A Sensitivity Analysis for the Pricing of European Call Options in a Binary Tree Model

The European call option prices have well-known formulae in the CoxRoss-Rubinstein model [2], depending on the volatility of the underlying asset. Nevertheless it is hard to give a precise estimate of this volatility. S. Muzzioli and C. Toricelli [6] handle this problem by using possibility distributions. In the first part of our paper we make some critical comments on their work. In the second part we present an alternative solution to the problem by performing a sensitivity analysis for the pricing of the option. This method is very general in the sense that it can be applied if one describes the uncertainty in the volatility by confidence intervals as well as if one describes it by fuzzy numbers. The conclusion is that the price of the option is not necessarily a strictly increasing function of the volatility.