以時變自我迴歸模型預測金融商品之風險值

Predicting Value at Risk of financial products by time-varying autoregressive model

朱慧培(Hui-Pei Chu)

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

隨著財務工程理論之發展，金融商品不斷推陳出新，資產部位趨於多元與複雜，使得風險隨之增加。風險值主要的目的是用以衡量投資部位在未來所面臨的最大損失，因此，如何有效評估風險實為投資者所關心的重要議題。許多財務金融文獻指出，資產報酬分配具有自我相關性及波動叢聚性(volatility clustering)，故常使用自我相關條件異質變異的GARCH族群模型，如：ARMA(p,q)-GARCH(m,n) 模型進行資產報酬之風險值估計。
　　本論文主要目的是建立金融商品報酬風險值（VaR）的模型，其概念來自於Tesheng Hsiao(2008) 所提及的時變自我迴歸模型。此模型有別於一般自我迴歸模型，一般自我迴歸模型假設常數項與落遲項的係數均為常數，不會隨著時間而改變，但金融商品報酬風險值通常並不滿足此假設。因此，本研究考慮建立時變自我迴歸模型，建模方式為先以滾動 (rolling) 方式對不同時間點估計其AR模型之常數項r0(t)與落遲項之係數r1(t)、r2(t)；GARCH模型之常數項a0(t)與過去變異數項之係數a1(t)、及干擾項之係數b1(t)，以建構金融商品報酬風險值 (VaR) 的時變AR-GARCH模型。
在實證方面，本文以Dow Jones和NASDAQ為例，針對所建立的模型進行實證分析，評估在1%、5%及10%信賴水準下，其模型所計算出來的風險值之特性，並計算其穿透率，即損失超過風險值的比率，來評估VaR的預測能力。

關鍵字

時變自我迴歸 ； GARCH族群模型 ； 滾動估計 ； 風險值

並列摘要

The fast growing of the theory of financial engineering and well developing of variety financial products in the financial market cause the evaluation of asset positions tends to diversification and complex, and the risk of access is increased as well. The major function of VaR (value at risk) is to measure the maximum loss of investment positions; therefore, how to assess VaR effectively is an important issue concerned by investors. It is already shown on many finance literatures that the distribution of assets return have the properties of autocorrelation and volatility clustering. Hence, models of GARCH (autocorrelation conditional heteroskedasticity) family, such as: ARMA (p, q)-GARCH (m, n) models are suggested to estimate the risk of assets return.
The purpose of this study is to establish the VaR of assets return of financial products. The major idea of this study is applying time-varying autoregressive model by Tesheng Hsiao (2008). This model differs from general autoregressive model on assuming that the constant term and lag coefficients are fixed and not change over time. This assumption seems inadequate for modeling the VaR of assets return of financial products. The technique of this study obtains time varying coefficients by using rolling estimation to estimate the coefficient of AR-GARCH model and then obtains a time varying model.
Finally, the Dow Jones and NASDAQ indices are illustrated for empirical analysis. And the penetration rate of 1%, 5% and 10% confidence level are calculated to assess the predictive ability.

並列關鍵字

time-varying autoregressive ； GARCH family model ； rolling estimation ； value at risk

參考文獻

吳亭穎 (2008), 投資組合風險值估算模型之探討-多變量MAR-GARCH模型,

邱思妤 (2011), 在風險值限制下考量動態波動的最適投資組合, 國立台北大學

Black, F. (1976) “Studies in stock price volatility changes.” Proceedings of the American Statistical Association. Business and Economic Statistics Section, 177-181.

Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroskedasticity,”

Journal of Econometrics, 31, 307-327.