Science Journal of Applied Mathematics and Statistics
Volume 2, Issue 2, April 2014, Pages: 42-52
Received: Mar. 7, 2014;
Accepted: Apr. 9, 2014;
Published: Apr. 20, 2014
Views 3502 Downloads 222
Osei Antwi, Mathematics & Statistics Department, Accra Polytechnic, Accra, Ghana
One of the approaches to determining and quantifying the credit risk of a loan portfolio is by obtaining the distribution of losses of the portfolio and determining the risk quantities from such distributions. In this paper, we describe the challenges to using this approach and illustrate a practical solution where simulation methods are used to obtain loss distribution for a two obligor portfolio. This is then extended to ten and hundred obligor portfolios. Existing probability distributions with specified parameters are then used to approximate the loss distributions obtained. Using such parameters of the existing probability distributions, we obtain the risk quantities associated with the loan portfolio including Expected and Unexpected losses. We realized that depending on the confidence interval for which we measure the Unexpected Loss, Stress Losses are needed to account for the total loss of the portfolio
Measuring Portfolio Loss Using Approximation Methods, Science Journal of Applied Mathematics and Statistics.
Vol. 2, No. 2,
2014, pp. 42-52.
Martin, Hansen, Dr. Gary, van Vuuren and Mariarosa, Verde Basel II Correlation Values., An Empirical Analysis of EL, UL and the IRB Model, Credit Market Research Financial Institutions Special Report, Fitch Rating, 2008, pp3
Merton, R. (1974): On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, 29, 449-470.
David Saunders, Costas Xiouros, Stavros A. Zenios, Credit risk optimization using factor models. Annals of Operations Research, (2007), pp.49-77
Peter J¨ackel, Monte Caro methods in finance Wiley Finance & Sons Ltd. Chichester, England (2002), PP 1-6
Phelim P. Boyle, Journal of Financial Economics, Volume 4, Issue 3, May 1977, Pages 323–338
Enrique Navarrete, Practical Calculation of Expected and Unexpected Losses on Operational Risk by Simulation Methods, Banca & Finanzas: Documentos de Trabajo, 2006 Vol. I, pp. 7-9
Hoogbruin, Peter P, Journal of Global Association of Risk Professionals, (September/October 2006), pp. 34-39.
Loffler, Gunter and Posch, Peter N. Credit Risk Modeling using Excel and VBA, Wiley Finance Series, John Wiley & Sons, Ltd., New York, NY, USA, 2007.
GIOVANNI BARONE-ADESI, Efficient Analytic Approximation of American Option Values, The Journal of Finance, Volume 42, Issue 2, 1987, pp 301 -320.
John S. Ramberg, Pandu R. Tadikamalla, Edward J. Dudewicz, Edward F. Mykytka, A Probability Distribution and Its Uses in Fitting Data. American Statistical Association and American Society for Quality Technometrics, v ol.2 1, no. 2, may, 1979
AbouRizk, S., Halpin, D., and Wilson, J. Fitting Beta Distributions Based on Sample Data Journal of Construction Engineering and Management Volume 120, Issue 2 (June 1994). Pp 288-289
Bluhm, Ludger Overbeck and Wagner, C. An Introduction to Credit Risk Modeling, Christian Chapman & Hall/CRC, London, UK, 2003.
Barreto, Humberto and Howland, Frank M. Introductory Econometrics, Cambridge University Press, Cambridge, UK, 2006; pp 215-235.
Berenson, Mark L., Levine, David M. Basic Business Statistics, Prentice-Hall International inc New Jersey, NJ, USA, 1999; pp 45-75.
David Vose, Risk Analysis a Quantitative Guide, John Wiley & Sons Ltd., New York, NY, USA, 2003; pp 59
Haigh, J. Probability Models, Springer Undergraduate Mathematical Series, Springer, New York, NY, USA, 2005, pp. 1-86