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On certain representations of pricing functionals

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  • Carlo Marinelli

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.

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  • Carlo Marinelli, 2021. "On certain representations of pricing functionals," Papers 2109.05564, arXiv.org.
    • Handle: RePEc:arx:papers:2109.05564
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    References listed on IDEAS

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    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    2. Jarno Talponen & Lauri Viitasaari, 2013. "Note on multidimensional Breeden-Litzenberger representation for state price densities," Papers 1305.5963, arXiv.org, revised Jan 2014.
    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. 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.
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    Cited by:

    1. Carlo Marinelli & Stefano d’Addona, 2023. "Nonparametric estimates of option prices via Hermite basis functions," Annals of Finance, Springer, vol. 19(4), pages 477-522, December.

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