Abstract
Abstract This paper presents a Markov chain Monte Carlo (MCMC) algorithm to estimate parameters and latent stochastic processes in the asymmetric stochastic volatility (SV) model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution and the marginal density of asset returns has heavy-tails. We employed the Bayes factor and the Bayesian information criterion (BIC) to examine whether the Box-Cox transformation of squared volatility is favored against the log-transformation. When applying the heavy-tailed asymmetric Box-Cox transformed SV model, three competing SV models and the t -GARCH(1,1) model to continuously compounded daily returns of the Australian stock index, we find that the Box-Cox transformation of squared volatility is strongly favored by Bayes factors and BIC against the log-transformation. While both criteria strongly favor the t -GARCH(1,1) model against the heavy-tailed asymmetric Box-Cox transformed SV model and the other three competing SV models, we find that SV models fit the data better than the t -GARCH(1,1) model based on a measure of closeness between the distribution of the fitted residuals and the distribution of the model disturbance. When our model and its competing models are applied to daily returns of another five stock indices, we find that in terms of SV models, the Box-Cox transformation of squared volatility is strongly favored against the log-transformation for the five data sets.
Highlights
The volatility of asset returns often exhibits a time-varying feature
One approach to modelling volatility is to employ the autoregressive conditional heteroskedasticity (ARCH) model developed by Engle (1982) or the generalized ARCH (GARCH) model by Bollerslev (1986)
This paper presents an Markov chain Monte Carlo (MCMC) algorithm for sampling parameters and latent stochastic processes of volatilities and jumps of the heavy-tailed asymmetric stochastic volatility (SV) model, in which the Box-Cox transformation of squared volatility is assumed to follow an autoregressive Gaussian distribution
Summary
The volatility of asset returns often exhibits a time-varying feature. The SV model has received increased attention in the finance literature, because it provides an alternative approach to the Black-Scholes option pricing formula (Hull and White, 1987). Where pt is the price of an asset at time t and (w1t, w2t) is a bivariate standard Brownian motion. The correlation between dw1t and dw2t, denoted by ρ = corr(dw1t, dw2t), captures the leverage effect, which refers to the asymmetric behaviour that price movements are negatively correlated with volatility and is often observed in returns of equity prices (see, e.g., Nelson, 1991; Gallant, Rossi and Tauchen, 1992, 1993; Campbell and Kyle, 1993; Engle and Ng, 1993; among others).
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