Numerical Remarks on the Estimation of the Option Price

The computation of the European options price in a Black-Scholes market, characterized by the presence of no arbitrage condition, is an important applicative problem. In this paper we are interested in highlighting some numerical issues related to this problem. The proposed procedure is mainly divided into three parts: the test of the lognomality of the risk asset, the estimation of the volatility of the underlying and, finally, the determination of the price. As concerns the first point, we propose the adoption of the the Shapiro-Wilk test, in the second one we suggest to estimate the volatility by the sample standard deviation and in the third point we apply the Black-Scholes formula and we introduce an approximation for a Normal function value by means of a quadrature formula.