On the discrepancy between the objective and risk neutral densities in the pricing of European options

dc.contributor.authorVisagie, I.J.H. (Jaco)
dc.contributor.authorGrobler, G.L.
dc.contributor.emailjaco.visagie@up.ac.zaen_ZA
dc.date.accessioned2020-08-17T11:24:40Z
dc.date.available2020-08-17T11:24:40Z
dc.date.issued2019-06
dc.description.abstractA technique known as calibration is often used when a given option pricing model is fitted to observed financial data. This entails choosing the parameters of the model so as to minimise some discrepancy measure between the observed option prices and the prices calculated under the model in question. This procedure does not take the historical values of the underlying asset into account. In this paper, the density function of the log-returns obtained using the calibration procedure is compared to a density estimate of the observed historical log-returns. Three models within the class of geometric Lévy process models are fitted to observed data; the Black-Scholes model as well as the geometric normal inverse Gaussian and Meixner process models. The numerical results obtained show a surprisingly large discrepancy between the resulting densities when using the latter two models. An adaptation of the calibration methodology is also proposed based on both option price data and the observed historical log-returns of the underlying asset. The implementation of this methodology limits the discrepancy between the densities in question.en_ZA
dc.description.departmentStatisticsen_ZA
dc.description.librarianpm2020en_ZA
dc.description.urihttp://orion.journals.ac.zaen_ZA
dc.identifier.citationVisagie, I. J. H. & Grobler, G. L. 2019,'On the discrepancy between the objective and risk neutral densities in the pricing of European options', Orion: Operations Research in South Africa, vol. 35, no. 1, pp. 33-56.en_ZA
dc.identifier.issn0259–191X (print)
dc.identifier.issn2224–0004 (online)
dc.identifier.other10.5784/35-1-647
dc.identifier.urihttp://hdl.handle.net/2263/75769
dc.language.isoenen_ZA
dc.publisherOperations Research Society of South Africaen_ZA
dc.rights© 2019. This work is published under a Attribution CC BY license.en_ZA
dc.subjectPricingen_ZA
dc.subjectOptimisationen_ZA
dc.subjectFinancial marketsen_ZA
dc.subjectStochastic processesen_ZA
dc.subjectCalibrationen_ZA
dc.subjectDensity functionen_ZA
dc.subjectHistorical log-returnsen_ZA
dc.subjectLog-returnsen_ZA
dc.titleOn the discrepancy between the objective and risk neutral densities in the pricing of European optionsen_ZA
dc.typeArticleen_ZA

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