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Interval LU-fuzzy arithmetic in the Black and Scholes option pricing

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Author Info

  • Maria Letizia Guerra

    ()
    (Department of Mathematics for Social and Economic Sciences, University of Bologna and Department of Economics, Università di Urbino "Carlo Bo")

  • Laerte Sorini

    ()
    (Department of Economics, Università di Urbino "Carlo Bo")

  • Luciano Stefanini

    ()
    (Department of Economics, Università di Urbino "Carlo Bo")

Abstract

In financial markets people have to cope with a lot of uncertainty while making decisions. Many models have been introduced in the last years to handle vagueness but it is very difficult to capture together all the fundamental characteristics of real markets. Fuzzy modeling for finance seems to have some challenging features describing the financial markets behavior; in this paper we show that the vagueness induced by the fuzzy mathematics can be relevant in modelling objects in finance, especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years. We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini and improved in Stefanini, Sorini and Guerra, in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations by the interval fuzzy arithmetic approach and an illustrative example are also incuded.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_07_04.pdf
File Function: First version, 2007
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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 0704.

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Length: 19 pages
Date of creation: 2007
Date of revision: 2007
Publication status: published in International Journal of Applied Mathematics, Vol 19/2, 171-200
Handle: RePEc:urb:wpaper:07_04

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Web page: http://www.econ.uniurb.it/
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Related research

Keywords: Fuzzy Operations; Option Pricing; Black and Scholes;

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  1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  2. Zmeskal, Zdenek, 2001. "Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option," European Journal of Operational Research, Elsevier, vol. 135(2), pages 303-310, December.
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