  This study presents contemporaneous modeling of asset return and price range
within the framework of stochastic volatility with leverage. A new
representation of the probability density function for the price range is
provided, and its accurate sampling algorithm is developed. A Bayesian
estimation using Markov chain Monte Carlo (MCMC) method is provided for the
model parameters and unobserved variables. MCMC samples can be generated
rigorously, despite the estimation procedure requiring sampling from a density
function with the sum of an infinite series. The empirical results obtained
using data from the U.S. market indices are consistent with the stylized facts
in the financial market, such as the existence of the leverage effect. In
addition, to explore the model's predictive ability, a model comparison based
on the volatility forecast performance is conducted.
