On an implicit assessment of fuzzy volatility in the Black and Scholes environment
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.
|Date of creation:||01 Oct 2012|
|Date of revision:|
|Contact details of provider:|| Postal: via Pascoli, 20 - 06123 Perugia|
Phone: +39 075 5855279
Fax: +39 075 5855299
Web page: http://www.econ.unipg.it/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:pia:wpaper:106/2012. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Davide Castellani)
If references are entirely missing, you can add them using this form.