A survey of computational methods for pricing Asian options
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.