JFRM  Vol.8 No.3 , September 2019
An Analytical Portfolio Credit Risk Model Based on the Extended Binomial Distribution
The binomial distribution describes the probability of the number of successes for a fixed number of identical independent experiments, each with binary out-put. In real life, practical applications like portfolio credit risk management trials are not identical and have different realization probabilities. In addition to the number, the quantitative impacts of the respective outputs are also important. There exist no complete model-side implementations for the expansion of the binomial distribution, especially not in the case of specific quantitative parameters up to now. Here, a solution of this issue is described by the extended binomial distribution. The key for solving the problem lies in the use of bijection between the elementary events of the binomial distribution and the digit sequences of binary numbers. Based on the extended binomial distribution, an analytical portfolio credit risk model is described. The binomial distribution approach minimizes the approximation error in modeling. In particular, the edges of the loss distribution can be determined in a realistic manner. This analytical portfolio credit risk model is especially predestined for management of risk concentrations and tail risks.
Cite this paper: Fischer, S. (2019) An Analytical Portfolio Credit Risk Model Based on the Extended Binomial Distribution. Journal of Financial Risk Management, 8, 177-191. doi: 10.4236/jfrm.2019.83012.

[1]   Albrecht, P. (2004). Risk Measures. In Encyclopedia of Actuarial Science. New York: John Wiley & Sons.

[2]   Basel Committee on Bank Supervision (2004). International Convergence of Capital Measurement and Capital Standards. Bank for International Settlements.

[3]   CSFB (1997). CreditRisk + A Credit Risk Management Framework. London: Credit Suisse First Boston International.

[4]   Fischer, S. (2012). Ratio calculandi periculi-ein analytischer Ansatz zur Bestimmung der Verlustverteilung eines Kreditportfolios. Dresden, Saxony, Germany: Technical University Dresden.

[5]   Fisz, M. (1981). Wahrscheinlichkeitsrechnung und mathematische Statistik. Berlin: VEB Deutscher Verlag der Wissenschaften.

[6]   Gnedenko, B. W. (1987). Lehrbuch der Wahrscheinlichkeitsrechnung. Berlin: Akademie Verlag.

[7]   Gordy, M. B. (2002). A Risk-Factor Model Foundation for Rating-Based Bank Capital Rules. Federal Reserve System.

[8]   Gribakin, G. (2002). Chapter 3: Probability Generating Functions. In Probability and Distribution Theory (pp. 39-49). Belfast, Northern Ireland: Queen’s University Belfast.

[9]   KMV (1997). Modeling Default Risk. San Francisco, CA: KMV LLC.

[10]   Lukacs, E. (1960). Characteristic Functions. London: Griffin.

[11]   McKinsey and Company (1998). CreditPortfolioViewTM Approach Documentation and User’s Documentation. Zurich: McKinsey and Company.

[12]   McNeil, A., Frey, R., & Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton, NJ: Princeton University Press.

[13]   J.P. Morgan (1997). CreditMetricsTM—Technical Document. New York: J.P. Morgan & Co. Incorporated.

[14]   Panjer, H. (1981). Recursive Evaluation of a Family of Compound Distributions. ASTIN Bulletin, 12, 22-26.

[15]   Rényi, A. (1971). Wahrscheinlichkeitsrechnung. Berlin: VEB Deutscher Verlag der Wissenschaften.

[16]   Smirnow, N., & Dunin-Barkowski, I. W. (1969). Mathematische Statistik in der Technik. Berlin: VEB Deutscher Verlag der Wissenschaften.

[17]   Statistisches Bundesamt (2017). Insolvenzen. Wiesbaden.

[18]   Wilson, T. (1998). Portfolio Credit Risk. FRBNY Economic Policy Review, 4, 71-82.