本文考慮門檻隨機波動模型與門檻隨機波動跳躍模型之貝氏分析。在給定主觀先驗分佈下，以馬可夫鏈蒙地卡羅方法估計模型中之未知參數，進而討論未來觀測值與風險值之預測。關於隨機跳躍部份，本文亦分別考慮跳躍幅度與跳躍機率可能會隨門檻值改變的情形。實務分析中，可以 DIC 準則做為模型選擇的依據。

This thesis presents a threshold stochastic volatility model and a threshold stochastic volatility jump model with unknown threshold from a Bayesian viewpoint. Bayesian inferences of the unknown parameters are obtained with respect to a subjective prior distribution via Markov chain Monte Carlo (MCMC) method.
In addition, the value at risk (VaR) of the distribution of the next future observation is also developed based on predictive distribution. For jump component in the threshold stochastic volatility model, we consider the situations where the jump size and jump probability might be changed by the threshold value. In practice, the deviance information criterion (DIC) is suggested for model selection.

Akgiray, V. and Booth, G. G., (1986). “Compound distribution models of stock returns: an empirical comparison.” Journal of Financial Research. 10, 259-280.
Andersen, T. G., Benzoni, L. and Lund, J., (1999). “An empirical investigation of continuous-time equity returns models.” Journal of Finance. 57, 1239-1294.
Andersen, T. G., Bollerslev, T., Diebold, F. X and Ebens, H., (2001). “The distribution of realized stock return volatility.” Journal of Finance. 61, 43-76.
Bakshi, C. C. and Chen, Z., (1997). “Empirical performance of alternative option pricing models.” Journal of Finance. 52, 2003-2050.
Ball, C. A. and Torous, W. N., (1985). “On jumps in stock returns.” Journal of Financial Quantitative Analysis. 10, 337-351.
Berger, J. O., (1985). Statistical decision theory and Bayesian analysis, 2nd Edition. New York: Springer–Verlag
Ball, C., Torous, W., (1985). On jumps in common stock prices and their impact on call option pricing. Journal of Financ. 40, 155-173.
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). “Generalized autoregressive conditional heteros-kedasticity.”Journal of Econometrics. 31, 307-327.58
Chang, Y. P., Hung, M. C. and Wu, Y. F., (2003). “Nonparametric estimation for risk in Value-at-Risk estimator.” Communications in Statistics: Simulation and Computation. 32, 1041-1064.
Celeux, G., Forbes, F., Robert, C. and Titterington, M., (2006), “Deviance information criteria for missing data models.” Bayesian Analysis. 1, 651-674.
Christie, A., (1982). “The stochastic behaviour of common stock variances: value, leverage and interest rate effects.” Journal of Financial Economics. 10, 407-432.
Engle, R. F., (1982). “Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation.” Econometrica. 50, 987-1008.
Gallant, A. R., Hsieh, D., and Tauchen, G., (1997). “Estimation of stochastic volatility models with diagnostics.” Journal of Econometrics. 81, 159-192.
Geman, S. and Geman, D., (1984). “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.” IEEE Trans. On Pattern Analysis and Machine Intelligence. 6, 721-741.
Harvey, A. C. and Shephard, N., (1993). “Estimation and testing of stochastic variance models.” STICERD Econometrics Discussion Paper, LSE.
Harvey, A. C., Ruiz, E. and Shephard, N., (1994). “Multivariate stochastic variance model.” Review of Economic Studies. 61, 247-264.
Harvey, A. C. and Shephard, N., (1996). “Estimation of an asymmetric stochastic volatility model for asset returns.” Journal of Business and Statistics. 14, 429-434.59
Hastings, W. K., (1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika. 57, 97-109.
Hsieh, G. D. and Tauchen, G., (1997). “Estimation of stochastic volatility models with diagnostic.” Journal of Econometrics. 81, 159-201.
Jacquier, E., Polson, N. G. and Rossi, P. E., (1994). “Bayesian analysis of stochastic volatility models.” Journal of Business and Economic Statistics. 12, 371-389.
Jarrow, R. A. and Rosenfeld, E. R., (1984). “Jump risks and the intertemporal capital asset pricing model.” Journal of Business. 57, 337-351.
Jorion, P., (1988). “On jump processes in the foreign exchange and stock markets.” The Review of Financial Studies. 1(4): 427-445.
Kim, D. and Kon, S. J., (1994). “Alternative models for the conditional heteroscedasiticy of stock returns.” Journal of Business. Vol. 67, No. 4, pp.563-598.
Kim, S., Shephard, N. and Chib, S., (1998). “Stochastic volatility: likelihood inference and comparison with ARCH models.” Review of Economic Studies. 65, 361-393.
Menezes, C., Geiss, C. and Tressler, J., (1980). “Increasing down side risk.” The American Economic Review.
Merton, R. C., (1976). “Option pricing when underlying stock returns are discontinuous.” Journal of Financial Economics. 3, 125-144.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E., (1953). “ Equations of state calculations by fast computing machines.” Journal of Chemical Physics. 21, 1087-1091.
Muller, P., (1994). “A generic approach to posterior integration and Gibbs sampling.”
Journal of the American Statistical Association, to appear. Schwert, G. W., (1989). “Why does stock market volatility change over time?” Journal of Finance. 44, 1115-1153.
Shephard, N., (1993). “Fitting nonlinear time-series models with applications to stochastic variance models.” Journal of Applied Econometrics. 8, S135-S152.
Shephard, N., (1994). “Partial non-Gaussian state space.” Biometrika. 81, 115-131.
So, M. K. P., Li, W. K. and Lam, K., (2002). “A threshold stochastic volatility model.” Journal of Forecasting. 21, 473-500.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Linde A., (2002). “Bayesian measures of model complexity and fit (with discussion).” Journal of Royal Statistical Society, Series B. 64, 583-639.
Tsay, R. S., (2002). Analysis of Financial Time Series. John Wiley. Taylor, S. J., (1982). “Financial returns modelled by the product of two stochastic processes, a study of daily sugar prices 1961-79.” In Time Series Analysis: Theory and Practice 1, Anderson, O. D.(ed.). North-Holland: Amsterdam; 203-226.
Taylor, S. J., (1986). Modelling Financial Time Series. John Wiley: New York.
Taylor, S. J., (1994). “Modelling stochastic volatility.” Mathematical Finance. 4,183-204.