CAViaR-based forecast for oil price risk
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)
- et al.
Oil price dynamics (2002–2006)
Enery Economics
(2008) - et al.
A subsampling approach to estimating the distribution of diverging statistics with application to assessing financial market risk
Journal of Econometrics
(2004) - et al.
Market risk in commodity markets: a VaR approach
Energy Economics
(2003) - et al.
Dynamic quantile models
Journal of Econometrics
(2008) - et al.
Estimating the commodity market price of risk for energy prices
Energy Economics
(2008) Quasi-maximum likelihood estimation for conditional quantile
Journal of Econometrics
(2005)A semiparametric approach to short-term oil price forecasting
Energy Economics
(2001)Oil price shocks and stock market activity
Energy Economics
(1999)- et al.
Evaluating the predictive performance of value-at-risk models in emerging markets: a reality check
Journal of Forecasting
(2006) - et al.
Estimating oil price value-at-risk using the historical simulation approach
Energy Economics
(2003)
Evaluating interval forecasts
International Economic Review
Forecasting extreme financial risk: a critical analysis of practical methods for the Japanese market
Monetary and Economic Studies
CAViaR: conditional autoregressive value at risk by regression quantiles
Journal of Business and Economic Statistics
Cited by (36)
VaR and ES forecasting via recurrent neural network-based stateful models
2024, International Review of Financial AnalysisA novel interval-based hybrid framework for crude oil price forecasting and trading
2024, Energy EconomicsEstimation of value at risk for copper
2023, Journal of Commodity MarketsRisk measurement of oil price based on Bayesian nonlinear quantile regression model
2021, Alexandria Engineering JournalThe impact of extreme events on energy price risk
2021, Energy EconomicsThe transmission of default risk between banks and countries based on CAViaR models
2021, International Review of Economics and Finance