A New Approximation to Standard Normal Distribution Function

[摘要] This paper, presents three news-improved approximations to the Cumulative Distribution Function (C.D.F.). The first approximation improves the accuracy of approximation given by Polya (1945). In this first new approximation, we reduce the maximum absolute error (MAE) from0.000314 to 0.00103. For this first new approximation, Aludaat and Alodat were reduce the (MAE) from 0.000314 to 0.001972. The second new approximation improve Tocher’s approximation, we reduce the (MAE) from, 0.166 to 0.00577. For the third new approximation, we combined the two previous approximations. Hence, this combined approximation is more accurate and its inverse is hard to calculate. This third approximation reduces the (MAE) to be less than 2.232e-004. The two improved previous approximations are less accurate, but his inverse is easy to calculate. Finally, we give an application to the third approximation for pricing a European Call using Black-Scholes Model.

[关键词] Cumulative distribution function;Normal distribution;Maximum absolute error