Finite Elements Solutions to the Black - Scholes Equation
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Date
2020-05-01
Authors
Zhanatova, Nazym
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Sciences and Humanities
Abstract
Nowadays, for the financial industry it is important to implement mathematical tools of
the advanced level. World’s well-known economists Fischer Black and Myron Scholes
introduced the distinguished equation for option pricing in 1973. This Capstone project aims to
find finite element solutions to the Black-Scholes Equation. For this, the Black-Scholes
Equation is solved as a convection dominated problem through the Local Projection
Stabilization, where Galerkin finite element method is applied to the parabolic equation. Hence,
for the Local Projection Stabilization, the functions of L2 – orthogonal finite element basis of
arbitrary order are constructed. These functions result in a diagonal mass matrix which are
useful for time discretization.
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Research Subject Categories::MATHEMATICS