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Implicit quantiles and expectiles

  • S.I. : Risk Management Decisions and Value under Uncertainty
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Abstract

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.

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Notes

  1. We distinguish between in-the-money, at-the-money, and out-of-the-money regions as regions in which the future value of the underlying is higher, equal to, or lower than its current value.

  2. For more details see http://www.cboe.com/products/weeklys-options/available-weeklys.

  3. This was indeed a correct approach, due to the low liquidity of short date options before the advent of weekly options.

  4. As for longer term options, also weekly options have a larger distance for less liquid options. From more to less liquid, the distance between consecutive price goes from $5 to $25.

  5. The abbreviation “MARS” is trademarked and licensed exclusively to Salford Systems. For this reason the MARS algorithm might be identified with alternative names, e.g.: in R and Python is identified as the earth algorithm (Enhanced Adaptive Regression Through Hinges).

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Authors and Affiliations

  1. Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy

    Fabio Bellini & Edit Rroji

  2. Department of Financial Management and Control, University Ramon Llull, ESADE, Avenida de Torreblanca 59, Sant Cugat, 08172, Barcelona, Spain

    Carlo Sala

Authors
  1. Fabio Bellini
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  2. Edit Rroji
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  3. Carlo Sala
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Correspondence to Carlo Sala.

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Bellini, F., Rroji, E. & Sala, C. Implicit quantiles and expectiles. Ann Oper Res 313, 733–753 (2022). https://doi.org/10.1007/s10479-021-04054-8

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  • DOI: https://doi.org/10.1007/s10479-021-04054-8

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