風險值估算模型的正確性評估－以台灣加權股價指數為例

Evaluating the Accuracy of Value-at-Risk Models－The Case of Taiwan Weighted Stock Index

湯富佳(Fu-Chia Tang)

指導教授 ： 洪茂蔚

國立臺灣大學/管理學院/國際企業學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.10309

摘要

在看了許多的文獻與網路上相關文章後，發現在計算風險值時，多數人都以極值理論做出發點，原因在於該理論不用事先對整個投資組合分配做假設，只需要估計該投資組合的尾部分配。該理論雖然廣被採納，但在極端值沒有發生的情況下，使用一般的估算模型即可，如歷史模擬法、蒙地卡羅模擬法與GARCH模型。而在有極端值的情況下，極值理論可提供一個較精確的方法來估算風險值。

在2008年一月的The Journal of Risk Finance中，Colin J. Thompson與Michael A. McCarthy提出了另外一種風險值衡量方法，本篇研究以台灣加權股價指數報酬率作為資料基礎，對該方法、歷史模擬法、非條件常態分配模型與極值理論下常被使用的兩模型來做正確性評估。

根據不同模型算出的風險值來看，極值理論的風險值通常大於其他一般的模型，但是極值分配通常要先對參數做估計，相較於其他模型，更容易產生誤差。所以，若非確定會有極端值的產生，使用其他方法則較佳。

關鍵字

極值理論 ； 參數估計 ； 一般化極值分配 ； 一般化柏拉圖分配

並列摘要

After reading lots of papers and related articles, I find that most people use extreme value theory to calculate value-at-risk. The reason is that it is not necessary to assume the distribution of the portfolio in advance by using the theory. All that we need to do is to estimate the tail distribution of the portfolio. Although the theory is adopted commonly by everyone, it is fine to use general estimating models, such as historical simulation method, Monte Carlo simulation method, and GARCH model, with no extreme values. Extreme value theory can provide a more accurate value-at-risk with extreme values.

In The Journal of Risk Finance of Jan. 2008, Colin J. Thompson and Michael A. McCarthy propose another method for evaluating value-at-risk. This paper uses Taiwan weighted stock index to evaluate the accuracy of this new method, historical simulation method, model of non-conditional Normal distribution , and the two models of extreme value theory, which are Block Maximum Method (BMM) and Peak over Threshold Method (POT).

According to value-at-risks calculated by different models, value-at-risk of extreme value theory is usually bigger than others. Comparing to other models, extreme value theory usually needs to estimate parameters in advance. That makes the method generate errors easily. If you are not sure that there will be extreme values, it will be better to use other methods.

並列關鍵字

extreme value theory(EVT) ； estimation of parameters ； generalized extreme value distribution(GEV) ； generalized Pareto distribution(GPD) ； value-at-risk(VaR)

參考文獻

1. Colin J. Thompson, Michael A. McCarthy,”Alternative Measures to Value at Risk,” The Journal of Risk Finance. Vol.9 No.1, 2008, pp.81-88.

2. Philippe Jorion（2007）, Value at Risk－The New Benchmark for Managing Financial Risk, 3rd edition. McGraw-Hill Company.

5. JIN ZHANG,” LIKELIHOOD MOMENT ESTIMATION FOR THE GENERALIZED PARETODISTRIBUTION,” Aust. N. Z. J. Stat. 49(1), 2007, 69–77

6. TURAN G. BALI,” A Generalized Extreme Value ApproachtoFinancial Risk Measurement,” Journal of Money, Cr edit and Banking, Vol. 39, No. 7 (October 2007)

7. Fotios C Harmantzis; Linyan Miao; Yifan Chien,” Empirical study of value-at-risk and expected shortfall models with heavy tails,” The Journal of Risk Finance; 2006; 7, 2; ABI/INFORM Global pg. 117