tend to be statistically significant in explaining variation in power price changes, with the exceptions in the QLD region for 1-year, 2-year, and 4-year out-of-sample periods. This is consistent with and conforms to the results for 99 percent VaRs, where both forecasted volatility and accurate VaR tend to explain the price change in power markets. The coefficient’s sign for forecasted volatility tends to be negative (with the exceptions only in the QLD region for 1-year, 3-year, and 4-year out-of-sample periods). This also indicates that higher forecasted volatility predicts negative price change at 95 percent VaR. The coefficient sign for accurate VaR is negative for both generator and retailer. Again, this means that an accurate VaR explains a decrease in price change. Thus, the accurate VaR leads to an unfavorable price change for the generator, yet a favorable price change for the retailer in the power markets. The explanatory powers are also sensible numbers (even though they are a bit lower), ranging from upper 5 percent to upper 19 percent.

Exhibit 5A and Exhibit 5B report the results of the regression equation (3) at 90 percent VaR. Again, we find that forecasted volatility and accurate VaR tend to be statistically significant in explaining variation in power price changes, with the exceptions in the QLD region for 1-year, 2-year, and 4-year out-of-sample periods. This is consistent with and conforms to the result for 95 and 99 percent VaRs, where both forecasted volatility and accurate VaR tend to be able to explain the price change in power markets. Likewise, we also find that the coefficient sign for forecasted volatility tends to be negative (with the exceptions only in the QLD region for 1-year, 3-year, and 4-year out-of-sample periods). Again, this indicates that higher forecasted volatility predicts negative price change at 90 percent VaR. The coefficient sign for accurate VaR is negative for both generator and retailer. We also find that an accurate VaR explains a decrease in price change. We also obtain sensible numbers for the explanatory powers. They range from upper 5 percent to lower 31 percent.

Overall, we find that: (i) forecasted volatility and accurate VaR variables tend to be statistically significant in explaining variation in power price changes, (ii) the coefficients of forecasted volatility tend to be negative, indicating that higher forecasted volatility predicts negative price change, (iii) accurate VaR tends to lead to a decrease in price change, implying that well-functioning market risk management explains an unfavorable price change for the generator, but a favorable price change for the retailer. The results are strong for both generator and retailer, at different VaR confidence levels and different out-of-sample periods in both NSW and QLD power markets. We also see that the explanatory powers of model (4) are sensible enough, yet the better GARCH(p,q) models with higher log likelihood values tend to have lower explanatory powers in model (4).

## CONCLUSION

This article addresses the relationship among price changes, volatility forecasts, and accurate VaRs in the power market. We use various GARCH(p,q) methods to model daily volatility and VaR in the NSW and QLD regions. Then, we explore the relationship among price changes, volatility forecasts, and accurate VaRs. We perform the tests for both generator and retailer sides, at 99 percent, 95 percent, and 90 percent VaR, at six different out-of-sample periods in the NSW and QLD power markets.

We find that forecasted volatility and accurate VaR variables tend to be statistically significant in explaining variation in price changes in the power markets. The sensible explanatory power indicates strong relationships among price changes, forecasted volatility, and accurate VaRs in power markets. We also find that the coefficients of forecasted volatility tend to be negative. This indicates that higher forecasted volatility predicts negative price changes. Therefore, market participants in the power markets, either generator or retailer, should expect negative price change when their volatility forecast is high. Our result is consistent with Pindyck [2004] in analyzing the natural gas market. Therefore, we discover a similar property in non-storable commodities (both natural gas and power). Furthermore, we find that is the case, because accurate VaRs tends to lead to a decrease in price changes. This implies that well-functioning market risk management explains an unfavorable price change for the generator, but a favorable price change for the retailer in the Australian power markets. Our results are robust for different VaR confidence levels and different out-of-sample periods. However, our research is limited in standard GARCH(p,q) models. Future research using more advanced GARCH models is highly encouraged to explore the relationship between price changes, volatility forecasts, and accurate VaRs in the power markets in greater depth.

## ENDNOTES

We thank to the anonymous referee who provide valuable comments and suggestions to improve the quality of our manuscript.

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^{1}http://www.aemo.com.au/Electricity/National-Electricity-Market-NEM/Data-dashboard#aggregated-data, as viewed January 17, 2018.

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