Semiparametric Modeling of Multiple Quantiles

Catania, Leopoldo; Luati, Alessandra

doi:10.2139/ssrn.3494995

“…We discussed the handling of non-tail time series observations, inference on deterministic and time-varying parameters, and how to relate tail variation to observed covariates. The model therefore complements and extends recent work based on different methodologies, such as the non-parametric approach to tail index variation of de Haan and Zhou (2020), the time-varying quantile (and ES) approaches of Patton et al (2019) and Catania and Luati (2019), and the parametric modeling approach of Massacci (2017). We applied the model to study the impact of bond purchases within the Eurosystem's SMP between 2010 and 2012 on the extreme upper tail of sovereign bond yield changes measured at a high frequency, concluding that the program had a beneficial impact on extreme tail quantiles, leaning against the risk of extremely adverse market outcomes while active.…”

Section: Resultssupporting

confidence: 61%

“…1 in line with robust updates of the time-varying parameters. This distinguishes our current set-up sharply from an approach directly based on quantile functions; see Patton et al (2019) and Catania and Luati (2019), in particular for risk measures such as ES. In Patton et al (2019), ES reacts linearly to the VaR exceedance.This can result in noisy or unstable ES estimates.…”

Section: Figure 1: News Impact Curvesmentioning

confidence: 99%

See 1 more Smart Citation

Modeling Extreme Events: Time-Varying Extreme Tail Shape

Schwaab

¹

,

Zhang

²

,

Lucas

³

2020

View full text Add to dashboard Cite

A dynamic semi-parametric framework is proposed to study time variation in tail fatness of sovereign bond yield changes during the 2010-2012 euro area sovereign debt crisis measured at a high (15-minute) frequency. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail shape parameters. The score-driven updates used improve the expected Kullback-Leibler divergence between the model and the true data generating process on every step even if the GPD only fits approximately and the model is mis-sepcified, as will be the case in any finite sample. This is confirmed in simulations. Using the model, we find the ECB program had a beneficial impact on extreme upper tail quantiles, leaning against the risk of extremely adverse market outcomes while active.

show abstract

“…1 in line with robust updates of the time-varying parameters. This distinguishes our current set-up sharply from an approach directly based on quantile functions; see Patton et al (2019) and Catania and Luati (2019), in particular for risk measures such as ES. In Patton et al (2019), ES reacts linearly to the VaR exceedance.This can result in noisy or unstable ES estimates.…”

Section: Time-varying Tail Shape and Scalementioning

confidence: 99%

“…where ⇢  (u t ) = u t ( 1{u t < 0}), and ⌧ t evolves as in (10). See also Engle and Manganelli (2004) and Catania and Luati (2019) for the use of this objective function in a di↵erent dynamic context. In practice, we estimate all thresholds ⌧ t via (12) before maximizing (11).…”

Section: Parameter Estimationmentioning

confidence: 99%

Modeling Extreme Events: Time-Varying Extreme Tail Shape

Schwaab

¹

,

Lucas

²

,

Zhang

³

2021

SSRN Journal

0

View full text Add to dashboard Cite

A dynamic semi-parametric framework is proposed to study time variation in tail fatness of sovereign bond yield changes during the 2010-2012 euro area sovereign debt crisis measured at a high (15-minute) frequency. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail shape parameters. The score-driven updates used improve the expected Kullback-Leibler divergence between the model and the true data generating process on every step even if the GPD only fits approximately and the model is mis-sepcified, as will be the case in any finite sample. This is confirmed in simulations. Using the model, we find the ECB program had a beneficial impact on extreme upper tail quantiles, leaning against the risk of extremely adverse market outcomes while active.

show abstract