On an implicit assessment of fuzzy volatility in the Black and Scholes environment

Authors:
Andrea Capotorti;Gianna Figà-Talamanca
Affiliations:
Dip. Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06126, Perugia, Italy;Dip. Economia, Finanza e Statistica, Università degli Studi di Perugia, Italy
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

In this work we suggest a methodology to obtain the membership of a non-observable parameter through implicit information. To this aim we profit from the interpretation of membership functions as coherent conditional probabilities. We develop full details for the well known Black and Scholes pricing model where the membership of the volatility parameter is obtained from a sample of either asset prices or market prices for options written on that asset.