On an implicit assessment of fuzzy volatility in the Black and Scholes environment
AbstractIn 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.
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Bibliographic InfoPaper provided by Università di Perugia, Dipartimento Economia, Finanza e Statistica in its series Quaderni del Dipartimento di Economia, Finanza e Statistica with number 106/2012.
Length: 23 pages
Date of creation: 01 Oct 2012
Date of revision:
Fuzzy membership elicitation; Implicit Information; Coherent Conditional Probability Assessments and Extension; Probability Possibility Transformation.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-24 (All new papers)
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- 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.
- 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.
- 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 327-43.
- Coletti, Giulianella & Scozzafava, Romano, 2006. "Conditional probability and fuzzy information," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 115-132, November.
- 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.
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