Abstract
A default risk model is provided by using option pricing theory in a fuzzy framework in consideration of a simple company comprised of a single type of the debt that is free from profit payment and a single type of capital that is liberated from dividend. The model is based on the assumption that asset value of a company is the sum of total market value of stock and debt value, considering a situation where the asset value becomes below the debt value is default. For constructing the default risk model, a new variable is defined to derive a formula to evaluate the probability of default. Thus, an EDP (estimated default probability) model with the first and second moment is proposed and since debt value is fluctuated as asset price some bounds are established to somehow admit the fluctuation of the debt values, employing fuzzy number in the total market value of asset value.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Black, F., Scholes, M.: The Pricing of Options and Corporate Liabilities. J. Political Economy 81(3), 637–654 (1973)
Merton, R.C.: On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. J. Finance 29, 449–470 (1974)
Black, F., Cox, J.C.: Valuing Corporate Securities: Some Effects of Bond Indenture Provisions. J. Finance 31, 351–367 (1976)
Longstaff, F.A., Schwartz, A.E.S.: A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. J. Finance 50, 789–821 (1995)
Turnbull, S., Wakeman, L.: A Quick Algorithm for Pricing European Average. J. Financial Quantitative Analysis, 377–389, September 26 (1991)
Levy, E.: Pricing European Average Rate Currency Options. J. International Money and Finance 11, 474–491 (1992)
Inoue, H., Miyake, M., Takahashi, S., Yu, M.: Option Pricing for which Payoff Depends on Weighted Sums of Prices. In: Proc. of Hawaii International Conference on Statistics, Mathematics and Related Fields (2007)
Miyake, M., Inoue, H.: Note on Weighted Average Strike Asian Options. In: Proc. IPMU 2008 (Information Processing and Management of Uncertainty in Knowledge-Based Systems), pp. 601–607 (2008)
Miyake, M., Inoue, H.: A Default Probability Estimation Model: An Application to Japanese Companies. Journal of Uncertain Systems, 3(3), 210–220 (2009)
Ronn, E.I., Verma, A.K.: Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model. J. Finance 41, 871–895 (1989)
Boness, A.J.: Elements of a Theory of Stock-option Value. J. Political Economy 72(2), 163–175 (1964)
Ando, T., Marushige, K.: Estimation Method of Default Probability with Knock-out Option Approach~Comparative Analysis with European Option Approach~ IMES Discussion Paper (in Japanese) No. 2001-J-4 (2001)
Carlsson, C., Fuller, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 (2001)
Carlsson, C., Fuller, R.: A fuzzy approach to real option valuation. Fuzzy Sets and Systems 139, 297–312 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Inoue, H., Miyake, M. (2010). A Default Risk Model in a Fuzzy Framework. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-14058-7_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14057-0
Online ISBN: 978-3-642-14058-7
eBook Packages: Computer ScienceComputer Science (R0)