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Nonparametric 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 nonparametrically 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, 2019. "Nonparametric pricing and hedging of exotic derivatives," Papers 1905.00711, arXiv.org.
    • Handle: RePEc:arx:papers:1905.00711
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    References listed on IDEAS

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    1. M. R. Grasselli & T. R. Hurd, 2002. "A Monte Carlo method for exponential hedging of contingent claims," Papers math/0211383, arXiv.org.
    2. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
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    5. Terry Lyons, 2014. "Rough paths, Signatures and the modelling of functions on streams," Papers 1405.4537, arXiv.org.
    6. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    7. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    10. Imanol Perez Arribas, 2018. "Derivatives pricing using signature payoffs," Papers 1809.09466, arXiv.org.
    11. Flint, Guy & Hambly, Ben & Lyons, Terry, 2016. "Discretely sampled signals and the rough Hoff process," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2593-2614.
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    13. Candia Riga, 2016. "A pathwise approach to continuous-time trading," Papers 1602.04946, arXiv.org.
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    Citations

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    Cited by:

    1. Samuel N. Cohen & Derek Snow & Lukasz Szpruch, 2021. "Black-box model risk in finance," Papers 2102.04757, arXiv.org.
    2. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Numerical method for model-free pricing of exotic derivatives using rough path signatures," Papers 1905.01720, arXiv.org, revised Feb 2020.
    3. Imanol Perez Arribas & Cristopher Salvi & Lukasz Szpruch, 2020. "Sig-SDEs model for quantitative finance," Papers 2006.00218, arXiv.org, revised Jun 2020.
    4. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Oct 2024.

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