Collateralized Debt Obligations: A Moment Matching Pricing by Enrico Marcantoni

By Enrico Marcantoni

The writer specializes in a style to cost Collateralized Debt duties (CDO) tranches. the unique approach is constructed by means of Castagna, Mercurio and Mosconi in 2012. The Thesis presents an extension of the unique paintings via generalizing the Gaussian dependence by way of Copula capabilities. specifically the version is rewritten for the explicit case of the Clayton copula. the strategy is utilized to cost the tranches of a CDX. by means of evaluating the tranches costs, it's attainable to note that the Clayton procedure ends up in smaller fairness and mezzanine tranches. The senior and large senior tranches degrees are better whilst the dependence is modeled by way of a Clayton copula.

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This expression is analytically tractable in order to compute several information about the portfolio of loans. 20 provided an accurately way to estimate the quantile for high confidence level , through a Taylor Expansion. This method is really accurate for a high level of confidence but it is break down for lower level of confidence such that request for CDO pricing. In this setup lies the Moment Matching method21 explained in the following. 3 The Moment Matching The Moment Matching (MM) method is useful in working with unknown distributions whose characteristics are difficult to compute.

The independence assumption in credit risk are useful as well they are so far away from the reality. For this reason modeling credit risk has to take in consideration the modeling of the correlation issue. This challenge is presented in the following models. 1 The general case Assuming independency in credit risk model and leaving out correlation issue is not realistic. In the Bernoulli Mixture Model the loss of a portfolio has marginal losses again distributed with a Bernoulli distribution, that is .

These do not have a simple closed expression. Explicit copulas are constructed following mathematical steps and have simple closed expression; Archimedean copulas are examples of explicit copulas. 1 Product copula This is the simplest example of a copula and corresponds to the uniform distribution on . The product copula, also called the independence copula, is given by: ∏ As the name suggest it is the copula of independent random variables. 2 Gaussian Copula Let that ) be a vector of normally distributed random variables, such .

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