The estimation and forecasting of Value-at-Risk for financial commodities

• Main Authors: Jung-Bin Su, 蘇榮斌
• Other Authors: Ming-Chih Lee
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/44579485554304505365

博士 === 淡江大學 === 財務金融學系博士班 === 96 === This study focuses on VaR measurement and Option pricing, and it contains three parts. The first part is titled “Value-at-Risk Forecasts in Gold Market under Oil Shocks”, the second part is named “Value-at-Risk Forecasts in U.S. Crude Oil Market with Skewed Generalized Error Distributions.”, and the last one is “Option Pricing with Skewed Generalized Error Distributions.” A brief introduction of these three parts is described as follow: The first part investigates the value-at-risk in gold markets by considering both oil volatilities and the flexible model construction. The oil volatility is estimated using the dynamic jump model, and the volatility is distinguished further into stochastic and jump volatility. The flexible models include the BHK and PGARCH models. Finally, by combining the data with the rolling window approach, the appropriate out-of-sample VaR estimates are clearly obtained in this paper. The empirical results demonstrate that the BHK-PGARCH-HV-type model, which distinguish both the crude oil volatility and focus on the high volatilities, perform best in this paper. That is to say, the high volatility and jump volatility cannot be ignored in forecasting gold VaR. In the second part, we propose a composite Simpson’s rule, a numerical integral method, for estimating quantiles on the skewed generalized error distribution (SGED). Daily spot prices of Brent and WTI crude oil are used to examine the one-day-ahead VaR forecasting performance of the ARJI-N and ARJI-SGED models. Empirical results show that Brent crude oil exhibits slightly skewed to the left while WTI exhibits slightly skewed to the right. Therefore the ARJI-N model may overestimate the true VaR for Brent crude oil and underestimate the true VaR for WTI crude oil. These findings demonstrate that the use of SGED distribution, which explicitly accommodates both skewness and kurtosis, is essential for out-of-sample VaR forecasting in U.S. oil markets. The last part presents a novel option-pricing model based on the Skewed Generalized Error Distribution (SGED). A composite Simpson’s rule is used to acquire numerical results under the SGED and its degenerative distributions with varying degrees of skewness and kurtosis. The impact of skewness and kurtosis on Black-Scholes biases is investigated. The following analytical results are based on numerical analyses. Some asymmetrical phenomena exist. For any ( ), the extent of overpricing or underpricing increases when the absolute value of ( ) increases (decreases). For the impact of skewness, when =2, the Black-Scholes model overprices (underprices) the options price for a negative (positive) on the left of the homo-bias point, whereas the model underprices (overprices) for a negative (positive) on the right of the homo-bias point. For = 1.5 and 1.0, the overpricing areas shift to the right when the value of increases from to 0.25. The degree of underpricing or overpricing increases when decreases from 2.0 to 1.0. For the impact of kurtosis, when = 0, the Black-Scholes model underprices the options price on the left of the left homo-bias point and on the right of the right homo-bias point, and overprices between these two points. For = (0.2), the overpriced areas shift to the right (left) and then increase in size when decreases from 2.0 to 1.0. This survey will help explain the various known Black-Scholes biases.