A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data
28 Pages Posted: 30 Jan 2018 Last revised: 24 Feb 2019
Date Written: February 15, 2019
Abstract
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect.
We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and mean-reversion effects, consistent with the results in the literature.
Keywords: Oscillating Brownian motion, leverage effect, realized volatility, mean-reversion, Self-Exciting Threshold Autoregressive model, Regime-Switch
JEL Classification: C, C5, C52
Suggested Citation: Suggested Citation