Finding Default Barrier and Optimal Cutoff Rate in KMV Structural Model based on the best Ranking of Companies

Document Type : Original Article


1 MSc in Financial Engineering , Faculty of Financial Engineering, Kharazmi University, Tehran, Iran

2 Assistant professor, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran (Corresponding author)


According to the adverse consequences that are brought by financial distress for companies, economy and financial –monetary institutions, the use of methods that can predict the occurrence of financial failure and prevent the loss of wealth is of great importance. The major models of credit risk assessment are based on retrospective information and using the methods which use the updated market data for prediction of the probability of default can lead to the increase of the reliability of results. The purpose of this study is to obtain optimal default barrier in KMV model by using an approach based on genetic algorithm and compare the performance of the proposed model to KMV model. Research data included all data of listed companies in the Tehran stock exchange that were bankrupted from 2009 to 2014 according to the article 141 of the commercial code. In total, 25 companies were considered as distressed companies and 50 non-bankrupted companies were also selected as the control group and then results of the two models were compared. The study results showed that the performance of the presented model in prediction of bankruptcy and separating distressed from non-distressed companies is better than KMV model. At the end, the optimal cut off rate was calculated to determine whether a specific company will be bankrupt or healthy according to its probability of default. The results showed that the calculated optimal value led to 80% correct prediction in 2015.


1)     Afik, Z., O. Arad and K. Galil (2012). "Using Merton model: an empirical assessment of      alternatives."
2)     Agarwal, V. and R. Taffler (2008). "Comparing the performance of market-based and accounting-based bankruptcy prediction models." Journal of Banking & Finance 32(8): 1541-1551.
3)     Altman, E. I. (2000). "Predicting financial distress of companies: revisiting the Z-score and ZETA models." Stern School of Business, New York University: 9-12.
4)     Bharath, S. T. and T. Shumway (2004). "Forecasting default with the KMV-Merton model."
5)     Bharath, S. T. and T. Shumway (2008). "Forecasting default with the Merton distance to default model." Review of financial studies 21(3): 1339-1369.
6)     Black, F. and M. Scholes (1973). "The pricing of options and corporate liabilities." Journal of political economy 81(3): 637-654.
7)     Bohn, J. and P. Crosbie (2003). "Modeling default risk." KMV Corporation.
8)     Campbell, J. Y., J. Hilscher and J. Szilagyi (2008). "In search of distress risk." The Journal of Finance 63(6): 2899-2939.
9)     Committee, B. (1999). ". Principles for management of credit risk." Basel Committee on Banking Supervision.
10)  Doumpos, M., D. Niklis, C. Zopounidis and K. Andriosopoulos (2015). "Combining accounting data and a structural model for predicting credit ratings: Empirical evidence from European listed firms." Journal of Banking & Finance 50: 599-607.
11)  Engelmann, B., E. Hayden and D. Tasche (2003). "Testing rating accuracy." Risk 16(1): 82-86.
12)  Han, L. and R. Ge (2016). "Wavelets Analysis on Structural Model for Default Prediction." Computational Economics: 1-30.
13)  Hillegeist, S. A., E. K. Keating, D. P. Cram and K. G. Lundstedt (2004). "Assessing the probability of bankruptcy." Review of accounting studies 9(1): 5-34.
14)  Jovan, M. and A. Ahčan (2017). "Default prediction with the Merton-type structural model based on the NIG Lévy process." Journal of Computational and Applied Mathematics 311: 414-422.
15)  Lee, W.-C. (2011). "Redefinition of the KMV model’s optimal default point based on genetic algorithms–Evidence from Taiwan." Expert Systems with Applications 38(8): 10107-10113.
16)  Löeffler, G. and M. P. N. Posch (2011). Credit risk modeling using Excel and VBA, John Wiley & Sons.
17)  Ma, Y. and W. Xu (2016). "Structural credit risk modelling with Hawkes jump diffusion processes." Journal of Computational and Applied Mathematics 303: 69-80.
18)  Merton, R. C. (1974). "On the pricing of corporate debt: The risk structure of interest rates." The Journal of finance 29(2): 449-470.
19)  Sobehart, J. and S. Keenan (2001). "Measuring default accurately." Risk 14(3): 31-33.
20)  Vassalou, M. and Y. Xing (2004). "Default risk in equity returns." The Journal of Finance 59(2): 831-868.