本研究以蒙地卡羅模擬分析的方法首先討論如何驗證股票報酬與波動的長記憶性，比較在有限樣本下不同的檢定方法在驗證長記憶波動性的績效。實證分析結果發現，在檢驗波動度之長記憶性時Lo(1991)之MRS test在使用Date-dependent rule以建立核定量之變異數值時，有很大的size distortion。其次對美國與亞太股票市場進行長記憶波動模型檢定及分析並進行比較，以驗證長記憶波動現象是否存在及此類模型在這些資本市場之適用性。研究發現除新加坡外，亞太地區股市具有長記憶波動現象，進一步分析長記憶波動性是否是因結構不穩定性(structure break)或加總(aggregation)的原因而衍生的虛假性(spurious)現象時發現，加總因素並非導致指數報酬有長記憶現象之主因。而波動度的結構性改變則是重要原因。其中虛假性長記憶波動度現象存在於泰國、香港及日本股價指數。此外以Andersen and Bollerslev (1997b)的模式為基礎提出一個可以解釋長記憶波動現象的財務理論模型。最後此類長記憶波動模型如FIGARCH與FIEGARCH模式運用於衍生性金融商品如S&P100指數選擇權的訂價，研究發現忽略此長記憶波動性特性時所造成選擇權訂價偏誤大小受波動度的持續性大小的影響很大，即波動度的持續性大則選擇權訂價偏誤較大，但其關係並非線性。
One of the important questions in studies of asset return and volatility has been how long the effects of shocks persist. In this research, the modified R/S statistic of Lo(1991) and the robust semiparametric method of Lobato and Robinson (1997) are applied to investigate the long memory properties in return and volatility of Asian financial markets. For the return series, we find little evidence of long memory, while the empirical results support the hypothesis of long memory in volatility for Asia-Pacific stock markets. We also discuss the possible causes of spurious long memory effect in volatility, namely aggregation, size distortion, and shifts in variance. Monte Carlo Simulation is conducted to investigate the test size of MRS test, GPH test and LM test. The simulation evidence shows that size distortion is more severe when the data-dependent rule for calculating the variance of test statistics is applied. Our empirical evidence shows that spurious long memory effect in volatility might occur as a result of shifts in variance for Thailand, Hong Kong, and Japan stock markets. This research then provides simulation results to investigate the bias in the option pricing when the true DGP of conditional volatility is long memory process, but use the simple GARCH option pricing model to price.
