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

Antoine Lejay () and Paolo Pigato
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Antoine Lejay: TOSCA - TO Simulate and CAlibrate stochastic models - CRISAM - Centre Inria d'Université Côte d'Azur - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique

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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 leverage effects. Mean-reversion effects are also detected, most markedly in crisis periods.

Keywords: Leverage effect; Self-Exciting Threshold Autoregressive model; parametric estimation; threshold diffusion; stock price model *; mean-reversion; Oscillating Brownian motion; realized volatility; Regime-Switching; regime-switch (search for similar items in EconPapers)
Date: 2019
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://inria.hal.science/hal-01669082v5
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Citations: View citations in EconPapers (5)

Published in International Journal of Theoretical and Applied Finance, inPress, ⟨10.1142/S0219024919500171⟩

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Related works:
Journal Article: A THRESHOLD MODEL FOR LOCAL VOLATILITY: EVIDENCE OF LEVERAGE AND MEAN REVERSION EFFECTS ON HISTORICAL DATA (2019)
Working Paper: A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01669082

DOI: 10.1142/S0219024919500171

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