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Estimation of Asymmetric Box-Cox Stochastic Volatility Models Using MCMC Simulation

Author

Listed:
  • Xibin Zhang
  • Maxwell L. King

Abstract

The stochastic volatility model enjoys great success in modeling the time-varying volatility of asset returns. There are several specifications for volatility including the most popular one which allows logarithmic volatility to follow an autoregressive Gaussian process, known as log-normal stochastic volatility. However, from an econometric viewpoint, we lack a procedure to choose an appropriate functional form for volatility. Instead of the log-normal specification, Yu, Yang and Zhang (2002) assumed Box-Cox transformed volatility follows an autoregressive Gaussian process. However, the empirical evidence they found from currency markets is not strong enough to support the Box-Cox transformation against the alternatives, and it is necessary to seek further empirical evidence from the equity market. This paper develops a sampling algorithm for the Box-Cox stochastic volatility model with a leverage effect incorporated. When the model and the sampling algorithm are applied to the equity market, we find strong empirical evidence to support the Box-Cox transformation of volatility. In addition, the empirical study shows that it is important to incorporate the leverage effect into stochastic volatility models when the volatility of returns on a stock index is under investigation.

Suggested Citation

  • Xibin Zhang & Maxwell L. King, 2003. "Estimation of Asymmetric Box-Cox Stochastic Volatility Models Using MCMC Simulation," Monash Econometrics and Business Statistics Working Papers 10/03, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2003-10
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp10-03.pdf
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    More about this item

    Keywords

    Box-Cox transformation; leverage effect; sampling algorithm.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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