Series representations and approximation of some quantile functions appearing in finance

摘要: It has long been agreed by academics that the inversion method is of choice for generating random variates, given availability a cheap but accurate approximation quantile function. However several probability distributions arising in practice satisfactory approximating these functions not available. The main focus this thesis will be to develop Taylor and asymptotic series representations following distributions; Variance Gamma, Generalized Inverse Gaussian, Hyperbolic, -Stable Snedecor’s F distributions. As secondary matter we briefly investigate problem entire Indeed with new analytic expressions whole host possibilities become We outline algorithms particular provide C++ implementation variance gamma case. To our knowledge fastest available algorithm its sort.