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Projection of Functionals and Fast Pricing of Exotic Options

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  • Valentin Tissot-Daguette

Abstract

We investigate the approximation of path functionals. In particular, we advocate the use of the Karhunen-Lo\`eve expansion, the continuous analogue of Principal Component Analysis, to extract relevant information from the image of a functional. Having accurate estimate of functionals is of paramount importance in the context of exotic derivatives pricing, as presented in the practical applications. Specifically, we show how a simulation-based procedure, which we call the Karhunen-Lo\`eve Monte Carlo (KLMC) algorithm, allows fast and efficient computation of the price of path-dependent options. We also explore the path signature as an alternative tool to project both paths and functionals.

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  • Valentin Tissot-Daguette, 2021. "Projection of Functionals and Fast Pricing of Exotic Options," Papers 2111.03713, arXiv.org, revised Apr 2022.
    • Handle: RePEc:arx:papers:2111.03713
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    References listed on IDEAS

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    1. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(6), pages 583-597, November.
    2. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Learning for Exotic Option Valuation," Papers 2103.12551, arXiv.org, revised Sep 2021.
    3. Imanol Perez Arribas & Cristopher Salvi & Lukasz Szpruch, 2020. "Sig-SDEs model for quantitative finance," Papers 2006.00218, arXiv.org, revised Jun 2020.
    4. Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, vol. 4(1), pages 79-93, January.
    5. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2021. "Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 11-27, January.
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    Cited by:

    1. Bruno Dupire & Valentin Tissot-Daguette, 2022. "Functional Expansions," Papers 2212.13628, arXiv.org, revised Mar 2023.

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