A survey of computational methods for pricing Asian options

[摘要] In this thesis, we investigate two numerical methods to pricenancial options.We look at two types of options, namely European options andAsian options. The numerical methods we use are thenite di erencemethod and numerical inversion of the Laplace transform. We applynitedi erence methods to partial di erential equations with both uniform andnon-uniform spatial grids. The Laplace inversion method we use is due toTalbot. It is based on the midpoint-type approximation of the Bromwichintegral on a deformed contour. When applied to Asian options, we havethe problem of computing the hypergeometric function of therst kind.We propose a new method for numerically calculating the hypergeometricfunction. This method too is based on using Talbot contours. Throughoutthe thesis, we use the Black-Scholes equation as our benchmark problem.

[发布机构] Stellenbosch University