Fuzzy structural risk of default for banks in Southern Africa

Abstract

This paper proposes and examines a new structural risk of default model for banks in frictional and fuzzy financial markets. It is motivated by the need to fill the shortcomings of probability-based credit risk metric models that are characterised by unrealistic assumptions such as crisply precise and constant risk-free rates of return. The problem investigated here specifically proposes a new Kealhofer–Merton–Vasicek (KMV)-type model for estimation of the risk of default for banks extended for both market friction represented by transaction costs and uncertainty modelled by fuzziness. The novel risk of default model is then validated using cross-sectional financial data of eight commercial banks drawn from several emerging economies in Southern Africa. The results from the proposed model are fairly stable and consistent compared to those from hazard function and structural credit risk models currently used in the markets. The model is relevant in that it fairly captures practical conditions faced by banks that influence their risks of default in their quest to improve financial performance and shareholders’ wealth. The study recommends that banks in frictional and fuzzy financial markets, such as those in emerging economies, can adopt and implement the proposed risk of the default model.

Keywords:

• risk of default
• fuzzy financial markets
• risk metrics
• market friction
• fuzziness

JEL Classification:

• C13 and G24

Public interest statement

Risk of default measures the probability that a bank will not fulfil its principal and interest loan obligations due to its past commitments, current market, economic and liquidity circumstances. Investors must accurately measure the risk of default facing their financial investments in markets characterised by high transaction costs, also called market friction. The work proposes a model that incorporates vague concepts, such as high, medium and low volatility, covered in fuzzy logic or fuzziness, and market friction which characterise most emerging economies, in estimation of risks of default of banks. The results of the study are that banks’ risks of default are inversely related to their asset values, volatilities and returns on equity and directly correlated to market frictions and liabilities. Therefore, the study ends by recommending that banks must efficiently and effectively manage their investments in frictional and fuzzy financial markets to improve corporate performance and sustainability.

Acknowledgements

We are very grateful to Mrs Chido Matewe for providing us with typing and proofreading services during the compilation of the paper. Last but not least we extend our special thanks to Drs Edison Vengesai and Frank R. Matenda of the Universities of the Free State and Kwa-Zulu Natal, South Africa, respectively, for providing us with the much-needed editing services for the whole paper.20112010

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the University’s Research Board.

Notes on contributors

Ephraim Matanda

The authors usually work in asset valuation and credit risk modelling over and above having mathematics of finance, financial modelling and engineering as their other research interests. Banks in emerging economies are mainly characterised by market friction and fuzziness, which must be incorporated in new risk of default models to improve their estimation precision, rigour and efficiency. The paper extends the structural credit risk models to the case for market friction and fuzziness in estimation of the risks of default of banks. By combining results from a new risk of default model with those from similar exposure at default and loss given default models, precision in assessment of banks’ expected losses can be achieved. Rigorous risk metrics’ assessments in banks can go a long way in improving their credit risk ratings, and management of non-performing losses in their quest to improve overall financial performance and generate wealth for shareholders.