Evolutionary Algorithms in Finance: Deriving the Dependence Structure
Correct modeling of default time dependence is essential for the valuation of multi-name credit derivatives, because structured products are extremely sensitive to the level of correlation and the shape of the correlation structure (see Sections 220.127.116.11, 3.2, and 3.8.4). Although it is still of interest to find empirical sources of correlation data, people increasingly use the CDO market to derive information about the dependence structure among the underlying assets of a CDO. In the CDO market, an observed tranche spread is considered to be a direct indicator of asset correlation. Increasingly often, a single implied correlation parameter is derived from the tranche spread of a traded CDO. The standard market model forms the basis for computation of the implied correlation parameter, assuming that all pairwise default time correlations are equal. The implied correlation parameter is supposed to reflect the level of dependence in the portfolio. However, we observe that different tranches of a CDO trade at different implied correlation levels, even though the underlying portfolio is the same for all tranches. This is illustrated by the emerging implied correlation smile, a topic we discussed in Chapter 3. The implied correlation of a traded CDO tranche is often used to price off-market products with the same underlying as the traded CDO. The correlation smile shows clearly that it is not appropriate to rely on the implied correlation of a traded CDO tranche for valuing non-standard tranches on the same collateral pool.
KeywordsCorrelation Matrix Dependence Structure Correlation Matrice Neighbor Algorithm Default Time
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