Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing

Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilisticmean, variance and covariance of fuzzy numbers and Fuller andMajlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers. Recently, Thavaneswaran et al. [A. Thavaneswaran, K. Thiagarajah, S.S. Appadoo, Fuzzy coefficient volatility (FCV)modelswith applications,Mathematical and ComputerModelling 45 (2007) 777–786] have defined non-centered nth 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 theminimumsquare error forecast through anumerical example. Finally,weprovide a description of option price specification errors using the fuzzyweighted possibilistic option valuation model. © 2008 Elsevier Ltd. All rights reserved.