| dc.description.abstract | This thesis consist of four papers on dynamic dependence modelling in portfolio
credit risk. The emphasis is on valuation of portfolio credit derivatives. The
underlying model in all papers is the same, but is split in two different submodels,
one for inhomogeneous portfolios, and one for homogeneous ones. The latter
framework allows us to work with much bigger portfolios than the former. In both
models the default dependence is introduced by letting individual default intensities
jump when other defaults occur, but be constant between defaults. The models
are translated into Markov jump processes which represents the default status in
the credit portfolio. This makes it possible to use matrix-analytic methods to find
convenient closed-form expressions for many quantities needed in dynamic credit
portfolio management and valuation of portfolio credit derivatives.
Paper one presents formulas for single-name credit default swap spreads and kth-
to-default swap spreads in an inhomogeneous model. In a numerical study based
on a synthetic portfolio of 15 telecom bonds we study, e.g., how kth-to-default swap
spreads depend on the amount of default interaction and on other factors.
Paper two derives computational tractable formulas for synthetic CDO tranche
spreads and index CDS spreads. Special attention is given to homogenous portfolios.
Such portfolios are calibrated against market spreads for CDO tranches , index CDSs,
the average CDS and FtD baskets, all taken from the iTraxx Europe series. After
the calibration, which leads to perfect fits, we compute spreads for tranchelets and
kth-to-default swap spreads for different subportfolios of the main portfolio. We also
investigate implied tranche-losses and the implied loss distribution in the calibrated
portfolios.
Paper three is devoted to derive and study, in an inhomogeneous model, convenient
formulas for multivariate default and survival distributions, conditional multivariate
distributions, marginal default distributions, multivariate default densities,
default correlations, and expected default times. We calibrate the model for two different
portfolios (with 10 obligors), one in the European auto sector, the other in the
European financial sector, against their market CDS spreads and the corresponding
CDS-correlations.
In paper four we perform the same type of studies as in Paper 3, but for a
large homogenous portfolio. We use the same market data as in Paper 2. Many of
the results differ substantially from the corresponding ones in the inhomogeneous
portfolio in Paper 3. Furthermore, these numerical studies indicates that the market
CDO tranche spreads implies extreme default clustering in upper tranches. | |
