Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing. (English) Zbl 1165.91414

Summary: C. Carlson and R. Fullér [Fuzzy Sets Syst. 122, 315–326 (2001; Zbl 1016.94047)] have introduced possibilistic mean, variance and covariance of fuzzy numbers and R. Fullér and P. Majlender [Fuzzy Sets Syst. 136, 363–374 (2003; Zbl 1022.94032)] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers. Recently, A. Thavaneswaran, K. Thiagarajah and S.S. Appadoo [Math. Comput. Modelling 45, No. 7–8, 777–786 (2007; Zbl 1165.91415)] have defined non-centered \(n\)th order possibilistic moments of fuzzy numbers. In this paper, we extend these results to centered moments and find the kurtosis for a class of FCA (Fuzzy Coefficient Autoregressive) and FCV (Fuzzy Coefficient Volatility) models. We also demonstrate the superiority of the fuzzy forecasts over the minimum square error forecast through a numerical example. Finally, we provide a description of option price specification errors using the fuzzy weighted possibilistic option valuation model.


91G80 Financial applications of other theories
62P05 Applications of statistics to actuarial sciences and financial mathematics
03E72 Theory of fuzzy sets, etc.
Full Text: DOI


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