本研究目的在於探討Put-Call Parity（PCP）所隱含的買權、賣權與標的資產間的價格變動關係。藉由探討PCP偏差程度的動態行為，推論若PCP的偏差為隨機漫步過程，則無法達到長期穩定，隱含PCP的廣義關係無法成立；反之，若PCP的偏差具有回歸平均特性，表示長期會達到穩定狀態，則PCP的廣義關係成立。
在研究方法上本文以變異數比率法檢定指數選擇權的PCP偏差是否為隨機漫步過程，採用隱含利率和實際無風險利率的差代表PCP的偏差程度，利用馬可夫轉換模型描繪PCP偏差的動態行為，並使用Gibbs Sampling演算法說明參數的不確定性。
本文以S&P500和DAX為研究標的，並探討股利不確定性是否影響PCP廣義關係，得到下列結論：
1、對於S&P 500指數選擇權而言，不論是以日資料或週資料估計VR，S&P 500的PCP偏差都無法提供回歸平均的證據，隱含S&P 500的PCP廣義關係無法成立。
2、對於DAX指數選擇權而言，檢定日資料的結果發現，DAX之PCP偏差在長期時（40~50日）有明顯的回歸平均的證據；而在檢定週資料時，使用原始資料法在90%信心水準下，不論取任何lag都可拒絕虛無假設，使用標準化資料則無法提供明顯的回歸平均證據。
3、比較S&P 500和DAX，檢定日資料與週資料的結果都發現，DAX的p-value都比S&P 500小，並且S&P 500的PCP偏差都無法提供回歸平均的證據，而DAX有明顯回歸平均現象，隱含在消除股利的不確定性後，指數選擇權PCP的廣義關係式成立之證據較強烈。

Albert, J. H., and Chib, S. (1993) “Bayesian Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts.” Journal of Business and Economic Statistics, 11(1), 1-15.
Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroscedasticity.” Journal of Econometrics, 31, 307-327.
Campbell, J. Y., Lo, A. W. and MacKinlay A. C. (1997) The Econometrics of Financial Markets., Princeton University Press
Casella, G. and George, E. I. (1993) “Explaining the Gibbs Sampler.” The American Statistician, 46(3), 167-174.
Chib, S. and Greenberg, E. (1996) “Markov Chain Monte Carlo Simulation Methods in Econometrics.” Econometric Theory, 12, 409-431.
Cochrane, J. H. (1988) “How big is the random walk in GNP?” Journal of Political Economy, 96, 893-920.
Dickey, D. A., and Fuller, W. A. (1979) “Distribution of the Estimates for Autoregressive Time Series with a Unit Root.” Journal of the American Statistical Association, 427-431.
Draper, P. and Fung, J. K. W. (2002) “A Study of Arbitrage Efficiency Between the FTSE-100 Index Futures and Options Contracts.” Journal of Futures Markets, 22(1), 31-58.
Enders, W. (1995) Applied Econometric Time Series. Wiley
Engle, R. F. (1982) “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica, 50, 987-1007.
de Roon, F. and Chris Veld, (1996) “Put-Call Parities and the Value of Early Exercise for Put Options on a Performance Index.” Journal of Futures Markets, 16(1), 71-80.
Franses, P. H. and Dijk, D. V. (2000) Nonlinear Time Series Models in Empirical Finance. Cambridge University Press
Finucane, T. J. (199) “Put-Call Parity and Expected Returns.” Journal of Financial Quantitative Analysis, 26(4), 445-457.
Fung, J. K. W. and Chan, K. C. (1994) “On the Arbitrage-free Pricing Relationship Between Index Futures and Index Options: A note.” Journal of Futures Markets, 14(8), 957–962.
Gefland, A. E. and Smith, A. F. M. (1990) “Sampling Based Approaches to Calculating Marginal Densities.” Journal of American Statistical Association, 85, 398-409.
Gefland, A. E., Smith, A. F. M. and Lee, T. M. (1990) “Bayesian Analysis of Constrained Parameters and Truncated Data Problems Using Gibbs Sampling.” Journal of American Statistical Association, 87, 523-532.
Geman, S. and Geman, D. (1984) “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
Goldfeld, S. M. and Quandt, R. E. (1973) “A Markov Model for Switching Regressions.” Journal of Econometrics, 1, 3-16.
Graflund, Andreas (2002) “A Bayesian Inference Approach to Testing Mean Reversion in the Swedish Stock Market.” Department of Economics, Lund University
Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press.
Hamilton, J. D. (1989) “A new Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica, 57(2), 357-384.
Hamilton, J. D. (1990) “Analysis of Time Series subject to Changes in Regime.” Journal of Econometrics, 45, 39-70.
Hamilton, J. D. (1991) “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions.” Journal of Business and Economic Statistics, 19, 23-39.
Hamilton, J. D. and Susmel, R. (1994) “Autoregressive Conditional Heteroskedasticity and Changes in Regime.” Journal of Econometrics, 64, 307-333.
Hull, J. C. (2000) Options, Futures, & Other Derivatives 4th ed. Prentice Hall
Kamara, A. and Miller, T. W. (1995) “Daily and Intradaily Tests of European Put-Call Parity.” Journal of Financial and Quantitative Analysis, 30(4), 519-539.
Kim, C. J. and Nelson, C. R. (1999) State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications., MIT Press
Kim, C. J. and Nelson, C. R. (1998) “Business Cycle Turning Points, a New Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model with Regime Switching.” The Review of Economics and Statistics, 80(2), 188-201.
Kim, C. J. and Nelson, C. R. (1998) “Testing for mean Reversion in heteroskedastic data II: Autocorrelation Tests based on Gibbs-Sampling-Augmented Randomization.” Journal of Empirical Finance, 5(2), 385-396.
Kim, C. J., Nelson, C. R. and Startz, R. (1991) “Mean reversion in stock prices? A Reappraisal of the Empirical Evidence” Review of Economic Studies, 58, 515-528.
Kim, C. J., Nelson, C. R. and Startz, R. (1998) “Testing for mean reversion in heteroskedastic data based on Gibbs-sampling-augmented randomization” Journal of Empirical Finance, 5(2), 131-154.
Kuan, C. M. “Lecture on the Markov Switching Model.” Institute of Economics Academia Sinica.
Lo, A. W. and MacKinlay, A. C. (1988) “Stock Market Prices do not follow Random Walks: Evidence from a Simple Specification Test.” The Review of Financial Studies, 1, 41-66.
Lo, A. W. and MacKinlay, A. C. (1989) “The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation.” Journal of Econometrics, 45, 203-238.
Malliaropulos, D. and Priestley, R. (1999) “Mean Reversion in Southeast Asian Stock Markets.” Journal of Empirical Finance, 6, 355-384.
Neal, R. (1996) “Direct Tests of Index Arbitrage Models.” Journal of Financial and Quantitative Analysis, 31(4), 541-562.
Noreen, E. W. (1989) Computer-Intensive Methods for Testing Hypotheses: An Introduction. Wiley
Poterba, J. M. and Summers, L. H. (1988) “Mean Reversion in Stock Prices: Evidence and Implications.” Journal of Financial Economics, 22(1), 27-60.
Stoll, H. R. (1969) “The Relationship between Put and Call Prices.” Journal of Finance, 24, 810-822.
Tsay, R. S. (2002) Analysis of Financial Time Series. Wiely
Zivney, T. L. (1991) “The Value of Early Exercise in Option Prices: An Empirical Investigation.” Journal of Financial and Quantitative Analysis, 26(1), 129-138.