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

Antoine Lejay 1 Paolo Pigato 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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.
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https://hal.inria.fr/hal-01669082
Contributor : Antoine Lejay <>
Submitted on : Wednesday, December 20, 2017 - 3:19:13 PM
Last modification on : Thursday, January 11, 2018 - 6:25:25 AM

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  • HAL Id : hal-01669082, version 1

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Antoine Lejay, Paolo Pigato. A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data. 2017. ⟨hal-01669082v1⟩

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