隨機波動模型之應用—厚尾與槓桿效應

Application of Stochastic Volatility Model with Fat-tail and Leverage Effects

王翊驊(Yi-Hua Wang)

指導教授 ： 黃宜侯

元智大學/管理學院/財務金融學系/碩士(2009年)

https://doi.org/10.6838/YZU.2009.00032

摘要

隨著風險管理日趨重要的趨勢，預測波動率的模型亦受到高度關注。隨機波動模型(Stochastic Volatility Model, SVM)具有較佳的彈性可以用來捕捉許多波動率之重要性質，增加其預測的準確性與效率。本研究利用門檻(threshold)設定提出兩個嶄新的模型，預期符合波動率之厚尾(fat-tail)以及非線性槓桿效應(leverage effects)等特性後，應用在實證資料上能提升SVM在預測波動率上的準確性與效率。結果顯示符合厚尾之新模型的表現和傳統SVM模型相當，約有60%之預測效力，證明SVM在實證應用在指數上有極佳的預測效果。

關鍵字

隨機波動模型 ； 風險值 ； 門檻 ； 槓桿效應

並列摘要

As risk management is getting more and more important, the volatility forecasting approaches of financial assets have extracted greater attention than ever. Stochastic Volatility Model (SVM) is designed to capture the dynamics of volatility with high flexibility and better accommodation of characteristics of volatility. This study wishes to improve the SVM with threshold modeling to incorporate two significant features of volatility: fat-tail and nonlinear leverage effects. Specifically, the back-testing technique from Value-at-Risk is applied in SVM to capture extreme down-side risk occurrences, and with nonlinear asymmetrical setting of the error terms between returns and volatilities, a SVM of threshold condition is presented to explain the quadratic leverage effects. Both models are proposed for the first time in literatures, and empirical data will be applied with these models for both in-sample and out-of-sample performance evaluations. Results show that the forecasting performances of the new SVM models with fat-tail feature are similar to basic SVM models. This study approves that SVM is suitable for forecasting in empirical data with the 60% adjusted R-square

並列關鍵字

Stochastic Volatility Model ； Value-at-Risk ； Threshold ； Leverage effect

參考文獻

Andersen, T.G. and B.E. Sorensen (1996), "Estimation of a stochastic volatility model: a Monte Carlo study," Journal of Business and Economic Statistics, 14, 328-352.

Andersen, T.G. and J. Lund (1997), "Estimating continuous time stochastic volatility models of the short term interest rate," Journal of Econometrics, 77, 343-377.

Andersen, T.G., H.J. Chung and B.E. Sorensen (1999), "Efficient method of moments estimation of a stochastic volatility model: a Monte Carlo study," Journal of Econometrics, 91, 61-87.

Bansal, R., A.R. Gallant, R. Hussey and G.E. Tauchen (1995), "Nonparametric estimation of structural models for high-frequency currency market data," Journal of Econometrics, 66, 251-287.

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