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On an implicit assessment of fuzzy volatility in the Black and Scholes environment


  • Andrea Capotorti
  • Gianna Figa'-Talamanca


In this work we suggest a methodology to obtain the membership of a non observable parameter through implicit information. To this aim we profit from the interpretation of membership functions as coherent conditional probabilities. We develop full details for the well known Black and Scholes pricing model where the membership of the volatility parameter is obtained from a sample of either asset prices or market prices for options written on that asset.

Suggested Citation

  • Andrea Capotorti & Gianna Figa'-Talamanca, 2012. "On an implicit assessment of fuzzy volatility in the Black and Scholes environment," Quaderni del Dipartimento di Economia, Finanza e Statistica 106/2012, Universit√† di Perugia, Dipartimento Economia.
  • Handle: RePEc:pia:wpaper:106/2012

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    References listed on IDEAS

    1. Bhattacharya, Mihir, 1980. "Empirical Properties of the Black-Scholes Formula Under Ideal Conditions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(05), pages 1081-1105, December.
    2. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Coletti, Giulianella & Scozzafava, Romano, 2006. "Conditional probability and fuzzy information," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 115-132, November.
    5. 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.
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