Handle URI:
http://hdl.handle.net/10754/624854
Title:
Error Analysis for Fourier Methods for Option Pricing
Authors:
Häppölä, Juho
Abstract:
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
6-Jan-2016
Type:
Presentation
Additional Links:
http://mediasite.kaust.edu.sa/Mediasite/Play/a03b9d319dec456694b21aecee2ff84f1d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
Appears in Collections:
Presentations; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorHäppölä, Juhoen
dc.date.accessioned2017-06-08T06:32:29Z-
dc.date.available2017-06-08T06:32:29Z-
dc.date.issued2016-01-06-
dc.identifier.urihttp://hdl.handle.net/10754/624854-
dc.description.abstractWe provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.en
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/a03b9d319dec456694b21aecee2ff84f1d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52en
dc.titleError Analysis for Fourier Methods for Option Pricingen
dc.typePresentationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
kaust.authorHäppölä, Juhoen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.