“Modeling jumps in organization of petroleum exporting countries basket price using generalized autoregressive heteroscedasticity and conditional jump”

This paper uses autoregressive jump intensity (ARJI) model to show that the oil price has both GARCH and conditional jump component. In fact, the distribution of oil prices is not normal, and oil price returns have conditional heteroskedasticity. Here the authors compare constant jump intensity with the dynamic jump intensity and evidences demonstrate that oil price returns have dynamic jump intensity. Therefore, there is strong evidence of time varying jump intensity Generalized Autoregressive Heteroscedasticity (GARCH) behavior in the oil price returns. The findings have several implications: first, it shows that oil price is highly sensitive to news, and it does settle around a trend in long-run. Second, the model separates variances of high volatilities from smooth volatilities. Third, the model rejects an optimal path for extracting oil and technology transmission. In fact, the lack of a long-term pattern can cause excessive oil extracting which can result in heavy climatic effects.


Introduction 
The subject of oil price includes an extensive literature consisting of both theoretical and practical researches. There are three primary methods for describing oil price behavior in the literature: first, Hotelling (1931) theory which indicates that oil is an infinite source and its price follows a long-term increasing pattern. There are different extensions of this primary model. Second, researches that likes of Krichen (2002) and Dees et al. (2007) who tried to describe oil price in the context of demand and supply in macroeconomics. The third method includes Dees et al. (2007), Kaufmann and Ulman (2009), which followed the subject in a more unorthodox way and focused on OPEC power and the role of speculation. The other important branch of the literature addresses the question that whether there is a permanent and systematic pattern for the price of exhaustible resources in the present time. Results obtained in this relation are not clear, but Slade (1998) does find practical evidence that the pattern is random; Slade (1982) and Lee et al. (2006) conclude that there is a second order, a permanent pattern with structural break, as it was expected. Finally, Pindyck (1999) concluded that the real price of oil fluctuates around a long-term pattern and the pattern itself is random. Previous models show that daily data on oil price and complex practical techniques are heavily used. Notwithstanding the fact that techniques such as GARCH models, artificial neural networks and jump-diffusion processes have been used, oil price behavior shows peculiar signals. In fact, change in true oil price historically tends to be permanent, difficult to predict, and led by very different regimes in different times.
In this paper, autoregressive jump intensity (ARJI) model is used for modeling volatility of oil price return. This paper shows that many oil price behaviors are the same as the stock market behavior, since one can use models, which are used for modeling volatility of stock return, to model volatility of oil price return. In the second section, we introduce the ARJI model. In addition, descriptive statistics and data analysis are presented in third section. Section four discusses empirical results, and finally in the last section, the implication is mentioned.

Literature review
Oil price has attracted significant attention from financial econometrics scholars. Many scientific studies address issues like volatility of oil price (Foster, 1995;Pindyck, 2004;Jebabli et al., 2014), and hedging (Lien et al., 2002). Ji and Guo (2015) analyzed the impacts effects of four types of oil-related events on world oil prices, using AR-GARCH model. Their results indicate that effect of the global financial crisis on oil price returns is negatively significant, while the effect of the Libyan war and hurricanes is positively significant. Diaz et al. (2016) investigated the relationship between oil price volatility and stock returns in the G7 economies in the period 1970 to 2014 for monthly data. Results show that there is a negative response of G7 economies' stock markets to an increase in oil price volatility. Outcomes also show that volatility of world oil price is usually more significant for G7 economies' stock markets than the national oil price volatility. Loren-

Autoregressive jump intensity model for oil volatility.
The aim of this study is modeling the oil price volatility. One of the features of crude oil markets is very intense volatility and, in some cases, such as during the Gulf war, jump in the time series data associated to crude oil. In this study, ARJI model proposed by Chan and Maheu (2002) is used for measuring the volatility of crude oil.Assume that the information set of data at time 1 is Ω ,…., and two shocks , and , have happened. A jump model is presented as follows: , ,

1
In this equation, is growth rate of oil price which is calculated byln and is oil price at time; furthermore, , is a normal stochastic process and it is assumed that: Let smooth conditional variance be a 1,1 process. We can write: , , 3 On the other hand, , is the shock associated with jump which its conditional expectation is zero and Where is a variable that affects stock return in 1, interval and equals∑ , . It'sassumed that the jump size , comes from a normal distribution with average , and variance . is a variable that represents a separate counting process that records the number of jumps in 1, and follows a Poisson distribution with parameter 0. The probability density function is: Both the average and variance of the random variable is which is called jump intensity and is assumed to be an autoregressive process with the following moving average: 6 Where is the shock for and is aimed to measure the unexpected jumps at and updating the existing information set: ≡ |Ω |Ω 7 |Ω is calledfilter and according to the given informational setΩ and |Ω that identifies expected number of jumps in 2, 1 interval, extracts . Note that according to definition is a martingale difference sequence with respect to the information inΩ ; therefore 0 and , 0, 0 and we can write jump intensity as: |Ω 8 where and 0, , The conditional variance of return is consisted of two parts; one part represents smooth conditional variance and is affected by past news. The other parts is conditional variance of arrival heterogeneous information which creates a jump. the conditional variance of returns is: 11 , , 0,1 , , ,

Conclusion
In this paper, we used the model of Chan and Maheu (2002) which was previously used to model stock return and exchange rate, to model OPEC oil price change. Two reasons supported this approach. First, there was evidence on similarities between oil data and stock market data and there was a possibility of using the models associated to stock market data in oil data analysis. Second, the above model could be effective in modeling unexpected events and news such as sudden increase in prices. In addition, low price elasticity of oil demand and supply and simultaneous large change in prices for clearing even small excess supply or demand was another motive for using such a model; but the thing that makes the Chan and Maheu (2002) model more interesting than other jump models, was the dynamic nature of jump variable and change of its magnitude and frequency over time. In fact, in other models, the jump variable was constant and this was a limiting assumption. Second, in contrast with most of the financial econometrics models that focus on techniques rather than results, findings of this model were associated to some theoretical findings of particular importance.
Hotelling (1931) stated a famous law on oil price; price of a finite resource in the optimal settings rises with interest rate. Later, the Hotelling theory was developed by considering global warming and greenhouse gas emissions. The result of this development was that ignoring greenhouse gas emissions can result in excessive oil extracting. Furthermore, the information extracted from oil price is crucial for technology change decisions and oil price is a better indicator of the lack of resources than the amount of oil production. Using the Chan and Maheu (2002) model showed strong evidence on GARCH model behaviors and also conditional jump intensity in daily data of oil price; that is, conditional heteroscedasticity variance exists and practical distribution has fat tail. Furthermore, this model has high sensitivity to events and news and, therefore, it does not fluctuate around a long-term pattern; and despite that previous theories hold that prices fluctuate around an increasing pattern and oil price contains information, this model rejects the existence of such information. The most important result of this model is the rejection of an optimal path for extracting oil and technology transmission. In fact, the lack of a long-term pattern can cause excessive oil extracting which can result in heavy climatic effects.