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Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration

Author

Listed:
  • Eduardo Abi Jaber

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Soukaïna Bruneau

    (X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Nathan de Carvalho

    (Engie Global Markets, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Dimitri Sotnikov

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, Engie Global Markets)

  • Laurent Tur

    (Engie Global Markets)

Abstract

In energy markets, joint historical and implied calibration is of paramount importance for practitioners yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from the option market. We address this crucial problem with a parsimonious multiplicative multi-factor Heath-Jarrow-Morton (HJM) model for forward curves, combined with a stochastic volatility factor coming from the Lifted Heston model. We develop a sequential fast calibration procedure leveraging the Kemna-Vorst approximation of futures contracts: (i) historical correlations and the Variance Swap (VS) volatility term structure are captured through Level, Slope, and Curvature factors, (ii) the VS volatility term structure can then be corrected for a perfect match via a fixed-point algorithm, (iii) implied volatility smiles are calibrated using Fourier-based techniques. Our model displays remarkable joint historical and implied calibration fits -to both German power and TTF gas marketsand enables realistic interpolation within the implied volatility hypercube.

Suggested Citation

  • Eduardo Abi Jaber & Soukaïna Bruneau & Nathan de Carvalho & Dimitri Sotnikov & Laurent Tur, 2025. "Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration," Working Papers hal-04879087, HAL.
    • Handle: RePEc:hal:wpaper:hal-04879087
    Note: View the original document on HAL open archive server: https://hal.science/hal-04879087v1
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