摘要(英) |
The VIX volatility index, which is known as the "CBOE Volatility Index," is the index that Chicago Option Exchange based on S&P 500 Index to calculate the implied volatility, then obtain through weighted average. We use the copula based Markov chain model to explore the relevance of the volatility index. Since the volatility index is positive, we use gamma distribution as the marginal distribution. Because the model sets the part with the cumulative probability function, the cumulative probability function of the gamma allocation is not closed, and the problems arising from partial differentiation of the model, we decided to use Bayesian theory to estimate the parameters of the model. The Metropolis-Hastings algorithm can be used to estimate the parameters in our model, and then use the conditional probability method to generate correlated simulation data to verify the Bayesian theory method under the copula-based Markov chain model can be estimated. In empirical analysis, we use the VIX index as our empirical analysis data. |
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