A New Algorithm for the Quantile Function of the Standard Gaussian Distribution. A Financial Application

One of the most common problems when applying Monte Carlo and Quasi-Monte Carlo methods is sampling from a given cumulative distribution. In this paper, we refer to the Inverse Transform method and we propose a new algorithm for performing the inversion of the standard Gaussian cumulative distribution. In order to focus on the computational aspects of the algorithm, we show a simple financial application. We evaluate a European call option on an underlying asset with normal returns, and formulate the problem in both a one-dimensional and a multidimensional framework. In both cases, we demonstrate that the proposed algorithm is comparable for speed and accuracy to the other ones existing in literature. In addition, it is implementable on a traditional personal computer and it can be easily generalized for inverting various other distributions.