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On certain representations of pricing functionals

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  • Carlo Marinelli

    (University College London)

Abstract

We revisit two classical problems: the determination of the law of the underlying with respect to a risk-neutral measure on the basis of option prices, and the pricing of options with convex payoffs in terms of prices of call options with the same maturity (all options are European). The formulation of both problems is expressed in a language loosely inspired by the theory of inverse problems, and several proofs of the corresponding solutions are provided that do not rely on any special assumptions on the law of the underlying and that may, in some cases, extend results currently available in the literature. Furthermore, we consider a related problem, arising from nonparametric option pricing, on the reconstruction of put option prices in an approximation scheme where a sequence of measures converges to the (image) measure of the underlying’s return at fixed maturities.

Suggested Citation

  • Carlo Marinelli, 2024. "On certain representations of pricing functionals," Annals of Finance, Springer, vol. 20(1), pages 91-127, March.
    • Handle: RePEc:kap:annfin:v:20:y:2024:i:1:d:10.1007_s10436-024-00438-5
    DOI: 10.1007/s10436-024-00438-5
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    References listed on IDEAS

    as
    1. Jarno Talponen & Lauri Viitasaari, 2013. "Note on multidimensional Breeden-Litzenberger representation for state price densities," Papers 1305.5963, arXiv.org, revised Jan 2014.
    2. Marinelli, Carlo & d’Addona, Stefano, 2017. "Nonparametric estimates of pricing functionals," Journal of Empirical Finance, Elsevier, vol. 44(C), pages 19-35.
    3. Andrey Itkin, 2020. "Fitting Local Volatility:Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 11623, December.
    4. Carlo Marinelli & Stefano d'Addona, 2022. "Nonparametric estimates of option prices via Hermite basis functions," Papers 2209.09656, arXiv.org, revised Aug 2023.
    5. Sébastien Bossu & Peter Carr & Andrew Papanicolaou, 2021. "A functional analysis approach to the static replication of European options," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 637-655, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Option pricing; Breeden-Litzenberger formula; Convex payoffs; Distributions (generalized functions);
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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