Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2009. / In this thesis, we investigate two numerical methods to price nancial options.
We look at two types of options, namely European options and
Asian options. The numerical methods we use are the nite di erence
method and numerical inversion of the Laplace transform. We apply nite
di erence methods to partial di erential equations with both uniform and
non-uniform spatial grids. The Laplace inversion method we use is due to
Talbot. It is based on the midpoint-type approximation of the Bromwich
integral on a deformed contour. When applied to Asian options, we have
the problem of computing the hypergeometric function of the rst kind.
We propose a new method for numerically calculating the hypergeometric
function. This method too is based on using Talbot contours. Throughout
the thesis, we use the Black-Scholes equation as our benchmark problem.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2118 |
| Date | 03 1900 |
| Creators | Nieuwveldt, Fernando Damian |
| Contributors | Weideman, J. A. C., Roux, A., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Stellenbosch |
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