Pricing portfolio credit derivatives

Abstract

This thesis consist of four papers on dynamic dependence modelling in portfolio\ncredit risk. The emphasis is on valuation of portfolio credit derivatives. The\nunderlying model in all papers is the same, but is split in two different submodels,\none for inhomogeneous portfolios, and one for homogeneous ones. The latter\nframework allows us to work with much bigger portfolios than the former. In both\nmodels the default dependence is introduced by letting individual default intensities\njump when other defaults occur, but be constant between defaults. The models\nare translated into Markov jump processes which represents the default status in\nthe credit portfolio. This makes it possible to use matrix-analytic methods to find\nconvenient closed-form expressions for many quantities needed in dynamic credit\nportfolio management and valuation of portfolio credit derivatives.\nPaper one presents formulas for single-name credit default swap spreads and kth-\nto-default swap spreads in an inhomogeneous model. In a numerical study based\non a synthetic portfolio of 15 telecom bonds we study, e.g., how kth-to-default swap\nspreads depend on the amount of default interaction and on other factors.\nPaper two derives computational tractable formulas for synthetic CDO tranche\nspreads and index CDS spreads. Special attention is given to homogenous portfolios.\nSuch portfolios are calibrated against market spreads for CDO tranches , index CDSs,\nthe average CDS and FtD baskets, all taken from the iTraxx Europe series. After\nthe calibration, which leads to perfect fits, we compute spreads for tranchelets and\nkth-to-default swap spreads for different subportfolios of the main portfolio. We also\ninvestigate implied tranche-losses and the implied loss distribution in the calibrated\nportfolios.\nPaper three is devoted to derive and study, in an inhomogeneous model, convenient\nformulas for multivariate default and survival distributions, conditional multivariate\ndistributions, marginal default distributions, multivariate default densities,\ndefault correlations, and expected default times. We calibrate the model for two different\nportfolios (with 10 obligors), one in the European auto sector, the other in the\nEuropean financial sector, against their market CDS spreads and the corresponding\nCDS-correlations.\nIn paper four we perform the same type of studies as in Paper 3, but for a\nlarge homogenous portfolio. We use the same market data as in Paper 2. Many of\nthe results differ substantially from the corresponding ones in the inhomogeneous\nportfolio in Paper 3. Furthermore, these numerical studies indicates that the market\nCDO tranche spreads implies extreme default clustering in upper tranches.

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