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

  • Authors:

  • A. Thavaneswaran;S. S. Appadoo;A. Paseka

  • Affiliations:

  • Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada;Department of Supply Chain Management, University of Manitoba, Winnipeg, Manitoba, Canada;Department of Accounting and Finance, University of Manitoba, Winnipeg, Manitoba, Canada

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2009

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Abstract

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 possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [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) models with applications, Mathematical and Computer Modelling 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 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.