Abstract :
We use t he set of propositions of s ome pre v i ous p apers to define a f uzzy version of t he Black-Scholes v alue where t he r i sk freeinstantaneous interest intensit y, t he volatilit y and t he initial s to ck pr ice are fuzzy nu mbers w hose par ameters are built w ithstatistical financial d ata. Wi th our Black-Sch oles f uzzy nu mbers we define indexes of per for mance v ar ing in time. As an example,w i th data of the Italian Stock Exchange on M IB30, we see t hat i n 2004 and 2006 our indexes are n egative, that is, t he y are indexes ofthe refuse to i nvest and this refuse increased. S o, on November 11, 2006 we co uld forecast t hat t he mar ket w i l l become w i th morer i sk: t he r i sk of loss w il l increase. Now, on Janu ar y 25, 2010, we know that this fore cast has h app ened. O bv i ously, the p ar ametersof our Black-Scholes fuzzy numbers can be valued also w ith incomplete, possibilistic data. With respect to the probabilistic one,our f uzzy method is more simple and immediate to have a forecast on t he financial m ar ke t.
