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Signature volatility models: pricing and hedging with Fourier

Author

Listed:
  • Eduardo Abi Jaber

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

  • Louis-Amand Gérard

    (UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is remarkably universal, as it includes, but is not limited to, the celebrated Stein-Stein, Bergomi, and Heston models, together with some path-dependent variants. Second, we derive the joint characteristic functional of the log-price and integrated variance provided that some infinitedimensional extended tensor algebra valued Riccati equation admits a solution. This allows us to price and (quadratically) hedge certain European and path-dependent options using Fourier inversion techniques. We highlight the efficiency and accuracy of these Fourier techniques in a comprehensive numerical study.

Suggested Citation

  • Eduardo Abi Jaber & Louis-Amand Gérard, 2024. "Signature volatility models: pricing and hedging with Fourier," Working Papers hal-04435238, HAL.
    • Handle: RePEc:hal:wpaper:hal-04435238
    Note: View the original document on HAL open archive server: https://hal.science/hal-04435238
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