پیش بینی نوسانات آتی کربن با استفاده از مدل گارچ با نوسانات انرژی

This article examines the volatility forecasting abilities of three approaches: GARCH-type model that uses carbon futures prices, an implied volatility from carbon options prices, and the k-nearest neighbor model. Based on the results, we document that GARCH-type models perform better than an implied volatility and the k-nearest neighbor model. This result suggests that carbon options have little information about carbon futures due to their low trading volume. We also investigate whether the volatilities of energy markets, i.e., Brent oil, coal, natural gas, and electricity, forecast following day's carbon futures volatility. According to the results, we suggest that Brent oil, coal, and electricity may be used to forecast the volatility of carbon futures

GARCH-type models are widely used to estimate volatility of financial asset returns and show good performance. However, according to the survey results of Poon and Granger (2003), GARCH-type models are not necessarily the best forecasting model, as they give satisfactory results for in-sample forecasts, but not for out-of-sample forecast estimation. Generally, there are two alternatives to GARCH-type models: historical volatility and implied volatility (IV). The historical volatility approach predicts volatility using the past volatility of a sample. The random walk, historical average, simple moving average, exponential smoothing, exponentially weighted moving average, and k-nearest neighbor (k-NN) methods all belong to this approach. Apart from random walk and historical average, successful applications of the historical volatility approach normally involve searching for the optimal lag length or weighting scheme in an estimation period for out-of-sample forecasting. The second alternative to GARCH-type models, IV, uses the Black–Scholes option pricing formula. In this formula, all parameters other than volatility are observed in financial markets. After inserting these parameters into the Black–Scholes formula, volatility is the only unknown parameter. The formula is then inverted to derive an estimate of volatility implied by the observed option price. Eventually, an estimate of volatility becomes IV. The choice of method to forecast returns volatility depends on comparing the performance of several alternatives. Poon and Granger (2003) point out that, in a forecasting exercise, comparing the forecasting performance of the different methods is most important. There are several approaches to assess the performance of forecasts. These approaches comprise computing the difference between the forecasts and the observed value, running regression to investigate the information content of forecasts, and measuring the relative usefulness of forecasts on the basis of a utility function or in relation to common uses of volatility forecasts in financial markets (Agnolucci, 2009). This article focuses on the first two of these approaches. Agnolucci (2009) indicates that these two approaches are traditional in financial econometric literature. Although there are many studies on most financial assets, much remains to be done in the carbon market. The carbon market has been active under the EU Emission Trading Scheme (ETS) since 2005, after the Kyoto Protocol came into force. Under the EU ETS, spot, futures, and options of the EU allowance (EUA; the legal aspect) and Certified Emission Reduction (CER; the voluntary aspect) are traded, with the trading volume of the EUA being larger than that of CER.1 Following the Kyoto Protocol, phase I was from 2005 to 2007, phase II from 2008 to 2012, and phase III is from 2013 to 2020. Following Daskalakis et al. (2009), there was a market correction which resulted from the interphase banking restriction and the over-allocation problem. However, since the advent of phase II, this restriction has moderated and the amount of the allocation has been adjusted (Chevallier, 2011b). Moreover, the trading volume and market evolution have grown since 2005.2 Therefore, the carbon market is moving to mature state, and the econometric application to the carbon market is a valuable exercise. Here, we focus only on EUA futures in phase II because of its high trading volume. The purpose of this article is to examine the predictive power of GARCH-type, IV, and k-NN models of EUA futures returns in phase II. The predictive power of each is assessed using various loss functions, such as the mean square error (MSE), MSE-LOG, mean absolute error (MAE), MAE-LOG, and QLIKE, as well as the regression-based approach, the Diebold–Mariano test, the superior predictive ability test, and the model confidence set. In GARCH-type models, we use various types of GARCH models and error distributions. Another contribution of this article is to investigate whether EUA futures volatility is related to energy market volatility. In contrast to previous literature, for example Chevallier, 2009 and Chevallier, 2010, and Chevallier and Sévi (2011), we first assess the relationship between EUA futures volatility and energy market volatility using the linear regression approach. This article is organized as follows. Section 2 details the methodology used in this article and discusses previous literature. Section 3 describes the data used. Section 4 presents the results from the GARCH-type models estimation. Section 5 contains the results from the model comparison. Section 6 describes the results using GARCH-type model with energy volatilities. Section 7 concludes this article.

In this article, we have investigated the specification of different GARCH-type models to forecast carbon futures volatility. First of all, according to information criteria, the models with more complicated specifications of AR, MA, ARCH, and GARCH terms are rejected confirming previous literature (Benz and Trück, 2009). Secondly, through fitting to GARCH-type models, the residuals approach a normal distribution. Thirdly, the estimated parameters in the models are robust to the distribution assumed for the residuals. Finally, the asymmetric effect is observed in carbon futures, and this phenomena is also reported in Chevallier, 2009 and Chevallier, 2011b. When combining the above results and model selection criteria, we can conclude that the GJR-GARCH model performs better than other models. When comparing models, the GARCH-type models perform better than implied volatility (IV) model, probably due to the low trading volume of carbon options. The GARCH-type models outperform the k-nearest neighbor model, because the process of carbon futures volatility possibly has a different pattern from the past movement, and is affected by some shocks from the exterior condition. In addition, the GJR-GARCH model with a normal distribution shows the best forecast performance among GARCH-type models. The GJR-GARCH model with a normal distribution outperforms the combination of two forecasts from IV, k-NN, and GARCH-type models. Therefore, the GJR-GARCH model with a normal distribution has the most information content about carbon futures volatility. When we introduce the volatilities of energy markets into the forecasting equation, Brent oil, coal, and electricity present a good predictive ability to forecast carbon futures volatility. As a result, to forecast the following day's carbon futures volatility, we can use the forecast from the GJR-GARCH model with the present day's volatilities of Brent oil, coal, and electricity. This article has several important implications for both the risk management practices of firms that are involved in trading carbon futures and for investors. As noted in Daskalakis et al. (2009), the ability of market participants to speculate and hedge their positions in the EU ETS is important to maintain a high trading volume and to ensure market efficiency. Using the best forecast model of this article, market participants can hedge their positions by forecasting the volatility of carbon futures. Therefore, more sophisticated risk management for carbon futures market participants is available. Moreover, with respect to the trading volume of carbon futures, we can state that the carbon futures market has a different characteristic from other financial markets. According to Donaldson and Kamstra (2005), GARCH-type forecasting models perform better than IV in the stock market during low-trading volume periods, and vice versa. From this result, Donaldson and Kamstra (2005) report that market prices contain more information relative to historical sources in high-trading volume periods than in low-trading volume periods. This result is inconsistent with the results of this article. Although the trading volume of carbon futures market is steadily growing, the predictability of the GARCH-type forecasting model is much better than that of IV. Therefore, the result of the carbon futures market seems to come from the immaturity of the carbon option market. From this result, we can suggest that if the carbon option market becomes mature state, then the predictability of IV would be better. With regard to the policy about the carbon market, we can make two suggestions from our results. The first suggestion is that the trading in the carbon option market should be invigorated so that the forecast from IV becomes more accurate as mentioned above. The other is that, when the policy makers formulate the policy about the carbon market, they had better consider the interaction between the carbon market and other energy markets, and set up the policy with the comprehensive and long-term view. Following Kossoy and Guigon (2012), it is definite that the policy about carbon market has an effect on the price of carbon futures market. They state that the oversupply of EUA and the recent economic recession of EU lead to the recent price drop of EUA. As a result, the policy for the EU ETS, which causes the oversupply of EUA, influences the downward tendency of the EUA price. Heimdal et al. (2012) and Kossoy and Guigon (2012) state that the intervention to elevate EUA price is needed, but this intervention should come into action with careful consideration and the long-term view.19 Therefore, if the economic status becomes a normal state, and the allocation process of EUA is more elaborate, then the price of EUA would increase to the economically meaningful level. With this increase of the EUA price, the result of this article would be much more useful to forecast the volatility of carbon futures.