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Non-parametric Pricing and Hedging of Exotic Derivatives

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  • Terry Lyons
  • Sina Nejad
  • Imanol Perez Arribas

Abstract

In the spirit of Arrow–Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to non-parametrically price and hedge exotic derivatives in the scenario where one has access to price data for other exotic payoffs. The methodology leads to a computationally tractable and accurate algorithm for pricing and hedging using market prices of a basket of exotic derivatives that has been tested on real and simulated market prices, obtaining good results.

Suggested Citation

  • Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2020. "Non-parametric Pricing and Hedging of Exotic Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(6), pages 457-494, November.
    • Handle: RePEc:taf:apmtfi:v:27:y:2020:i:6:p:457-494
    DOI: 10.1080/1350486X.2021.1891555
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    Citations

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    Cited by:

    1. Christa Cuchiero & Philipp Schmocker & Josef Teichmann, 2023. "Global universal approximation of functional input maps on weighted spaces," Papers 2306.03303, arXiv.org, revised Feb 2024.
    2. Christa Cuchiero & Guido Gazzani & Janka Moller & Sara Svaluto-Ferro, 2023. "Joint calibration to SPX and VIX options with signature-based models," Papers 2301.13235, arXiv.org.
    3. Christa Cuchiero & Sara Svaluto-Ferro & Josef Teichmann, 2023. "Signature SDEs from an affine and polynomial perspective," Papers 2302.01362, arXiv.org.
    4. Christa Cuchiero & Francesca Primavera & Sara Svaluto-Ferro, 2022. "Universal approximation theorems for continuous functions of c\`adl\`ag paths and L\'evy-type signature models," Papers 2208.02293, arXiv.org, revised Aug 2023.
    5. Ming Min & Tomoyuki Ichiba, 2023. "Convolutional signature for sequential data," Digital Finance, Springer, vol. 5(1), pages 3-28, March.
    6. Christa Cuchiero & Guido Gazzani & Sara Svaluto-Ferro, 2022. "Signature-based models: theory and calibration," Papers 2207.13136, arXiv.org.
    7. John Armstrong & Andrei Ionescu, 2023. "Gamma Hedging and Rough Paths," Papers 2309.05054, arXiv.org, revised Mar 2024.
    8. Erdinc Akyildirim & Matteo Gambara & Josef Teichmann & Syang Zhou, 2023. "Randomized Signature Methods in Optimal Portfolio Selection," Papers 2312.16448, arXiv.org.
    9. S'ebastien Bossu & St'ephane Cr'epey & Hoang-Dung Nguyen, 2024. "Spanning Multi-Asset Payoffs With ReLUs," Papers 2403.14231, arXiv.org.

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