A research report submitted to the Faculty of Science,
University of the Witwatersrand, in ful lment of the
requirements for the degree of Master of Science.
School of Mathematics
Johannesburg
February 15, 2016 / We obtain a solution of the Black-Scholes equation with a non-smooth bound-
ary condition using symmetry methods. The Black-Scholes equation along
with its boundary condition are rst transformed into the one dimensional
heat equation and an initial condition respectively. We then nd an appro-
priate general symmetry generator of the heat equation using symmetries of
the heat equation and the fundamental solution of the heat equation. The
method we use to nd the symmetry generator is such that the boundary
condition is left invariant and yet the symmetry can still be used to solve
the heat equation. We then use the help of Mathematica to nd the solution
to the heat equation. Then the solution is then transformed backwards to
a solution of the Black-Scholes equation using the same change of variables
that were used for the forward transformations. The solution is then nally
checked if it satis es the boundary condition of the Black-Scholes equation.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/20351 |
| Date | 10 May 2016 |
| Creators | Mamba, Siphamandla |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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