In this report, we study, using real data from the market, the impact of the uncertainty in the volatility on the European options pricing and hedging strategy in the single asset and the multi assets case. This effect was measured and quantified by using a variety of methods mainly Polynomial Chaos, Monte Carlo and sparse grid. These methods provide a means of computing the variables of interest statistics such as the expected value, the variance and the density estimation. Numerical tests show that Polynomial Chaos in the 1D case as well as sparse grid in the multidimensional case yield results with high precision and relatively less computational time than the standard Monte Carlo method.