A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data

TL;DR

This paper introduces a threshold local volatility model capturing leverage and mean-reversion effects in stock prices, supported by empirical evidence from NYSE and S&P 500 data, highlighting regime switches during crises.

Contribution

It proposes a novel stochastic differential equation model with regime switching based on a threshold, extending the continuous-time analogy of SETAR models, with an estimation procedure validated on real market data.

Findings

Empirical evidence of leverage effects in stock prices.

Detection of mean-reversion effects, especially during crises.

Model effectively captures regime switches in volatility.

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. Parameters estimated on the daily prices of 348 stocks of NYSE and S\&P 500, on different time windows, show consistent empirical evidence for leverageeffects. Mean-reversion effects are also detected, most markedly in crisis periods.