Realized Volatility or Price Range: Evidence from a Discrete Simulation of the Continuous Time Diffusion Process

Abstract

The study provides evidence in favour of the price range as a proxy estimator of volatility in financial time series, in the cases that either intra-day datasets are unavailable or they are available at a low sampling frequency.

A stochastic differential equation with time varying volatility of the instantaneous logreturns process is simulated, in order to mimic the continuous time diffusion analogue of the discrete time volatility process. The simulations provide evidence that the price range measures are superior to the realized volatility constructed at low sampling frequency. The high-low price range volatility estimator is more accurate than the realized volatility estimator based on five, or less, equidistance points in time. The open-high-low-close price range is more accurate than the realized volatility estimator based on eight, or less, intraperiod log-returns.

Keywords: Integrated Volatility, Intra-day Volatility, Price range, Realized volatility, Stochastic Differential Equation

JEL Classification: C15, C53, G17