Summary
There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions and thereby default probabilities of companies. As the likelihood of the model turns out to be a non-convex function of the parameters to be estimated, we apply heuristics to find the ML estimators. To this end, we outline the model and its likelihood function, and present both a Particle Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm to maximize the likelihood function. Numerical results are shown which suggest a further application of evolutionary optimization techniques for credit risk management.
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References
Brabazon, A., O’Neill, M.: Biologically inspired algorithms for financial modelling. Natural Computing Series. Springer, Berlin (2006)
Brabazon, A., O’Neill, M. (eds.): Natural Computing in Computational Finance, Studies in Computational Intelligence, vol. 100. Springer, Heidelberg (2008)
Brabazon, A., O’Neill, M. (eds.): Natural Computing in Computational Finance, vol. 2. Studies in Computational Intelligence, vol. 185. Springer, Heidelberg (2009)
Duffie, D., Singleton, K.J.: Credit Risk: Pricing, Measurement, and Management. Princeton University Press, Princeton (2003)
Hager, S., Schöbel, R.: Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006, Part IV. LNCS, vol. 3994, pp. 340–347. Springer, Heidelberg (2006)
Hochreiter, R.: An evolutionary computation approach to scenario-based risk-return portfolio optimization for general risk measures. In: Giacobini, M. (ed.) EvoWorkshops 2007. LNCS, vol. 4448, pp. 199–207. Springer, Heidelberg (2007)
Hochreiter, R.: Evolutionary stochastic portfolio optimization. In: Brabazon, A., O’Neill, M. (eds.) Natural Computing in Computational Finance. Studies in Computational Intelligence, vol. 100, pp. 67–87. Springer, Heidelberg (2008)
Hochreiter, R., Wozabal, D.: Evolutionary approaches for estimating a coupled markov chain model for credit portfolio risk management. In: Giacobini, M., Brabazon, A., Cagnoni, S., Di Caro, G.A., Ekárt, A., Esparcia-Alcázar, A.I., Farooq, M., Fink, A., Machado, P. (eds.) EvoCOMNET. LNCS, vol. 5484, pp. 193–202. Springer, Heidelberg (2009)
Kaniovski, Y.M., Pflug, G.C.: Risk assessment for credit portfolios: A coupled markov chain model. Journal of Banking and Finance 31(8), 2303–2323 (2007)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE Computer Society, Los Alamitos (1995), doi:10.1109/ICNN.1995.488968
Markowitz, H.M.: Mean-variance analysis in portfolio choice and capital markets. Basil Blackwell, Oxford (1987)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative risk management. Princeton University Press, Princeton (2005)
Merton, R.: On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29, 449–470 (1974)
Schönbucher, P.J.: Credit Derivatives Pricing Models: Models, Pricing, Implementation. Wiley Finance, Chichester (2003)
Zhang, J., Avasarala, V., Subbu, R.: Evolutionary optimization of transition probability matrices for credit decision-making. European Journal of Operational Research 200(2), 557–567 (2010)
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Hochreiter, R., Wozabal, D. (2010). Evolutionary Estimation of a Coupled Markov Chain Credit Risk Model. In: Brabazon, A., O’Neill, M., Maringer, D.G. (eds) Natural Computing in Computational Finance. Studies in Computational Intelligence, vol 293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13950-5_3
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DOI: https://doi.org/10.1007/978-3-642-13950-5_3
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