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Exponential Finite Difference Method For Nonlinear Black-Scholes Equation

BROWSE_DETAIL_CREATION_DATE: 25-05-2017

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BROWSE_DETAIL_TYPE: Thesis

BROWSE_DETAIL_SUB_TYPE: Masters

BROWSE_DETAIL_PUBLISH_STATE: Unpublished

BROWSE_DETAIL_FORMAT: PDF Document

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: Mathematics,

BROWSE_DETAIL_CREATORS: Omar, Fathia Shebani Abdusalam (Author),

BROWSE_DETAIL_CONTRIBUTERS: , Abubakar Sanı (Advisor),

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exponential finite difference method, nonlinear Black-Scholes equation,illiquid market


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In this thesis, we investigate exponential finite difference method for nonlinear Black-Scholes equation arising in an illiquid market. Chapter 1 is devoted to the literaturesurvey with some basic definitions and terminology of the option pricing problem. InChapter 2 we review the Black-Scholesmodel and finite differencemethods for Black-Scholes equation. In Chapter 3, an explicit finite difference method for a nonlinearBlack-Scholes equation is studied with the monotonicity, stability and consistency results.In Chapter 4, we apply the exponential finite difference method to linear andnonlinear Black-Scholes equations. Moreover, we investigate consistency and convergenceof the method. Numerical experiments are performed to verify theoreticalresults. Exponential finite difference method is compared with an explicit finite differencemethod proposed for linear and nonlinear Black-Scholes equation. Numericalresults show that exponential finite differencemethod exhibits better performance thenexplicit method. Finally, we give a brief conclusion in Chapter 5.


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