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

Xibin Zhang () and Maxwell L. King ()

No 10/03, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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.

Keywords: Box-Cox transformation; leverage effect; sampling algorithm. (search for similar items in EconPapers)
JEL-codes: C6 C22 C52 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cmp, nep-ecm, nep-ets and nep-rmg
Date: 2003-04
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