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Meshfree methods in option pricing
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab). (Financial Mathematics)
2011 (engelsk)Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
Abstract [en]

A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. By the next step, the option price is approximated in space with radial basis functions (RBF) with unknown parameters, in particular, we con- sider multiquadric radial basis functions (MQ-RBF). In case of Ameri- can options a penalty method is used, i.e. removing the free boundary is achieved by adding a small and continuous penalty term to the Black- Scholes equation. Finally, a comparison of analytical and finite difference solutions and numerical results from the literature is included.

sted, utgiver, år, opplag, sider
2011. , s. 59
Emneord [en]
Financial Mathematics, option pricing, RBF, PDE, meshfree methods
HSV kategori
Identifikatorer
URN: urn:nbn:se:hh:diva-16383Lokal ID: IDE1124OAI: oai:DiVA.org:hh-16383DiVA, id: diva2:444783
Fag / kurs
Financial Mathematics
Presentation
2011-05-30, Wigforssallen, Halmstad University, Halmstad, 10:01 (engelsk)
Uppsök
Physics, Chemistry, Mathematics
Veileder
Examiner
Tilgjengelig fra: 2011-09-30 Laget: 2011-09-30 Sist oppdatert: 2011-10-03bibliografisk kontrollert

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