臺灣博碩士論文加值系統

在本研究計畫中，研究 jump GARCH 模型的預測和模型的比較，跳躍過程中是具
有時間異質性的和非獨立的。主要使用貝氏方法以及馬可夫鏈蒙地卡羅演算法來對模型
參數有更好的估計，跳躍模型允釵陰囓騤嚽D的強度隨時間改變且近似自我迴歸移動平
均模型的形式。透過財務時間序列分析顯示跳躍模型比傳統的廣義自迴歸條件異方差模
型的結果指出跳躍模型能顯示更多跳躍的動態和波動結構等重要的特徵。此外，利用邊
際最大概估計能用來選擇最佳的模型，而我們也發現jump GARCH模型較一般常用的
GARCH 能夠良好描述資料。最後，應用模擬分析闡明所提方法之估計表現並使用各國
時間序列資料利用貝氏方法來預測風險值和預期損失。

In this thesis, inference, quantile forecasting, and model comparison for a jump GARCH model is investigated, where jump arrivals are time inhomogeneous and state-dependent. The Bayesian inference of jump GARCH via MCMC methods is employed to obtain better estimates. The model permits the conditional jump intensity to be time-varying and follows an approximate autoregressive moving average (ARMA) form. The jump GARCH model undergoes nancial time series analysis and is compared with GARCH models. In addition, two Bayesian model selection methods are used to choose the best model between GARCH and jump GARCH models. We illustrate the Bayesian method of parameter estimation by simulation experiments. A Bayesian model comparison, Value at-Risk forecasts, and on Expected Shortfall study are considered. The results indicate nd signi cant improvements of tness in the jump GARCH model.

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . .. . .. . . 1
2 Jump GARCH model . . . . . . . . . . . . . . . . . . . .. . .. 3
3 Bayesian inference . . . . . . . . . . . . . . . . .. . .. . .5
3.1 Prior and Posterior . . . . . . . . . . . . . . . . . . . . . 6
3.2 MCMC sampling scheme . . . . . . . . . . . . . . . . . . . . . 7
3.2.1 Random walk MH algorithm . . . . . . .. . . . . . . . . . .. 8
3.2.2 Independent kernel MH algorithm . . . . . . . . . . . . . . 8
4 Model Selection . . . . . . . . . . . . . . . .. . .. . . . ..9
5 Forecasting . . . . . . . . . . . . . . . .. . .. . . . .. ..10
5.1 Assessments of VaR and ES models . . . . . . . . . . . . . . 13
6 Simulation study . . . . . . . . . . . .. . .. . . . . . . . .16
7 Empirical study . . . . . . . . . . . .. . .. . . . . . . . ..19
7.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . .. . 19
7.2 Model comparisons . . . . . . . . . . . . . . . . . . . . . . 20
7.3 VaR forecast . . . . . . . . . . . . . . . . . . . . . .. . . 21
8 Conclusion and future research . . . . . . . . . . . . . . . . 23
A Computation detail of VaR and ES . . . . . . . . . . . . . .. .27

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