Modeling Path-Dependent State Transition by a Recurrent Neural Network

Yang, Bill Huajian (2022): Modeling Path-Dependent State Transition by a Recurrent Neural Network. Forthcoming in: Big Data and Information Analytics

Abstract

Rating transition models are widely used for credit risk evaluation. It is not uncommon that a time-homogeneous Markov rating migration model deteriorates quickly after projecting repeatedly for a few periods. This is because the time-homogeneous Markov condition is generally not satisfied. For a credit portfolio, rating transition is usually path dependent. In this paper, we propose a recurrent neural network (RNN) model for modeling path-dependent rating migration. An RNN is a type of artificial neural networks where connections between nodes form a directed graph along a temporal sequence. There are neurons for input and output at each time-period. The model is informed by the past behaviours for a loan along the path. Information learned from previous periods propagates to future periods. Experiments show this RNN model is robust.

• Item Type: MPRA Paper
• Language: English
• Keywords: Path-dependent, rating transition, recurrent neural network, deep learning, Markov property, time-homogeneity
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill; G - Financial Economics > G3 - Corporate Finance and Governance > G33 - Bankruptcy ; Liquidation; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M3 - Marketing and Advertising

References

[1] Abiodun, Oludare Isaac; Jantan, Aman; Omolara, Abiodun Esther; Dada, Kemi Victoria; Mohamed, Nachaat Abdelatif; Arshad, Humaira. (2018). State-of-the-art in artificial neural network applications: A survey. Heliyon. 4 (11): e00938. doi:10.1016/j.heliyon.2018.e00938. [2] Bottou, L. (2010). Large-scale machine learning with stochastic gradient descent. In Proceedings of COMPSTAT'2010 (pp. 177-186). Physica-Verlag HD. [3] Dupond, Samuel. (2019). A thorough review on the current advance of neural network structures. Annual Reviews in Control. 14: 200–230. [4] Elman, Jeffrey L. (1990). Finding Structure in Time. Cognitive Science. 14 (2): 179–211. doi:10.1016/0364-0213(90)90002-E. [5] Ge, R., Huang, F., Jin, C., & Yuan, Y. (2015, June). Escaping From Saddle Points-Online Stochastic Gradient for Tensor Decomposition. In COLT (pp. 797-842). [6] Graves, Alex; Liwicki, Marcus; Fernandez, Santiago; Bertolami, Roman; Bunke, Horst; Schmidhuber, Jürgen. (2009). A Novel Connectionist System for Improved Unconstrained Handwriting Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence. 31 (5): 855–868. doi:10.1109/tpami.2008.137. [7] Hyötyniemi, Heikki. (1996). Turing machines are recurrent neural networks. Proceedings of STeP '96/Publications of the Finnish Artificial Intelligence Society: 13–724. [8] Juhasz, Peter; Varadi, Kata; Vidovics-Dancs, Agnes; and Szaz, Janos. (2017). Measuring Path Dependency. Special issue, UTMS Journal of Economics 8 (1): 29–37. [9] Kiefer, Nicholas M.; Larson, C. Erik. (2014). Testing Simple Markov Structures for Credit Rating Transitions. OCC Economics Working Paper 2004-3 [10] Kiefer, Nicholas M.; Larson, C. Erik. (2007). A simulation estimator for testing the time homogeneity of credit rating transitions. Journal of Empirical Finance, Elsevier, vol. 14(5), pages 818-835 [11] Miu, P.; Ozdemir, B. (2009). Stress testing probability of default and rating migration rate with respect to Basel II requirements. Journal of Risk Model Validation, Vol. 3 (4), 3-38 [12] Reis, G. dos; Pfeuffer, M.; Smith, G. (2020). Capturing model risk and rating momentum in the estimation of probabilities of default and credit rating migrations, Quantitative Finance, 20:7, 1069-1083, DOI: 10.1080/14697688.2020.1726439 [13] Russo, Emilio. (2020). Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model, Risks 2020, 8(1), 9; doi:10.3390/risks8010009 [14] Schmidhuber, Jürgen. (2015). Deep Learning in Neural Networks: An Overview. Neural Networks. 61: 85–117. [15] Tealab, Ahmed. (2018). Time series forecasting using artificial neural networks methodologies: A systematic review. Future Computing and Informatics Journal. 3 (2): 334–340. doi:10.1016/j.fcij.2018.10.003. ISSN 2314-7288. [16] Yang, B. H.; Zunwei Du. (2016). Rating Transition Probability Models and CCAR Stress Testing. Journal of Risk Model Validation 10 (3), 1-19 [17] Yang, B. H. (2017). Forward ordinal models for point-in-time probability of default term structure. Journal of Risk Model Validation, Vol 11 (3), 1-18 [18] Yang, B. H. (2017). Point-in-time PD term structure models for multi-period scenario loss projection. Journal of Risk Model Validation, Vol 11 (1), 73-94 [19] Zhu, Steven; Lomibao, Dante. (2005). A Conditional Valuation Approach for Path-Dependent Instruments. August 2005SSRN Electronic Journal. DOI: 10.2139/ssrn.806704