اثر سرریز جهش در بازارهای آتی انرژی : مفاهیمی برای منافع متنوع

In this paper, we investigate jump spillover effects of five energy (petroleum) futures and their implications for diversification benefits. In order to identify the latent historical jumps for each of these energy futures, we use a Bayesian MCMC approach to estimate a jump-diffusion model for each. We examine the simultaneous jump intensities of pairs of energy futures and the probabilities that jumps in crude oil (and natural gas) cause jumps or usually large returns in other energy futures. In all cases, we find significant evidence that the diffusion-jump process is a better characterization for energy futures prices. We further find that jump spillovers significantly reduce the diversification benefits of an energy futures portfolio in a tranquil (rather than crisis) period.

There is strong evidence that jumps (price spikes) play an important role in the continuous diffusion process of asset price. Such models, which allow for the presence of jumps, are often referred to as event risk models. A number of recent theoretical studies analyze the impact of event risk on strategic asset allocation (Liu et al. (2003), Wu (2003)), on option pricing and its ability to explain the observed volatility smiles (Pan (2002), Eraker et al. (2003)), on calculations of risk measures such as value-at-risk (VaR) (Duffie and Pan (2001), and Gibson (2001)). Recently, Asgharian and Bengtsson (2006) employed such an event risk model to study jump spillover effects between a number of country equity indexes. They use a Bayesian approach to estimate a jump-diffusion model on each index and find significant evidence of jump spillover. The recent dramatic spikes in energy prices (in particular oil) that peaked in the summer of 2008 (see Fig. 1) have greatly emphasized the importance of understanding and managing risk in these markets. Askari and Krichene (2008) show that oil price dynamics during 2002–2006 have been characterized by high volatility, high intensity jumps, and strong upward drift. Market expectations, extracted from call and put option prices, indicated no change in underlying fundamentals in the short term. But markets expect oil prices to remain volatile and jumpy, and with higher probabilities of rising, rather than falling, above the expected mean. Observers of energy futures markets (crude oil, natural gas, heating oil, gasoline and fuel oil) have long noted that energy futures prices are very volatile and often exhibit jumps following important news. The main purpose of this paper is to estimate an event risk model for the above five energy (petroleum) futures contracts in order to identify the latent historical jump times of each energy futures, which we then use to quantify the degree of jump spillover between the different futures contracts. As we know, heating oil, gasoline and fuel oil are all refined products of crude oil, and natural gas is a close substitute for crude oil in many industrial processes. Past studies have established the existence of long-run price cointegrations between crude oil and its refined products (Girma and Paulson (1999); Gjølberg and Johnsen (1999); Asche et al. (2003)). Furthermore, a cointegrating relationship between crude oil and natural gas has also been found. In contrast to the prediction of the natural gas market liberalization theory, Panagiotidis and Rutledge (2007) found that the cointegrating relationship between UK wholesale natural gas prices and the Brent oil price continued to exist during the period of 1996–2003, although oil and natural gas prices had been “decoupled” since 1994. Although the integration of energy (petroleum) markets has been widely investigated, the jump spillover (or event risk) effect between energy markets has not received as much attention to date. We focus here on two forms of jump spillover. First, we calculate the simultaneous jump intensities for pairs of energy futures contracts and we test whether or not these simultaneous jump intensities are significant. Second, we analyze conditional jump spillover to examine to what extent jumps in a specific energy futures increase the probability of jumps in other energy futures, or in a weaker form, cause unusually large negative returns in other energy futures. To identify the historical jump times, we estimate a univariate affine jump-diffusion model with stochastic volatility on each energy futures contract.2 This model, which falls into the class of affine jump-diffusion models proposed by Duffie et al. (2000), is referred to as the stochastic volatility with correlated jumps (SVCJ) model and it assumes that jumps in returns and volatility arrive simultaneously and that the jump sizes are correlated. A relatively robust approach based on Markov Chain Monte Carlo (MCMC) methods is used for the estimation of event risk models. The MCMC method for inference and parameter estimation is a Bayesian and simulation-based estimation method. Its use to estimate stochastic volatility models was proposed by Jacquier et al. (1994) and the method was extended to models with jumps in returns and volatility by Eraker et al. (2003).3 Our empirical results show strong evidence for the existence of jump spillover. The estimated simultaneous jump intensities are in general significantly larger than the corresponding intensities under the null hypothesis that the different energy futures' jump processes are independent of each other. Most interestingly, however, we find that the historical sample correlations between the energy futures are not good measures to capture the jump spillover effects. We also look at the sizes of the simultaneous jumps and find that they can be positive or negative and, in general, larger (in absolute terms) than the sizes of the energy-futures-specifics jumps. This implies that both good and bad news (or events) cause jump spillover. In our analysis of conditional jump spillover from crude oil futures (and natural gas futures) to other energy futures, we also find strong evidence of jump spillovers. A large majority of the estimated conditional jump spillover probabilities are significantly larger than the corresponding probabilities under the null hypothesis of independent jump processes. Our findings motivate us to investigate whether jump spillovers affect the portfolio risk diversification benefits. Recently, Kurmann (2009) presented a double dynamic jump-diffusion model with positive and negative jumps to study the effect of jump risk on a risk-averse investor's optimum portfolio allocation. He found that jumps of many financial assets exhibit three properties: first, jumps seem to occur simultaneously across markets, second, jumps tend to cluster, and finally, there exist positive and negative jumps. Further, the current study provides empirical evidence that jump risk substantially alters the optimum portfolio allocation. In contrast with Kurmann (2009), the investigation of this paper (1) employs a SVCJ model and assumes that jumps in returns and volatility arrive simultaneously and that jump sizes are correlated; (2) uses a relatively robust approach based on MCMC method for the estimation of event risk model; (3) examines simultaneous and subsequent (conditional) jump spillover effects of energy futures; and (4) compares Sharpe ratios to investigate whether the benefits of portfolio diversification decline in the presence of jump spillover. This study is, to our knowledge, the first attempt to determine whether or not jump risks affect the benefits of portfolio diversification in the area of energy commodities. The structure of the rest of the article is as follows: Section 2 presents the event risk model and the estimation method and interprets the model accuracy through the comparison of Bayes factors. Section 3 contains the empirical results and the analysis of jump spillover. Section 4 investigates the diversification benefits of energy futures portfolios. Section 5 concludes