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: Université de Lorraine, IECL, UMR 7502, Vandœuvre-lés-Nancy F-54600, France2CNRS, IECL, UMR 7502, Vandœuvre-lés-Nancy F-54600, France3Inria, Villers-lés-Nancy F-54600, France

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 04, 1-24

Abstract: In financial markets, low prices are generally associated with high volatilities and vice-versa, this well-known stylized fact is usually referred to as the leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts for leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics according 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 351 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; realized volatility; mean-reversion; regime-switch; parametric estimation; threshold diffusion; stock price model (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Related works:
Working Paper: 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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DOI: 10.1142/S0219024919500171

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