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Exponential Fitting, Finite Volume and Box Methods in Option Pricing.
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE). Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE). Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
2010 (English)Independent thesis Advanced level (degree of Master (One Year)), 15 credits / 22,5 HE creditsStudent thesis
Abstract [en]

In this thesis we focus mainly on special finite differences and finite volume methods and apply them to the pricing of barrier options.The structure of this work is the following: in Chapter 1 we introduce the definitions of options and illustrate some properties of vanilla European options and exotic options.Chapter 2 describes a classical model used in the financial world, the  Black-Scholes model. We derive theBlack-Scholes formula and show how stochastic differential equations model financial instruments prices.The aim of this chapter is also to present the initial boundary value problem and the maximum principle.We discuss boundary conditions such as: the first boundary value problem, also called  Dirichlet problem that occur in pricing ofbarrier options and European options. Some kinds of put options lead to the study of a second boundary value problem (Neumann, Robin problem),while the Cauchy problem is associated with one-factor European and American options.Chapter 3 is about finite differences methods such as theta, explicit, implicit and Crank-Nicolson method, which are used forsolving partial differential equations.The exponentially fitted scheme is presented in Chapter 4. It is one of the new classesof a robust difference scheme that is stable, has good convergence and does not produce spurious oscillations.The stability is also advantage of the box method that is presented in Chapter 5.In the beginning of the Chapter 6 we illustrate barrier options and then we consider a novel finite volume discretization for apricing the above options.Chapter 7 describes discretization of the Black-Scholes equation by the fitted finite volume scheme. In  Chapter 8 we present and describe numerical results obtained by using  the finite difference methods illustrated in the previous chapters.

Place, publisher, year, edition, pages
2010. , 69 p.
Keyword [en]
Financial Mathematics, numerical methods, exponential fitting, option pricing
National Category
Computational Mathematics Computational Mathematics
Identifiers
URN: urn:nbn:se:hh:diva-6108OAI: oai:DiVA.org:hh-6108DiVA: diva2:356530
Presentation
2010-06-03, Haldasallen, Halmstad University, Halmstad, 10:31 (English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2010-10-13 Created: 2010-10-12 Last updated: 2010-10-13Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
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  • Other locale
More languages
Output format
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  • text
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