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

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.
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https://hal.inria.fr/hal-01669082
Contributor : Antoine Lejay <>
Submitted on : Thursday, February 21, 2019 - 5:11:36 PM
Last modification on : Thursday, April 11, 2019 - 3:18:22 PM

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  • HAL Id : hal-01669082, version 5
  • ARXIV : 1712.08329

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Antoine Lejay, Paolo Pigato. A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data. International Journal of Theoretical and Applied Finance, World Scientific Publishing, In press. ⟨hal-01669082v5⟩

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