Implicit quantiles and expectiles

Fabio Bellini, Edit Rroji, Carlo Sala

Research output: Indexed journal article Articlepeer-review

1 Citation (Scopus)


We compute nonparametric and forward-looking option-implied quantile and expectile curves, and we study their properties on a 5-year dataset of weekly options written on the S&P 500 Index. After studying the dynamics of the single curves and their joint behaviour, we investigate the potentiality of these quantities for risk management and forecasting purposes. As an alternative form of variability mesaures, we compute option-implied interquantile and interexpectile differences, that are compared with a weekly VIX-like index. In terms of forecasting power we investigate how different quantities related to the implicit quantile and expectile curves predict future logreturns and future realized variances.

Original languageEnglish
Pages (from-to)733-753
Number of pages21
JournalAnnals of Operations Research
Issue number2
Publication statusPublished - Jun 2022
Externally publishedYes


  • Expectiles
  • Forecasting
  • Quantiles
  • Risk management
  • Risk-neutral distribution
  • Weekly options


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