Discrete-time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous-time Volatility Modeling

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract We first propose a reduced form model in discrete time for S&P500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models which are able to reproduce the statistical features captured by the discrete-time model. We show that a single-factor model driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multi-factor Markovian model fully replicates the persistence of both volatility and leverage effect. The impact of jumps can be associated with a common jump component in price and volatility. Permanent

It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model

“…Similarly to the indirect inference method of Gourieroux et al (1993), the sequential matching involves the simulation of the trajectories of RV from the structural model such that the distance between the parameters estimates of the auxiliary model on the observed data and on the simulated series is minimized. In the RV context, the simulation-based inference methods have been already employed by Bollerslev and Zhou (2002), Andersen et al (2002) and Corsi and Reno (2012). We assume that the SV model follows a TFSV model:…”

“…The parameters κ and δ govern the speed of mean reversion, while η and ν determine the volatility of the volatility innovations. The parameter ω is the long-run mean of each volatility component and, as in Corsi and Reno (2012), it is assumed to be the same for both γ 2 (t) and ζ 2 (t).…”

“…Following Corsi and Reno (2012),W t is chosen as the inverse of the covariance matrix of the auxiliary parameters in each period t,W t = Q −1 t .…”

“…Similarly to Corsi and Reno (2012), past negative returns can be included as explanatory variables in TV-HAR model. Hence, the TV-HAR model (3) would be modified as (4) is to assume that the log-price, p(t), follows a jump-diffusion process.…”

“…For this purpose, a two factors SV model (TFSV) is chosen as structural model, since, as noted by Gallant et al (1999) and Meddahi (2002Meddahi ( , 2003, it successfully accounts for the long range dependence of the volatility process. Given the difficulty of a direct estimation of breaks in the TFSV parameters, we adapt the indirect inference procedure suggested by Corsi and Reno (2012) to the case in which the SV parameters are allowed to be recursively updated. We therefore propose a sequential matching of the parameters, exploiting a flexible specification for the auxiliary model, which is built on an ex-post measure of the integrated variance.…”