Extreme Value Theory and Value at Risk : Application to Oil Market

Recent increases in energy prices, especially oil prices, have become a principal concern for consumers, corporations, and governments. Most analysts believe that oil price fluctuations have considerable consequences on economic activity. Oil markets have become relatively free, resulting in a high degree of oil-price volatility and generating radical changes to world energy and oil industries. As a result oil markets are naturally vulnerable to significant negative volatility. An example of such a case is the oil embargo crisis of 1973. In this newly created climate, protection against market risk has become a necessity. Value at Risk (VaR) measures risk exposure at a given probability level and is very important for risk management. Appealing aspects of Extreme Value Theory (EVT) have made convincing arguments for its use in managing energy price risks. In this paper, we apply both unconditional and conditional EVT models to forecast Value at Risk. These models are compared to the performances of other well-known modelling techniques, such as GARCH, historical simulation and Filtered Historical Simulation. Both conditional EVT and Filtered Historical Simulation procedures offer a major improvement over the parametric methods. Furthermore, GARCH(1, 1)-t model may provide equally good results, as well as the combining of the two procedures.Extreme Value Theory, Value at Risk, oil price volatility, GARCH, Historical Simulation, Filtered Historical Simulation.

Prévision du NO2 en utilisant la méthode du réseau de neurones

Cet article décrit une procédure de modélisation du phénomène de dispersion de la concentration du dioxyde de nitrogène (NO2) en utilisant la technique du perceptron multicouche (MLP). Notre objectif est de prouver que la concentration du NO2 est une variable autorégressive et expliquée par des variables météorologiques. Pour ce faire, nous avons procédé par trois étapes : dans la première étape nous avons utilisé la variable concentration NO2 uniquement, dans la seconde étape nous avons utilisé les variables météorologiques uniquement et dans la troisième étape nous avons utilisé la concentration du NO2 combinée avec les variables météorologiques. Les résultats ont montré que le troisième cas est plus performant que les deux autres ce qui prouve notre hypothèse

Extreme Value Theory and Value at Risk : Application to Oil Market

Recent increases in energy prices, especially oil prices, have become a principal concern for consumers, corporations, and governments. Most analysts believe that oil price fluctuations have considerable consequences on economic activity. Oil markets have become relatively free, resulting in a high degree of oil-price volatility and generating radical changes to world energy and oil industries. As a result oil markets are naturally vulnerable to significant negative volatility. An example of such a case is the oil embargo crisis of 1973. In this newly created climate, protection against market risk has become a necessity. Value at Risk (VaR) measures risk exposure at a given probability level and is very important for risk management. Appealing aspects of Extreme Value Theory (EVT) have made convincing arguments for its use in managing energy price risks. In this paper, we apply both unconditional and conditional EVT models to forecast Value at Risk. These models are compared to the performances of other well-known modelling techniques, such as GARCH, historical simulation and Filtered Historical Simulation. Both conditional EVT and Filtered Historical Simulation procedures offer a major improvement over the parametric methods. Furthermore, GARCH(1, 1)-t model may provide equally good results, as well as the combining of the two procedures

Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation

This paper conducts a comparative evaluation of the predictive performance of various Value at Risk (VaR) models such as GARCH-normal, GARCH-t, EGARCH, TGARCH models, variance-covariance method, historical simulation and filtred Historical Simulation, EVT and conditional EVT methods. Special emphasis is paid on two methodologies related to the Extreme Value Theory (EVT): The Peaks over Threshold (POT) and the Block Maxima (BM). Both estimation techniques are based on limits results for the excess distribution over high thresholds and block maxima, respectively. We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the Tunisian stock exchange (BVMT) and CAC 40 indexes with the intension to compare the performance of various estimation methods on markets with different capitalization and trading practices. The sample extends over the period July 29, 1994 to December 30, 2005. We use a rolling windows of approximately four years (n= 1000 days). The sub-period from July, 1998 for BVMT (from August 4, 1998 for CAC 40) has been reserved for backtesting purposes. The results we report demonstrate that conditional POT-EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate

Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation

This paper conducts a comparative evaluation of the predictive performance of various Value at Risk (VaR) models such as GARCH-normal, GARCH-t, EGARCH, TGARCH models, variance-covariance method, historical simulation and filtred Historical Simulation, EVT and conditional EVT methods. Special emphasis is paid on two methodologies related to the Extreme Value Theory (EVT): The Peaks over Threshold (POT) and the Block Maxima (BM). Both estimation techniques are based on limits results for the excess distribution over high thresholds and block maxima, respectively. We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the Tunisian stock exchange (BVMT) and CAC 40 indexes with the intension to compare the performance of various estimation methods on markets with different capitalization and trading practices. The sample extends over the period July 29, 1994 to December 30, 2005. We use a rolling windows of approximately four years (n= 1000 days). The sub-period from July, 1998 for BVMT (from August 4, 1998 for CAC 40) has been reserved for backtesting purposes. The results we report demonstrate that conditional POT-EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate

Seasonal and Periodic Long Memory Models in the In�ation Rates

This paper considers the application of long memory processes to describe inflation with seasonal behaviour. We use three different long memory models taking into account the seasonal pattern in the data. Namely, the ARFIMA model with deterministic seasonality, the ARFISMA model, and the periodic ARFIMA (PARFIMA) model. These models are used to describe the inflation rates of four different countries, USA, Canada, Tunisia, and South Africa. The analysis is carried out using the Sowell's (1992) maximum likelihood techniques for estimating ARFIMA model and using the approximate maximum likelihood method for the estimation of the PARFIMA process. We implement a new procedure to obtain the maximum likelihood estimates of the ARFISMA model, in which dummies variables on additive outliers are included. The advantage of this parametric estimation method is that all parameters are estimated simultaneously in the time domain. For all countries, we find that estimates of differencing parameters are significantly different from zero. This is evidence in favour of long memory and suggests that persistence is a common feature for inflation series. Note that neglecting the existence of additive outliers may possibly biased estimates of the seasonal and periodic long memory models

Seasonal and Periodic Long Memory Models in the In�ation Rates

This paper considers the application of long memory processes to describe inflation with seasonal behaviour. We use three different long memory models taking into account the seasonal pattern in the data. Namely, the ARFIMA model with deterministic seasonality, the ARFISMA model, and the periodic ARFIMA (PARFIMA) model. These models are used to describe the inflation rates of four different countries, USA, Canada, Tunisia, and South Africa. The analysis is carried out using the Sowell's (1992) maximum likelihood techniques for estimating ARFIMA model and using the approximate maximum likelihood method for the estimation of the PARFIMA process. We implement a new procedure to obtain the maximum likelihood estimates of the ARFISMA model, in which dummies variables on additive outliers are included. The advantage of this parametric estimation method is that all parameters are estimated simultaneously in the time domain. For all countries, we find that estimates of differencing parameters are significantly different from zero. This is evidence in favour of long memory and suggests that persistence is a common feature for inflation series. Note that neglecting the existence of additive outliers may possibly biased estimates of the seasonal and periodic long memory models

Markov Switching and State-Space Approaches for Investigating the Link between Egyptian Inflation Level and Uncertainty

In this paper, we use the Markov switching model, the state-space model with Markov switching heteroskedasticity and the local level model with GARCH(1,1) disturbances to investigate the link between the level of Egyptian inflation and its uncertainty. We use different ways to measure inflation uncertainty. First, we consider it as the variance of unanticipated inflation. Second, we measure it as the unconditional variance of unanticipated changes in inflation. Finally, we measure it by the conditional variance modeled as GARCH effect. We find evidence of a positive effect of inflation level on inflation uncertainty for the three models. By making the distinction between the long run and the short run, we conclude that inflation has a significant positive effect on uncertainty in the short run but no effect in the long run. We state that the cost of inflation is mainly due to the association between higher inflation and higher short-run uncertainty. Reversing the causality link between inflation and its uncertainty, we find that inflation uncertainty has a positive effect on inflation level in the short run but this effect dies out in the long run, which is indicative of a stabilization monetary policy in Egypt. According to the likelihood-based information criteria (Akaike and Schwarz Bayesian criteria), the state-space model with Markov switching heteroskedasticity and the two-state Markov switching model outperform all others.