指數報酬率波動性之預測 - 分量回歸與核函數之實證研究

Volatility Forecasting with Quantile Regression and Kernel Estimation

彭煒驊(Wei-Hwa Peng)

指導教授 ： 黃宜侯

元智大學/管理學院/商學碩士班(財務金融學程)/碩士(2011年)

摘要

無論我們在做投資決策、選擇權的定價或是風險控管或是對任何的財務金融商品而言，波動性都是一種非常重要的衡量指標。由於風險與報酬是同等重要的，如何去衡量風險便是一個重要的課題。而這篇研究的重點就藉由提升風險值(Value at Risk)的預測能力來檢驗是否可以經由這樣的方式來提升我們對於波動性的預測能力。由過去的文獻提出，分量迴歸法所計算出來的風險值是會被低估的因此我們通過較新的核函數估計法(Kernel Estimator Approach)，去調整分量回歸法(Quantile Regression)所計算出來的風險值，再經由這新計算出來的風險值去預測波動性(Volatility)。資料的選取範圍由1980年1月1日到2008年8月31日為止，所選取的指數是經由MSCI Global Invested Market Indices所選取出來的，分別有12筆已開發國家的指數以及25筆開發中國家的指數。
本篇研究的主要結論如下，整體而言衡量風險值的方法在新興市場的表現相對而言較已開發市場差，但是依然是約有一半以上的指數是有改進的效果的。經由核函數估計法修正過後的分量所計算出來的波動性，相較於原本只用分量迴歸法計算出來的波動性是有明顯的改善的。相較於其他的波動性的估計方法，這個方法是優於GARCH以及I-GARCH模型，但是略差於GJR-GARCH、歷史模擬法以及狀態轉換模型(Regime switching model)的。

關鍵字

分量回歸與核函數之實證研究

並列摘要

Volatility forecasting is an important method in investing decision, option pricing and risk management. This research utilizes kernel estimation to improve quantile regression which would underestimate VaR. Then we examined whether the method we proposed could have better predictability comparing with other methods in developed markets and emerging markets. We use long period data which include 12 developed markets and 25 emerging markets.
The main conclusion of this research is that kernel estimation could improve the volatility forecasting ability of quantile regression. Comparing with other methods, it performs better than volatility forecasted by GARCH and I-GARCH, in contrast, Monte Carlo simulation and GJR-GARCH perform better than the method we proposed.

並列關鍵字

Volatility Forecasting ； Quantile Regression

參考文獻

Andersen, T. G. and T. Bollerslev, (1998) “Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts.” International Economic Review, 39, pp. 885-905.

Andersen, T. G., T. Bollerslev, and S. Lange, (1999) “Forecasting Finnacial Market Volatility: Sample Frequency vis-a-vis Forecast Horizon.” Journal of Empirical Finance, 6, pp. 457-77.

Ball, C. A. and W. N. Torous, (1984) “The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence and Application to Option Pricing” Journal of Business, 57, pp. 97-113.

Bollerslev, T., (1986) “A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rate of Return.” The Review of Economics and Statistics, 69, pp. 542-547.

Ding, Z., C. W. J. Granger, and R. F. Engle, (1993) “A Long Memory Property Of Stock Market Returns And A New Model.” Journal Empirical Finance, 1, pp. 83-106.