|
Abstract:
|
This paper proposes a new dynamic model called Stochastic Tail Index (STI) model to analyze time-varying tail index for financial assets based on high-frequency data. We design a new algorithm called ALSO to accurately approximate a given random variable using Gaussian mixture variables. By virtue of it, we use an existing approximation approach to build Bayesian tools for estimating the STI model, making inferences, and performing model selection. Our posterior sampler depends on Metropolis-Hastings algorithms. It takes advantage of the BFGS optimization method to tailor the proposal densities, and hence is computationally faster than the existing samplers. Our simulation study shows that the posterior sampler works well for the STI model. To illustrate the use of the STI model in the real world, we analyze a real data set. We find that the estimated daily tail indexes generally follow a time-varying pattern and tend to fall when large negative events occur. Besides, they significantly drop below 2 during some periods, which implies that the variances of the return distributions during those periods may be infinite and hence any variance based risk management may be inappropriate.
|
