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Option price sensitivities through fuzzy numbers. (English) Zbl 1217.91219

Summary: The main motivation in using fuzzy numbers in finance lies in the need for modelling the uncertainty and vagueness that are implicit in many situations. However, the fuzzy approach should not be considered as a substitute for the probabilistic approach but rather as a complementary way to describe the model peculiarities. Here, we consider, in particular, the Black and Scholes model for option pricing, and we show that the fuzzification of some key parameters enables a sensitivity analysis of the option price with respect to the risk-free interest rate, the final value of the underlying stock price, the volatility, and also better forecasts. The sensitivities with respect to the variables of the model are represented by different letters of the Greek alphabet and they play an important role in the definition of the shape of the fuzzy option price.

MSC:

91G80 Financial applications of other theories
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Buckley, J.J., The fuzzy mathematics of finance, Fuzzy sets and systems, 21, 57-73, (1987) · Zbl 0613.90017
[2] Fedrizzi, M.; Fedrizzi, M.; Ostasiewicz, W., Towards fuzzy modelling in economics, Fuzzy sets and systems, 54, 259-268, (1993)
[3] Li Calzi, M., Towards a general setting for the fuzzy mathematics of finance, Fuzzy sets and systems, 35, 265-280, (1990) · Zbl 0703.90002
[4] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 87, 637-659, (1973) · Zbl 1092.91524
[5] Guerra, M.L.; Stefanini, L., Approximate fuzzy arithmetic operations using monotonic interpolations, Fuzzy sets and systems, 150, 1, 5-33, (2005) · Zbl 1062.03050
[6] Stefanini, L.; Sorini, L.; Guerra, M.L., Parametric representations of fuzzy numbers and applications to fuzzy calculus, Fuzzy sets and systems, 157/18, 2423-2455, (2006) · Zbl 1109.26024
[7] Stefanini, L.; Sorini, L.; Guerra, M.L., Fuzzy numbers and fuzzy arithmetics, (), 249-284
[8] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
[9] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[10] ()
[11] M.L. Guerra, L. Sorini, L. Stefanini, Parametrized fuzzy numbers for option pricing, in: 2007 IEEE Conference on Fuzzy Systems, vol. 1, 2007, pp. 728-733.
[12] Thavaneswaran, A.; Appadoo, S.S.; Paseka, A., Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing, Mathematical and computer modelling, 49, 1-2, 352-368, (2009) · Zbl 1165.91414
[13] Yoshida, Y., The valuation of European options in uncertain environment, European journal of operational research, 145, 221-229, (2003) · Zbl 1011.91045
[14] Zmeskal, Z., Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option, European journal of operational research, 135, 303-310, (2001) · Zbl 0999.91044
[15] Lee, C.F.; Tzeng, G.H.; Wang, S.Y., A new application of fuzzy set theory to the black – scholes option pricing model, Expert systems with applications, 29, 330-342, (2005)
[16] Chrysafis, K.A.; Papadopoulus, B.K., On theoretical pricing of options with fuzzy estimators, Journal of computational and applied mathematics, (2007)
[17] Thiagarajah, K.; Appadoo, S.S.; Thavaneswaran, A., Option valuation model with adaptive fuzzy numbers, Computers & mathematics with applications, 53, 831-841, (2007) · Zbl 1213.91145
[18] Wu, H.C., Pricing European options based on the fuzzy pattern of black Scholes formula, Computers and operations research, 31, 1069-1081, (2004) · Zbl 1062.91041
[19] Wu, H.C., Using fuzzy sets theory and black – scholes formula to generate pricing boundaries of European options, Applied mathematics and computation, 185, 136-146, (2007) · Zbl 1283.91184
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