Credit Derivative Valuation and Parameter Estimation for Multi-Factor Affine CIR-Type Hazard Rate Model


The purpose of this paper is to derive or determine the Credit Derivative, especially, the Credit Default Swap which is under the hazard rate (or default intensity) distributed as a multi-factor of the Cox, Ingersoll and Ross (CIR, 1985) models. It is crucial to know how default should be modelled for the valuation of credit derivatives. We are motivated by the idea that CIR term structure model, for example, must be effective for modelling hazard rate, and has some significant properties: mean-reversion and affine. We use South Africa (SA) credit spread market data on Defaultable bonds to estimate parameters associated with the stochastic single-factor hazard rate type CIR.

Share and Cite:

Maboulou, A. and Mashele, H. (2015) Credit Derivative Valuation and Parameter Estimation for Multi-Factor Affine CIR-Type Hazard Rate Model. Journal of Mathematical Finance, 5, 273-285. doi: 10.4236/jmf.2015.53024.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] (2011) Dynamic Credit Risk Models. Lecture notes, Universitat Leipzig, Summer Term 2011. Princeton University Press, Princeton and Oxford.
[2] Edition, O.G. (2011) The Financial Crisis Inguiry Report: Final Report of the National Commission on the Cause of the Financial and Economic Crisis in the United States. Official Government Edition.
[3] Gregory, J. (2010) Counterparty Credit Risk: The New Challenge for Global Financial Markets. Wiley Finance Series.
[4] Barrett, R. and Ewan, J. (2006) BBA Credit Derivatives. British Bankers Association, London.
[5] Christophette, B.S. and Monique, J. (2004) Hazard Rate for Credit Risk and Hedging Defaultable Contingent Claims, Finance and Stochastics. Springer-Verlag, Berlin.
[6] Rutkowski, T. R. (2002) Credit Risk: Modeling, Valuation and Hedging. Springer-Verlag, Berlin.
[7] Bielecki, T., Jeanblanc, M. and Rustkowski, M. (2006) Credit Risk. LISBONN.
[8] Duffie, D. and Singleton, K. (1996) Modeling Term Structures of Defaultable Bonds. The Graduate School of Business, Stanford University, Stanford.
[9] David, M. and Mavroidis, T. (1997) Valuation and Potential Exposure of Default Swaps. Technical Note.
[10] Aonuma, K. and Nakagawa, H. (1998) Valuation of Credit Default Swap and Parameter Estimation for Vasicek-Type Hazard Rate Model. Working paper, University of Tokyo, Tokyo.
[11] Kalotychou, E., Remolona, E. and Wu, E. (2013) Intra-Regional Credit Contagion and Global Systemic Risk in International Sovereign Debt Markets. In: Hong Kong Institute for Monetary Research, Hong Kong Monetary Authority, Hong Kong, 41.
[12] Morkoetter, S., Pleus, J. and Westerfeld, S. (2012) The Impact of Counterparty Risk on Credit Default Swap Pricing Dynamics. Journal of Credit Risk, 8, 68-88.
[13] White, R. (2014) The Pricing and Risk Management of Credit Default Swaps, with a Focus on the ISDA Model. Open Gamma Quantitative Research No. 16, 43.
[14] Nakagawa, H. (1999) Valuation of Default Swaps with Affine-Type Hazard Rate. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 75, 43-46.
[15] Nakagawa, H., Yueh, M.L. and Hsieh, M.H. (2011) Valuation of Constant Maturity Credit Default Swaps. Analytical Mathematical Institute, Kyoto University (Mathematical Institute Exquisite Parsing Record), 27-32.
[16] Smit, L., Swart, B. and Niekerk, F.S. (2003) Credit Risk Models in South African Context. Investment Analysts Journal, No. 57, 41-46.
[17] Akshit, A., Chen, S., Debbini, D., Hu, P. and Ziaemohseni, M. (2011) On Estimating Recovery Rates. MS&E 444 Project Report.
[18] Praveen, V. and Cantor, R. (2005) Determinants of Recovery Rates on Defaulted Bonds and Loans for North American Corporate Issuers: 1983-2003. The Journal of Fixed Income, 14, 29-44.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.