Marinelli, Carlo;
(2024)
On certain representations of pricing functionals.
Annals of Finance
10.1007/s10436-024-00438-5.
(In press).
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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.
| Type: | Article |
|---|---|
| Title: | On certain representations of pricing functionals |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10436-024-00438-5 |
| Publisher version: | http://dx.doi.org/10.1007/s10436-024-00438-5 |
| Language: | English |
| Additional information: | © 2024 Springer Nature. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Option pricing, Breeden-Litzenberger formula, Convex payoffs, Distributions (generalized functions) |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10189932 |
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