許多學者致力於各種非均齊變異的模型之探討。為了估計出不能直接由原始資料看出的隱藏性波動，傳統的處理方式為假設條件變異數是過去觀測值平方與過去變異數的函數，Engle(1982)發展出應用普遍的自我迴歸條件異質變異模型(ARCH)﹐Bollerslev,Engle and Nelson (1994)則將之推廣至GARCH,EGARCH等統稱為GARCH族的各種模型。
在廣義的Black-Scholes 選擇權定價問題上Hull and White (1987)﹐首先提出了使條件變異數含有隨機變動的部份的看法﹐因而創造了不同於ARCH模型的SV(stochastic volatility)模型。從此,SV模型引起了廣泛的注意。

在SV模型下，要得到隱藏的波動是不容易的﹐因為SV模型包含了隱藏的變數以及隨機變動的部份；文獻上提出的估計方法有很多﹐例如Rothenberg(1973) GMM(generalized method of moments),Harvey,Ruiz and Shephard(1994) QML (quasi-likelihood)以及Shephard(1996)的MCMC(Markov chain Monte Carlo)等﹐其中Jacquier,Polson and Rossi (1994)已證實在SV模型的估計上，MCMC法優於GMM及QML法。JPR (1994) 與Shephard(1998)分別對MCMC的方法中隱藏波動之抽取法提出不同論點﹐其中JPR法利用Metropolis algorithm﹐Shephard法則利用Ripley(1987) accept-reject sampling。論文中針對這兩種方法之優劣來做比較﹐並進一步提出改進Shephard方法上疏失的部份。

1-1 研究動機與目的 …………………………….……..1

1-2 論文架構概述………………………………….……2

第二章 文獻回顧

2-1 Arch,Garch和SV 模型……………………….……3

2-2 參數估計方法

2-2-1 GMM法……..……………………………………4

2-2-2 QML法………..………………………………….5

2-2-3 MCMC法…………...……………………….……6

第三章 研究方法與討論

3-1 參數的抽取…………………….…………………7

3-2 抽取h的方法………………………………….……..9

3-3 改良方法…………………………………….………12

3-4 模擬實驗…………………………………………….13

3-5 Filtering過程………………………………….…….16

第四章 實證研究

4-1 亞洲金融風暴對台灣及香港之影響….………………19

4-2 NASDAQ是台灣電子類股之領先指標….….………..25

第五章 結論與建議 …………………………………..30

附錄 ……………………………………………………….31

參考文獻 ………………………………………………….33

BLACK,F.(1976)”Studies of stock price volatility changes.”
Proceedings of the American Statistical Association,Business and Economic Statistics Section,177-181.
BOLLERSLEV,T.(1986) “Generalised autoregressive conditional heteroscedasticity.”Journal of Econometrics,51,307-327.
BOLLERSLEV,T., ENGLE, R.F. and NELSON,D. B. (1994),”ARCH models”, in Engle,R.F. and Mcfadden,D.(eds), The Handbook of Econometrics Volume4 (Amsterdam:North-Holland),2959-3038.
CHIB,S.and GREENBERG,E.(1994),”Bayes inference for regression models with ARMA(p,q) errors”,Journal of Econometrics,64,183-206.
DURBIN,J.(1992) Personal correspondence to Andrew Harvey and Neil Shephard.
ENGLE,R.F.(1982),”Autoregressive conditional heteroskedasticity with estimates of the variance of the United Kingdom inflation”,Econometrica,50,987-1007.
ENGLE,R.F.,VK,N.G. and ROTHSCHILD,M.(1990),”Asset pricing with a factor ARCH covariance structure:empirical estimates for Treasury bills.” Journal of Econometrics,45,213-238.
ENGLE,R.F.and SUSMEL,V.K.(1993)”Measuring and testing the impact of news on volatility”Journal of Finance,48,1749-1801.
HARVEY,A.C.,RUIZ,E.,and SHEPHARD,N.(1994),”Multivariate Stochastic Variance Models “,Review of Economic Studies,61,247-264.
HULL,J.and WHITE,A.(1987),”The pricing of options on assets with stochastics volatilities”,Journal of Finance,42,281-300.
HAMILTON,J.(1994) Time Series Analysis. Princeton University Press,Princeton,NJ.
JACQUIER,E., POLSON,N.G. and ROSSI,P.E. (1994) “Baysian analysis of stochastic volatility models (with discussion)”. Journal of Business and Economic Statistics,12,371-417.
KIM,S. and SHEPHARD,N.(1998) “Stochastic volatility: Likelihood inference and comparison with ARCH models”. Review of Economic Studies,65,361-393.
MARRIOTT,J.M.and SMITH,A.F.M.(1992),”Reparameterization aspects of numerical Bayesian methodology for autoregressive moving-average models”.Journal of Time Series Analysis,13,327-343.
NELSON,D.B.(1991)”Conditional heteroscedasticity in asset pricing: a new approach” Econometrica,59,347-370.
QIAN,W.and TITTERINGTON,D.M.(1991)”Estimation of parameters in hidden Markov Chain models.” Philosophical Transactions of the Royal Society of London,Series A,337,407-428.
ROTHENBERG,T.J.(1973)”Efficient Estimation with A Priori Information.”Yale University Press,New Haven,CT.
RIPLEY,B.D.(1987) Stochastic Simulation (New York:Wiley).
SCHWERT,G.W.(1989) “Why does stock market volatility change over time?”Journal of Finance.
SHEPHARD,N.(1996),”Statistical aspects of ARCH and stochastic volatility”, in D.R.Cox,O.E.Barndorff-Nielson and D.V.Hinkley(eds.),Time Series Models in Econometrics, Finance and Other Fields(London:Chapman & Hall),1-67.
TAYLOR,S.(1986)”Modelling Financial Time Series,New York:John Wiley.
TSAY,R.S.(1999) “Financial Time Series Analysis”.Unpublished Teaching Material.