12.11 Other Applications

The MCMC method is applicable to many other financial problems. For example, Zhang, Russell, and Tsay (2008) use it to analyze information determinants of bid and ask quotes, McCulloch and Tsay (2001) use the method to estimate a hierarchical model for IBM transaction data, and Eraker (2001) and Elerian, Chib, and Shephard (2001) use it to estimate diffusion equations. The method is also useful in value at risk calculation because it provides a natural way to evaluate predictive distributions. The main question is not whether the methods can be used in most financial applications, but how efficient the methods can become. Only time and experience can provide an adequate answer to the question.

Exercises

12.1 Suppose that x is normally distributed with mean μ and variance 4. Assume that the prior distribution of μ is also normal with mean 0 and variance 25. What is the posterior distribution of μ given the data point x?

12.2 Consider the linear regression model with time series errors in Section 12.5. Assume that zt is an AR(p) process (i.e., zt = ϕ1zt−1 + ⋯ + ϕpztp + at). Let be the vector of AR parameters. Derive the conditional posterior distributions of , , and using the conjugate prior distributions, that is, the priors are

12.3 Consider the linear ...

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