Estimation of Asymmetric Box-Cox Stochastic Volatility Models Using MCMC Simulation
AbstractThe 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.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 10/03.
Length: 29 pages
Date of creation: Apr 2003
Date of revision:
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Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Find related papers by 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 &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-05-29 (All new papers)
- NEP-CMP-2003-05-29 (Computational Economics)
- NEP-ECM-2003-05-29 (Econometrics)
- NEP-ETS-2003-05-29 (Econometric Time Series)
- NEP-RMG-2003-05-29 (Risk Management)
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