European option pricing and hedges under heterogeneity with λ-fuzzy measures and choquet intergral

Classical option pricing formulas are facing many challenges among which heterogeneity of investors enjoys abroad concerns. This paper studies the option pricing in a single period in the presence of investorspsila heterogeneous beliefs. We aim to make use of fuzzy instruments to highlight non-identical rationality which enter into option pricing and influence hedge strategies of investors, and to deduce fuzzy price representation of the option. The price of the option is not a determinate number but an interval containing the Black Scholes price. Further we discuss some hedge ratios that can be represented by fuzzy numbers, which are convenient for application. The basic analysis is generalized to incorporate multiple sources of risk, disagreement about non-fundamentals, and multiple investors. Other applications involving portfolio insurance and credit risk measure are discussed.