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Fourth-Order Runge-Kutta Method for Generalized Black-Scholes Partial Differential Equations

The famous Black-Scholes partial differential equation is one of the most widely used and researched equations in modern financial engineering to address the complex evaluations in the financial markets. This thesis investigates a numerical technique, using a fourth-order discretization in time and space, to solve a generalized version of the classical Black-Scholes partial differential equation. The numerical discretization in space consists of a fourth order centered difference approximation in the interior points of the spatial domain along with a fourth order left and right sided approximation for the points near the boundary. On the other hand, the temporal discretization is made by implementing a Runge-Kutta order four (RK4) method. The designed approximations are analyzed numerically with respect to stability and convergence properties.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:mdh-56279
Date January 2021
CreatorsTajammal, Sidra
PublisherMälardalens högskola, Akademin för utbildning, kultur och kommunikation
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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