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Applied Computational Intelligence and Soft Computing
Volume 2010 (2010), Article ID 607214, 7 pages
Research Article

Black-Scholes Fuzzy Numbers as Indexes of Performance

Dipartimento di Statistica e Matematica per la Ricerca Economica, Università di Napoli Parthenope, Via Acton, 38, 80133 Naples, Italy

Received 10 June 2009; Accepted 29 January 2010

Academic Editor: Antonio Di Nola

Copyright © 2010 M. R. Simonelli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We use the set of propositions of some previous papers to define a fuzzy version of the Black-Scholes value where the risk free instantaneous interest intensity, the volatility and the initial stock price are fuzzy numbers whose parameters are built with statistical financial data. With our Black-Scholes fuzzy numbers we define indexes of performance varing in time. As an example, with data of the Italian Stock Exchange on MIB30, we see that in 2004 and 2006 our indexes are negative, that is, they are indexes of the refuse to invest and this refuse increased. So, on November 11, 2006 we could forecast that the market will become with more risk: the risk of loss will increase. Now, on January 25, 2010, we know that this forecast has happened. Obviously, the parameters of our Black-Scholes fuzzy numbers can be valued also with incomplete, possibilistic data. With respect to the probabilistic one, our fuzzy method is more simple and immediate to have a forecast on the financial market.