Bayesian Structural Credit Risk Model with Microstructure Noise in Nigeria

Authors

Olawale Basheer Akanbi

Independent Research (Nigeria)

Arisekola Akeem Akande

Department of Statistics, University of Ibadan, Ibadan (Nigeria)

Article Information

DOI: 10.51584/IJRIAS.2026.110200074

Subject Category: Statistics

Volume/Issue: 11/2 | Page No: 884-895

Publication Timeline

Submitted: 2026-02-15

Accepted: 2026-02-21

Published: 2026-03-12

Abstract

Financial markets rely on asset prices, which are often distorted by market frictions, liquidity constraints, and transaction costs, all of which influence a country’s structural credit risk. Traditional Markov Chain Monte Carlo (MCMC) estimation converges slowly and may not reliably capture rare, high-impact risks. To address this, the study develops a Bayesian structural credit risk model using Markov Chain Quasi-Monte Carlo (MCQMC) techniques, explicitly accounting for microstructure noise to improve the accuracy of asset value and default risk estimates in Nigeria. Comparative analysis shows that MCQMC achieves faster convergence, lower variance, and greater computational efficiency than MCMC, highlighting the benefits of noise-adjusted modeling for reliable credit risk assessment. The findings suggest that financial institutions should adopt MCQMC methods, while policymakers may consider incorporating noise-aware credit risk models into regulatory frameworks, offering a more robust and efficient approach to credit risk management in Nigerian financial practice.

Keywords

Financial market, Bayesian structural credit risk, Monte Carlo Quasi-Monte Carlo, Stochastic differential equations, Microstructure noise.

Downloads

References

1. A¨ıt-Sahalia, Y., Mykland, P.A., and L. Zhang (2009). Ultra high-frequency volatility estima- tion with dependent microstructure noise, Journal of Econometrics, forthcoming. [Google Scholar] [Crossref]

2. Akanbi O. B., Ojo J. F., and Oluneye M. O. (2018). Modelling GDP in Nigeria using Bayesian model averaging. International Journal of Applied Science and Mathematics 5 (3), 22-27 [Google Scholar] [Crossref]

3. Akanbi, Olawale Basheer (2021a). Bayesian Analysis of Poverty Rates in the South-Western Part of Nigeria. Asian Journal Probability and Statistics 15 (3), 1-10 [Google Scholar] [Crossref]

4. Akanbi, Olawale Basheer (2021b). Bayesian Regression of Government Expenditure on Revenue in Nigeria. Asian Journal of Probability and Statistics, 15 (4). pp. 21-37 [Google Scholar] [Crossref]

5. Akanbi, Olawale Basheer (2022). Stock Return Modeling of Some Insurance Companies in Nigeria. International Journal of Research in Humanities and Social Studies 9 (3), 42-57. [Google Scholar] [Crossref]

6. Akanbi, Olawale Basheer (2023). Enhancing Nigerian Oil Price Forecasting: A Comprehensive Analysis of Model Averaging Techniques. Asian Journal Probability and Statistics. 25 (2), 88-94. [Google Scholar] [Crossref]

7. Akanbi, Olawale Basheer (2024a). Prediction of Heart Disease Risk among Patients in Federal Medical Centre, Abeokuta Using Naïve Bayes. Asian Journal of Probability and Statistics 26 (10), 46-63. [Google Scholar] [Crossref]

8. Akanbi, Olawale Basheer (2024b). Applying Bayesian Networks for Detecting Bank Fraudulent Transactions in Nigeria. Asian Journal of Probability and Statistics 26 (11), 21-35. [Google Scholar] [Crossref]

9. Akanbi, O. B., and Bello, A. O. (2024). Fitting Autoregressive Integrated Moving Average with Exogenous Variables Model with Lognormal Error Term. Journal of Scientific Research & Reports 30 (10), 158-168. [Google Scholar] [Crossref]

10. Akanbi, O. B., and Fawole, O. A. (2024). Forcasting Stock Prices in Nigeria Using Bayesian Vector Autoregression. Journal of Scientific Research and Reports 30 (10), 197-210. [Google Scholar] [Crossref]

11. Akanbi, O. B., and Ajasa, H. O. (2025). Predicting Food Prices in Nigeria Using Machine Learning: Symbolic Regression. International Journal of Research and Innovation in Applied Science 10 (6), 979 – 995. [Google Scholar] [Crossref]

12. Akanbi, O. B., and Omokhua G. O. (2025). Forecasting Volatility of Cryptocurrencies using Bayesian GARCH Models. Technoarete Transactions on Advances in Social Sciences and Humanitiesv 5 (2), 2643. [Google Scholar] [Crossref]

13. Bandi, F. M., and J. Russell (2008). Microstructure noise, realized volatility, and optimal sampling. Review of Economic Studies, 75, 339 - 369. [Google Scholar] [Crossref]

14. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities, Journal of Political Economy 81, 637-659. [Google Scholar] [Crossref]

15. Duan, J.-C. (1994). Maximum likelihood estimation using price data of the derivative con- tract, Mathematical Finance, 4, 155-167. [Google Scholar] [Crossref]

16. Duan, J.-C. and A. Fulop, (2009). Estimating the Structural Credit Risk Model When Equity Prices are Contaminated by Trading Noises, Journal of Econometrics, 150, 288-296. [Google Scholar] [Crossref]

17. Duan, J.-C., Gauthier, G. and Simonato, J.G. (2004). On the equivalence of the KMV and maximum likelihood methods for structural credit risk models, Working Paper, University of Toronto. [Google Scholar] [Crossref]

18. Duan, J.-C., Gauthier, G., Simonato, J.-G. and Zaanoun, S. (2003). Estimating Merton’s model by maximum likelihood with survivorship consideration, Working Paper, Univer- sity of Toronto. [Google Scholar] [Crossref]

19. Ericsson, J. and Reneby, J. (2004). Estimating structural bond pricing models, Journal of Business, 78, 707-735. [Google Scholar] [Crossref]

20. Hansen, P., and A. Lunde, (2006). Realized volatility and market microstructure noise. Journal of Business & Economic Statistics. 24 ( 2), 127-161 [Google Scholar] [Crossref]

21. Hasbrouck, J. (1993). Assessing the quality of a security market: A new approach to transaction- cost measurement, Review of Financial Studies, 6, 191-212. [Google Scholar] [Crossref]

22. Lawal, M., and Akanbi, O. B. (2024). Bayesian Factor Analysis of a Unidimensional Urban Sprawl Index in Ibadan, Nigeria. Asian Journal of Environment & Ecology 23 (12), 211-227. [Google Scholar] [Crossref]

23. Merton, R. C. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance, 29 (2), 449-470. [Google Scholar] [Crossref]

24. Phillips, P.C.B. and J. Yu, (2006). Comments: Realized volatility and market microstructure noise by Hansen and Lunde. Journal of Business and Economic Statistics, 24, 202-208. [Google Scholar] [Crossref]

25. Phillips, P.C.B. and J. Yu, (2007). Information Loss in Volatility Measurement with Flat Price Trading. Working Paper, Yale University. [Google Scholar] [Crossref]

26. Roll, R. (1984). Simple implicit measure of the effective bid-ask spread in an efficient market. The Journal of Finance, 39(4), 1127–1139. [Google Scholar] [Crossref]

27. Tumala, M. M., Olubusoye, O. E., Yaaba, B. N., Yaya, O. S., and Akanbi, O. B. (2018). Investigating predictors of inflation in Nigeria: BMA and WALS techniques African Journal of Applied Statistics 5 (1), 301-321. [Google Scholar] [Crossref]

28. Tumala, M. M., Olubusoye, O. E., Yaaba, B. N., Yaya, O. S., and Akanbi, O. B. (2019). Forecasting Nigerian Inflation using Model Averaging methods: Modelling Frameworks to Central Banks. Empirical Economics Review 9 (1), 47-72 [Google Scholar] [Crossref]

29. Wong, H. and Choi, T. (2006). Estimating default barriers from market information, Working Paper, Chinese University of Hong Kong. [Google Scholar] [Crossref]

30. Yaya, O. S., Saka, L., and Akanbi, O. B. (2019). Assessing Market Efficiency And Volatility Of Exchange Rates in South Africa and United Kingdom: Analysis Using Hurst Exponent. The Journal of Developing Areas 53 (1). [Google Scholar] [Crossref]

31. Zhang, L., Mykland, P.A., and Y. A¨ıt-Sahalia (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data, Journal of the American Statistical Association, 100, 1394-1411 [Google Scholar] [Crossref]

32. Zhao, H., Chen, L., and Zhang, X. (2024). Enhancing Bayesian Estimation with MCQMC Techniques. Computational Finance Review, 12(1), 76-93. [Google Scholar] [Crossref]

Metrics

Views & Downloads

Similar Articles