Credit Rating Modelled with Reflected Stochastic Differential Equations


This research paper is focused on the modelling of credit rating, using reduced form approach, in which intensity is defined endogenously based on the firm’s cashflow. It was modelled with reflected stochastic differential equation; this was adopted to evaluate the credit rating of a firm where the reflection function Ø(t) (i.e. Brownian local time) was used to detect default and measure time spent at default. Through this, the credit rating is estimated within [0,1]; where “0” is the state of default and “1” is interpreted as undefaultable within a time interval t≥[0, ∞) under consideration.

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Sonubi, A. (2014) Credit Rating Modelled with Reflected Stochastic Differential Equations. Journal of Mathematical Finance, 4, 333-337. doi: 10.4236/jmf.2014.45031.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Protter, P. (2001) A Partial Introduction to Financial Assest Pricing Theory. Stochastic Processes and Their Applications, 91, 169-203.
[2] Hobson, D. (2004) A Survey of Mathematical Finance. Proceedings of the Royal Society A, 460, 3369-3401.
[3] Samuelson, P. (1965) Rational Theory of Warrant Pricing. Industrial Management Review, 6, 13-31.
[4] Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-659.
[5] Merton, C.R. (1973) The Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4, 141-183.
[6] Jeanblanc, M. and Rutkowski, M. (2000) Modelling of Default Risk: An Overview. Workshop Presentation, New York University, New York.
[7] Skorohod, A.V. (1961) Stochastic Equation for Diffusion Processes in a Bounded Region. Theory of Probability and Its Applications, 6, 264-274.
[8] Tanaka, H. (1979) Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions. Hiroshima Mathematical Journal, 9, 163-177.
[9] Ikeda, N. and Watanabe, S. (1989) Stochastic Differential Equation and Diffusion Process. 2nd Edition, North-Holland Publishing Company, Japan.
[10] Watanabe, S. (1971) On Stochastic Differential Equation for Multidimensional Diffusion Processes with Boundary Condition. Journal of Mathematics of Kyoto University, 11, 169-180.
[11] Duffie, D. and Lando, D. (2001) Term Structure of Credit Spreads with Incomplete Accounting Information. Econometrica, 69, 633-664.
[12] Giesecke, K. (2006) Default and Information. Journal of Economics and Control, 30, 2281-2303.
[13] Jarrow, R.A. and Protter, P. (2004) Structural versus Reduced form Models: A New Information Based Perspective. Journal of Investment Management, 2, 1-10.

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