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Abstracts

XVIII conference

The Mathematical Modelling of the Credit Derivatives Default Process

Stikhova O.V.

Russia,129085,Moscow,Bochkova str.5,fl.88

The liquid market of the credit default swaps(CDS) and collateralized debt obligation (CDO) has much developed recently. We considered the classical default models and we described the methods of the portofolio credit derivatives statistical dependence modeling structures [1]. The first models of credit risk assumed correlation of functions of intensity at exponential growth of parameters of correlation with increase of number of the emitters subject to default risk, but it is not effective in a case of more than two emitters subject to default risk [2]. Then, in the paper [3] copula functions have been applied for default modeling with stochastic intensities to threshold variable at calculation multivariate of default probabilities. Multivariate default distributions are taken into account in models on a copula basis, becoming by the market standard for an estimation of a basket credit derivatives, in particular, on the contracts CDO. With the help of Gaussian copula models from appropriate market data it can be predicted transhes correlation. Besides, there are numerous approaches using various copulas and set of degrees of freedom developed for fixation of correlations in the default period for simplification of risk semianalitical estimation by expressions of the quotation for avoidance of slowly converging procedures of modeling. We received expressions for probability of default approach, the communication of intensity and probability of default approach is established, is offered and the model of default approach under the credit obligations for one and set of the emitters is investigated, and also the tasks of definition of cost of credit valuable papers CDO and CDS for realization of numerical experiments are considered.

References

1. Stikhova O.V. Credit Derivatives Mathematical Modelling. /XLII The National Conference of the Mathematics, Informatics and Chemistry problems. Working Paper. -М: RUDN, 2009, стр.123-124.

1. Li, D. X. On Default Correlation: A Copula Approach.//The Journal of Fixed Income, (2000),Vol. 9.

2. Schönbucher P. J., Schubert D. Copula Dependent Default Risk in Intensity Models.// Working Paper, Department of Statistics, Bonn University, 2001.

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