Abstract—With the development of technology and financial engineering tools, oil markets are more competitive and volatile than ever before. This places the accurate and reliable measurement of market risks in the crucial position for both investment decision and hedging strategy designs. This paper tackles the measurement of risks from a Value at Risk (VaR) perspective. Since traditional ARMA-GARCH approach doesn’t suffice, this paper proposes ex-ante based approach for hybrid algorithm design and further applies this methodology with a wavelet approach to VaR estimates. Empirical studies of the proposed Wavelet Decomposed Value at Risk (WDVaR) have been conducted on two major oil markets (I.e. WTI & Brent). Experiment results suggest that the performance of WDVaR improves upon ARMA-GARCH model at higher confidence levels. Meanwhile, WDVaR offer considerable flexibility during modeling process. WDVaR can be tailored to specific market characteristics and its performance can be further improved with more careful parameter tuning. I. INTRODUCTION HE crude oil is one of the most important industry inputs and remains the major sources of world’s energy consumption. The price paths of crude oil and its volatilities affect different market movements (E.g. various commodities markets, etc) and the economic status as a whole[1], [2]. Oil markets have long been the most volatile ones since shocks and the associated risks of losses could prevail in the market due to low inventory level hindered by extremely high storage costs. As the role of market forces increase continuously with the shifts of market from more managed market agreement to the more flexible market based environment, market is getting more volatile and vulnerable to unexpected extreme events[2]. Thus proper measurement and management of market risks are increasingly valued by investors to protect themselves against adverse market movements. This paper investigates the risk measurement issue in oil markets. The measurement of risks in oil markets are complicated processes since oil prices receive joint influences from numerous risk factors. To name just a few, these may include economic aspects, weather changes, political aspects, K. K. Lai is with the College of Business Administration, Hunan University, Changsha, Hunan, China. He is also with the Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong (phone: +852 2788 8563; fax: +852 27888560 ; email: mskklai@cityu.edu.hk). KJ. HE is with the College of Business Administration, Hunan University, Changsha, Hunan, China (email: paulhekj@hnu.cn). C. Xie is with the College of Business Administration, Hunan University, Changsha, Hunan, China (email: xiechi@hnu.cn) S. Chen is with the College of Business Administration, Hunan University, Changsha, Hunan, China (email: chenshou@hnu.cn) military, natural disasters, market sentiments and speculations, etc[3], [4], [5]. If these factors and their interrelationships can be identified and quantified, large scale econometric models can be built to understand and track risk exposure levels. However, in practice this approach is generally very costly and infeasible except for rare circumstances. Another approach would resolve to the reduced form model such as time series analysis for help. With reduced form model, information is extracted from the past data and used to guide the future forecasting. This approach is less costly and more suitable when specific information relating the underlying risk factors and their interactions are not available[5]. The methodology used in this paper follows the reduced form approach. Value at Risk (VaR), as the latest development in the risk management field, is adopted in this paper to quantify and measure market risks. VaR is a single, summarizing statistic number that measures the magnitude of downside risk under normal market conditions over certain investment horizon at given confidence levels[6]. The reliability and accuracy of VaR estimates are of particular interests to investors since they would affect their capital adequacy and profit level. On the other hand, oil markets, among various commodity markets, attract significant research efforts in recent years due to the following reasons: Firstly data have been made publicly available at sufficiently high frequency and long time period. This makes possible the development and testing of VaR estimates under statistical framework[7], [8]. Secondly, price series in oil markets exhibit much higher level of volatility than other commodities and stock markets. The considerable risks and unique characteristics of the market demand the development of new risk management tools[7], [8]. Thirdly despite the proliferation of volatility analysis and forecasting of oil prices, the open literature is surprisingly scarce in the development of appropriate risk measurement for the market. There have been few attempts to uncover the stylized features of oil markets, not to mention the estimation issue that lies at the heart of VaR implementation [3], [4], [9], [10], [11]. To estimate VaR at reliable and accurate level, various methods have been tried over years. They can be broadly categorized into parametric and non-parametric approaches. Non-parametric approaches give investors little insights and controls over underlying risk factors evolutions. Parametric approaches are ex-post in nature. They fit model into data with the hope that the data are mostly dominated by the expected data features and the model should be able to pick them up. Since this rarely holds in practice, their Market Risk Measurement for Crude Oil: A Wavelet Based VaR Approach Kin Keung LAI, Kaijian HE, Chi XIE, and Shou CHEN T U.S. Government work not protected by U.S. copyright 2006 International Joint Conference on Neural Networks Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006 2129