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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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    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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