| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 97 === In the last two decades, the volatility of the financial derivatives has been extremely large. One of the models that can capture the leptokurtosis and the volatility clustering
phenomenon commonly seen in financial data is the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models.
For the parameter estimation of such models, Harvey and Shephard ( 1993 ) and Harvey ( 1994 ) used the quasi-maximum Likelihood Estimation, So (1997) and Shephard (1994) applied the EM algorithm to get the estimates. In this study, we adapt the Bayesian analysis, in which the Metropolis - Hastings is employed to construct a long run of Markov chain. And the Bayesian estimates can be thus obtained, for example the
conditional sample means of desired parameters after some burn-in period.
For the model fitting problems, we use the reversible jump Markov Chain Monte Carlo (RJMCMC) method to automatically choose the
best models, in which models themselves are also
considered as a new parameter. We demonstrate that our approach is correct in the simulation studies. Finally, the real financial data are applied, and both the conditional model selection methods,such as AIC, and our Bayesian approach yieldto the similar result.
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