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

See all articles by Antoine Lejay

Antoine Lejay

University of Lorraine; INRIA

Paolo Pigato

University of Rome Tor Vergata - Department of Economics and Finance

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

Lejay, Antoine and Pigato, Paolo, A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data (February 15, 2019). Available at SSRN: https://ssrn.com/abstract=3101666 or http://dx.doi.org/10.2139/ssrn.3101666

Antoine Lejay (Contact Author)

University of Lorraine ( email )

Lorraine
France

INRIA ( email )

Domaine de Voluceau
Rocquencourt
Chesnay, 78153
France

HOME PAGE: http://www.iecl.univ-lorraine.fr/~Antoine.Lejay/

Paolo Pigato

University of Rome Tor Vergata - Department of Economics and Finance

Via Columbia 2
Rome, Rome 00123
Italy

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
43
Abstract Views
453
PlumX Metrics