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dc.contributor.advisorLombard, F.
dc.contributor.authorVisagie, Izak Jacobus Henning
dc.date.accessioned2016-01-08T09:50:17Z
dc.date.available2016-01-08T09:50:17Z
dc.date.issued2015
dc.identifier.urihttp://hdl.handle.net/10394/15765
dc.descriptionPhD (Risk Analysis), North-West University, Potchefstroom Campus, 2015en_US
dc.description.abstractIn this thesis we consider the calibration of models based on Lévy processes to option prices observed in some market. This means that we choose the parameters of the option pricing models such that the prices calculated using the models correspond as closely as possible to these option prices. We demonstrate the ability of relatively simple Lévy option pricing models to nearly perfectly replicate option prices observed in financial markets. We specifically consider calibrating option pricing models to barrier option prices and we demonstrate that the option prices obtained under one model can be very accurately replicated using another. Various types of calibration are considered in the thesis. We calibrate a wide range of Lévy option pricing models to option price data. We consider exponential Lévy models under which the log-return process of the stock is assumed to follow a Lévy process. We also consider linear Lévy models; under these models the stock price itself follows a Lévy process. Further, we consider time changed models. Under these models time does not pass at a constant rate, but follows some non-decreasing Lévy process. We model the passage of time using the lognormal, Pareto and gamma processes. In the context of time changed models we consider linear as well as exponential models. The normal inverse Gaussian (N 0 IG) model plays an important role in the thesis. The numerical problems associated with the N 0 IG distribution are explored and we propose ways of circumventing these problems. Parameter estimation for this distribution is discussed in detail. Changes of measure play a central role in option pricing. We discuss two well-known changes of measure; the Esscher transform and the mean correcting martingale measure. We also propose a generalisation of the latter and we consider the use of the resulting measure in the calculation of arbitrage free option prices under exponential Lévy models.en_US
dc.language.isoenen_US
dc.subjectCalibrationen_US
dc.subjectOption pricingen_US
dc.subjectLévy processesen_US
dc.subjectNormal inverse Gaussian distributionen_US
dc.subjectLognormal distributionen_US
dc.subjectPareto distributionen_US
dc.subjectGeneralised mean correcting martingale measureen_US
dc.subjectBarrier optionsen_US
dc.titleOn the calibration of Lévy option pricing modelsen
dc.typeThesisen_US
dc.description.thesistypeDoctoralen_US


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