{"title":"On certain representations of pricing functionals","authors":"Carlo Marinelli","doi":"10.1007/s10436-024-00438-5","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":"20 1","pages":"91 - 127"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10436-024-00438-5.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Finance","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s10436-024-00438-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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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.
期刊介绍：
Annals of Finance provides an outlet for original research in all areas of finance and its applications to other disciplines having a clear and substantive link to the general theme of finance. In particular, innovative research papers of moderate length of the highest quality in all scientific areas that are motivated by the analysis of financial problems will be considered. Annals of Finance''s scope encompasses - but is not limited to - the following areas: accounting and finance, asset pricing, banking and finance, capital markets and finance, computational finance, corporate finance, derivatives, dynamical and chaotic systems in finance, economics and finance, empirical finance, experimental finance, finance and the theory of the firm, financial econometrics, financial institutions, mathematical finance, money and finance, portfolio analysis, regulation, stochastic analysis and finance, stock market analysis, systemic risk and financial stability. Annals of Finance also publishes special issues on any topic in finance and its applications of current interest. A small section, entitled finance notes, will be devoted solely to publishing short articles – up to ten pages in length, of substantial interest in finance. Officially cited as: Ann Finance
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