Empirical evidence of the leverage effect in a stochastic volatility model: a realized volatility approach

Abstract

Increasing attention has been focused on the analysis of the realized volatility, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60-mi). Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency. The volatility persistence becomes weaker at the lower sampling frequency. We also find that the consistent-scaling and "optimal"-weighted realized volatility method proposed by Hansen and Lunde (2005) provide relatively better performances compared to other methods considered.