Elsevier

Energy Economics

Volume 31, Issue 4, July 2009, Pages 511-518
Energy Economics

CAViaR-based forecast for oil price risk

https://doi.org/10.1016/j.eneco.2008.12.006Get rights and content

Abstract

As a benchmark for measuring market risk, value-at-risk (VaR) reduces the risk associated with any kind of asset to just a number (amount in terms of a currency), which can be well understood by regulators, board members, and other interested parties. This paper employs a new VaR approach due to Engle and Manganelli [Engle, R.F., Manganelli, S., 2004. CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Journal of Business and Economic Statistics 22, 367–381] to forecasting oil price risk. In doing so, we provide two original contributions by introducing a new exponentially weighted moving average CAViaR model and developing a mixed data regression model for multi-period VaR prediction.

Introduction

Because of the key role of oil in the world economy, predicting the future price of this commodity and managing the risks associated with future oil prices are critical for central governments and businesses. Therefore oil price prediction and its risk measurement have been a common research theme in the last decades. Some examples of oil price prediction are 1) a semiparametric approach to shot-term oil price forecasting developed by Morana (2001), 2) a hybrid artificial intelligence system framework for crude oil price forecasting by integrating artificial neural networks and rule-based expert system with web-based text mining techniques proposed by Wang et al. (2004), and 3) a support vector machine method suggested by Xie et al. (2006). Our focus in this paper is on oil price risk measurement. Previous work in this area includes 1) Cabedo and Moya (2003) who proposed an ARMA historical simulation approach with value-at-risk (VaR) ideology and 2) Kuper (2002) who investigated (G)ARCH-based volatility performance with different historical data. A good literature review on oil price movements and their effects on economic and financial performance can be found in Sauter and Awerbuch (2002).

Our motivation for concentrating on quantifying oil price risk is that, as noted by Sauter and Awerbuch (2002), while most oil price movements from 1948–1985 were price increases, since 1986 the pattern has changed; more specifically, large price decreases are now commonplace, implying a rise in the volatility/risk of oil prices. More specifically, Jorion (2001) finds that the average volatility of crude oil prices is more than 37% a year, two and a half times that of the average US stock index and more than three times that of most major world currencies. Another interesting property of oil is that changes in oil prices have an impact on economic activity, but economic activity does not necessarily have an impact on oil prices (Sadorsky, 1999). In addition, Giot and Laurent (2003) show that oil prices exhibit excess kurtosis and that their volatility clusters over time. One may also refer to Kolos and Ronn (2008) and Ronn and Wimschulte (2008) for the estimation of market price of risk and its economic implications.

Compared with the more developed financial market risk measures, however, oil price risk management is still in its infancy. The empirical evidence is far from indicating any consensus about the existing models for oil price risk forecasting. Basically, empirical findings vary across models, time periods, and data frequencies. This is because, being a physical asset, oil has some additional attributes that are not associated with traditional financial assets. For example, as pointed out by Morana (2001), the price of oil is strongly influenced by inventory levels, weather, short-term demand and supply imbalances, and political issues. Thus, volatile oil price movements motivate consideration of how to quantify price risk. As a benchmark for measuring market risk, VaR reduces the risk associated with any kind of asset to just a number (amount in terms of a currency), which can be well understood by regulators, board members, and other interested parties.

The main objective of this paper is to investigate the predictive performance of various types of the conditional autoregressive value-at-risk (CAViaR) specifications for oil price risk prediction. The choice of this particular semiparametric method is motivated by the fact that CAViaR does not require any assumption on the distribution of a time series and computes the VaR directly by quantile regression, implying that the model allows the time series to switch from one stochastic process to another. With respect to oil price risk, Askari and Krichene (2008) use a Merton jump-diffusion process to model oil price returns and find that for the period 2002–2006, "oil price dynamics were dominated by discontinuous Poisson jump component…" There are two original theoretical contributions in this paper. First, we introduce a new exponentially weighted moving average CAViaR specification with only two parameters to be estimated, which in turn may reduce the model's estimation risk. Second, we develop a multi-period (weekly, biweekly, or monthly) VaR prediction model with daily VaR forecasting and returns.

The rest of the paper is structured as follows. Section 2 briefly summarizes the CAViaR model and then proposes a new asymmetric CAViaR model. Section 3 presents an approach for multi-period VaR prediction with different data frequencies. Section 4 provides criteria for performance comparison and some empirical results, followed by our concluding comments in Section 5.

Section snippets

Model

While the concept of VaR is intuitive, its modeling is a very challenging statistical problem. From a statistical point of view, VaR of a return series {rt}, conditional on the information set Ft  1, is defined as the negative θ-quantile, qt(θ), i.e., P(rt   qt(θ)|Ft  1) = θ.

Although the existing models for calculating VaR employ different methodologies, they can be generally classified into two broad categories: indirect-VaR approach and direct-VaR approach. The first category includes the

Multi-period CAViaR

We focus in this section on predicting multi-period VaR from one day to one week, two weeks, or one month because those time periods are typically used by practitioners.

The simplest approach to generating multi-period VaR forecasts is to multiply the one step-ahead prediction by the square root of the holding period k, a procedure usually used in RiskMetrics (1996). However, this approach implicitly requires that the variance of the time series is constant in the holding period, thereby

Empirical results

In this section, we apply the CAViaR model to oil price risk quantification and employ some statistical tests designed for evaluating the predictive quantile performance. As discussed in Section 1, due to some special properties of oil prices, it is unreasonable to assume that the dynamics of the oil return series follow a certain stochastic process. That is what motivated the consideration of the CAViaR model by accommodating different processes into the prediction horizon.

Conclusion

In this paper, we employ an extension of the CAViaR model to quantify oil price risk. Our model not only accommodates different stochastic processes, but also satisfies the property of dynamic quantile (Gourieroux and Jasiak, 2006). In addition, we introduce a mixed data regression model to predict multi-period VaR from different frequency VaR prediction and returns. For example, we can predict one-month-ahead VaR by using all information available, such as daily and weekly returns and the

Acknowledgements

We are grateful to the anonymous referee for helpful comments and suggestions. This work was partially supported by the National Basic Research Program of China (973 Program) (No. 2007CB814902) and the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.

References (29)

  • ChristoffersenP.

    Evaluating interval forecasts

    International Economic Review

    (1998)
  • DanielssonJ. et al.

    Forecasting extreme financial risk: a critical analysis of practical methods for the Japanese market

    Monetary and Economic Studies

    (2000)
  • Energy Information Administration:...
  • EngleR.F. et al.

    CAViaR: conditional autoregressive value at risk by regression quantiles

    Journal of Business and Economic Statistics

    (2004)
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