Estimation of Stochastic Volatility with High and Low Prices

Abstract

This paper suggests stochastic volatility models incorporating both leverage effect and information on daily high/low prices of stocks. We use open-to-close returns to estimate a stochastic log-volatility model and compare the model to two estimators, ranges, difference between daily high and low prices and extreme prices in order to detect asymmetric volatility behavior. The likelihood-based inferences of Markov Chain Monte Carlo (MCMC) are conducted to estimate parameters and volatility. Simulation study reveals that the proposed model is superior to the one using returns only but there is little difference of estimators using ranges or high/low prices. Performing an empirical analysis using E-mini S&P 500 and Nasdaq 100 Futures, we find the strong evidence of leverage effect even when information of high/low prices is incorporated