In this paper, we present a multi-name incomplete information structural model which possess the contagion mechanism and its efficient Monte Carlo algorithm based on Interacting Particle System. Along with the Credit Grades, which is industrially used single-name credit model, we suppose that investors can observe firm values and defaults but are not informed of the threshold level at which a firm is deemed to default. Additionally, in order to model the possibility of crisis normalization, we introduce the concept of memory period after default. During the memory period after a default, public investors remember when the previous default occurred and directly reflect that information for updating their belief. When the memory period after a default finish, investors forget about that default and shift their interest to recent defaults if exist. One of the variance reduction techniques, relying upon Interacting Particle System, is combined with the standard Monte Carlo method to address the rare but critical events represented by the tail of loss distribution of portfolio.
Takada, H. (2014) Multi-Name Extension to the Credit Grades and an Efficient Monte Carlo Method. Journal of Mathematical Finance, 4, 188-206. doi: 10.4236/jmf.2014.43017.
[1] Davis, M. and Lo, V. (2001) Infectious Defaults. Quantitative Finance, 1, 382-387. [2] Yu, F. (2007) Correlated Defaults in Intensity Based Models. Mathematical Finance, 17, 155-173. [3] Frey, R. and Backhaus, J. (2010) Dynamic Hedging of Synthetic SDO Tranches with Spread and Contagion Risk. Journal of Economic Dynamics and Control, 34, 710-724. [4] Frey, R. and Runggaldier, W. (2010) Credit Risk and Incomplete Information: A Nonlinear-Filtering Approach. Finance and Stochastics, 14, 495-526.
http://dx.doi.org/10.1007/s00780-010-0129-5 [5] Giesecke, K. (2004) Correlated Default with Incomplete Information. Journal of Banking and Finance, 28, 1521-1545. [6] Giesecke, K. and Goldberg, L. (2004) Sequential Defaults and Incomplete Information. Journal of Risk, 7, 1-26. [7] Giesecke, K., Kakavand, H., Mousavi, M. and Takada, H. (2010) Exact and Efficient Simulation of Correlated Defaults. SIAM Journal of Financial Mathematics, 1, 868-896. [8] Schonbucher, P. (2004) Information Driven Default Contagion. ETH, Zurich. [9] Takada, H. and Sumita, U. (2011) Credit Risk Model with Contagious Default Dependencies Affected by MacroEconomic Condition. European Journal of Operational Research, 214, 365-379. [10] McNeil, A., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton. [11] Takada, H. (2014) Structural Model Based Analysis on the Period of Past Default Memories. Research Institute for Mathematical Sciences (RIMS), Kyoto, 82-94. [12] Finger, C.C., Finkelstein, V., Pan, G., Lardy, J., Ta, T. and Tierney, J. (2002) Credit Grades. Technical Document, Riskmetrics Group, New York. [13] Fang, K., Kotz, S. and Nq, K.W. (1987) Symmetric Multivariate and Related Distributions. CRC Monographs on Statistics & Applied Probability, Chapman & Hall. [14] Carmona, R., Fouque, J. and Vestal, D. (2009) Interacting Particle Systems for the Computation of Rare Credit Portfolio Losses. Finance and Stochastics, 13, 613-633.
http://dx.doi.org/10.1007/s00780-009-0098-8 [15] Del Moral, P. and Garnier, J. (2005) Genealogical Particle Analysis of Rare Events. The Annals of Applied Probability, 15, 2496-2534. http://dx.doi.org/10.1214/105051605000000566 [16] Carmona, R. and Crepey, S. (2010) Particle Methods for the Estimation of Credit Portfolio Loss Distributions. International Journal of Theoretical and Applied Finance, 13, 577.
http://dx.doi.org/10.1142/S0219024910005905 [17] Del Moral, P. (2004) Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications. Springer, New York.
http://dx.doi.org/10.1007/978-1-4684-9393-1