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Addition Of The Fuzzy Logic Model To Black-Scholes, For Pricing Mexican Currency Options, La Incorporacion De La Logica Difusa Al Modelo Black-Scholes, Para La Determinacion Del Precio De La Opcion Cambiaria Mexicana

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  • Manuel Munoz Palma
  • Ezequiel Aviles Ochoa

Abstract

Since the introduction of uncertainty theory, a new paradigm in economics and finance has formed. This shift has included incorporation of new models that allow a greater degree of accuracy in modeling the reality of the environment of organizations based on fuzzy logic theory. This article emphasizes the importance of uncertainty present in the financial markets, which has provoked an increasing need for establishing models to determine its effect in pricing. Specifically we focus on futures and derivatives markets. A proposal is developed to determine the price of an exchange option applying triangular fuzzy numbers to exchange rate variables, to domestic interest rates, and foreign interest rates based on the classic Black-Scholes (B-S) model.

Suggested Citation

  • Manuel Munoz Palma & Ezequiel Aviles Ochoa, 2014. "Addition Of The Fuzzy Logic Model To Black-Scholes, For Pricing Mexican Currency Options, La Incorporacion De La Logica Difusa Al Modelo Black-Scholes, Para La Determinacion Del Precio De La Opcion Ca," Revista Internacional Administracion & Finanzas, The Institute for Business and Finance Research, vol. 7(7), pages 55-73.
    • Handle: RePEc:ibf:riafin:v:7:y:2014:i:7:p:55-73
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    References listed on IDEAS

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    1. Merton, Robert C, 1998. "Applications of Option-Pricing Theory: Twenty-Five Years Later," American Economic Review, American Economic Association, vol. 88(3), pages 323-349, June.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. 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 637-654, May-June.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Hull, John & White, Alan, 1988. "The Use of the Control Variate Technique in Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(3), pages 237-251, September.
    8. Samuelson, Paul A., 1967. "General Proof that Diversification Pays*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(1), pages 1-13, March.
    9. Scott, Elton & Tucker, Alan L., 1989. "Predicting currency return volatility," Journal of Banking & Finance, Elsevier, vol. 13(6), pages 839-851, December.
    10. Chang, Chuang-Chang, 2001. "Efficient procedures for the valuation and hedging of American currency options with stochastic interest rates," Journal of Multinational Financial Management, Elsevier, vol. 11(3), pages 241-268, July.
    11. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    12. Latane, Henry A & Rendleman, Richard J, Jr, 1976. "Standard Deviations of Stock Price Ratios Implied in Option Prices," Journal of Finance, American Finance Association, vol. 31(2), pages 369-381, May.
    13. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    14. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    More about this item

    Keywords

    Financial Risk; Fuzzy Numbers; Black-Scholes Model;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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