Bayesian range-based estimation of stochastic volatility models

Alizadeh, Brandt, and Diebold [2002. Journal of Finance 57, 1047-1091] propose estimating stochastic volatility models by quasi-maximum likelihood using data on the daily range of the log asset price process. We suggest a related Bayesian procedure that delivers exact likelihood based inferences. Our approach also incorporates data on the daily return and accommodates a nonzero drift. We illustrate through a Monte Carlo experiment that quasi-maximum likelihood using range data alone is remarkably close to exact likelihood based inferences using both range and return data.