利用期望百分位之條件自我迴歸模型評估風險值

Assessing Value at Risk by the Expectile Conditional Autoregressive model

溫婉菁(Wen,Wan-Ching)

指導教授 ： 李孟峰

國立臺北大學/商學院/統計學系/碩士(2012年)

摘要

在金融市場中,資產價格的波動是造成風險的主要因素之ㄧ,投資人在面對此風險時,會評估此風險可能帶來的損失,進而準備相對應的措施。因此,如何正確的衡量下方的風險為一很重要的議題。
文獻上,計算風險值 (VaR) 已逐漸成為預測及控管風險的重要工具, 風險值可以讓管理者 (或投資人) 預先了解投資部位的潛在風險可能有多少,並事先做好避險措施,或提撥相對的損失金額準備。近年來,計量分析已成為一種重要的衡量方式,較為著名的有 Koenker and Bassett(1978)所提出的分量法 (quantile method) 及 Newey and Powell(1987)所提出的 expectile 模型,這兩種方法皆能用來估計資產報酬的風險值。
在金融市場裡,大部分的資產報酬具有波動叢聚的現象,也就是資產報酬分配具有自我相關性,因此本文利用 Engel and Manganelli (2004)所提出的條件自我相關風險值模型 (CaViaR) 來估計風險值,並以 Newey and Powell(1987) 所提出的 expectile 值為架構，推廣出期望百分位之條件自我迴歸模型來估計風險值。
最後以 Dow Jones 和 NASDAQ 指數為實證資料,針對以上模型做實證分析,評估在不同的信賴水準下使用不同模型所計算出來的風險值的特質,並比較其穿透率，即每日投資損失超過風險值的比率。

關鍵字

風險值 ； 分位迴歸 ； Quantile 值 ； Expectile 值 ； CAViaR

並列摘要

In financial markets, one of the major factors which will cause risk is due to the fluctuation of assets price. When a Investor faces risk, he/she should evaluate how much losses will happen, and thus to propose the corresponding strategies. Therefore, how to properly measure the downside risk is a very important issue.
Value at risk (VaR) has become an important tool for predicting and managing risk. VaR is a measure of market risk which can be used by an investor to evaluate how much a portfolio could lose. Recently, the use of quantitative risk measures has become an essential management tool. Quantile regression is a famous method introduced by Koenker and Bassett (1978). Another method is expectile offerred by Newey and Powell (1987). These two methods both can estimate the value at risk of assets return.
In financial markets, volatility clustering is found on the distribution of most assets return. In other words, assets return tends to be autocorrelated. In this paper, we apply the condition autoregressive value at risk (CAViaR) model by quantiles regression method suggested by Engel and Manganelli (2004) to assessing the value at risk, and extend the CAViaR model by expectile regression method suggested by Newey and Powell (1987).
Finally, Dow Jones and NASDAQ indices are illustrated as practical analyses. The proposed modeling approach and CaViaR modeling approach are both applied to evaluate the value at risk in different confidence levels of two stock indices. The penetration rate of daily return is also compared to evaluate the accuracy of the two methods.

並列關鍵字

Value at risk ； quantile regression ； Quantile ； Expectile ； CAViaR

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