By Enrico Marcantoni
The writer specializes in a style to cost Collateralized Debt responsibilities (CDO) tranches. the unique process is constructed via Castagna, Mercurio and Mosconi in 2012. The Thesis presents an extension of the unique paintings by means of generalizing the Gaussian dependence by way of Copula capabilities. particularly the version is rewritten for the explicit case of the Clayton copula. the strategy is utilized to cost the tranches of a CDX. through evaluating the tranches costs, it truly is attainable to note that the Clayton method results in smaller fairness and mezzanine tranches. The senior and great senior tranches degrees are better whilst the dependence is modeled by way of a Clayton copula.
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Extra info for Collateralized Debt Obligations: A Moment Matching Pricing Technique based on Copula Functions
Loss given default (LGD) and the effective impact a default of a firm causes on another firm. The latter issue, named default correlation, plays an important role on the determination of the loss distribution. The literature about the CDO pricing model is based on two main approaches called respectively structural models and reduced form models. Structural models use the firm's fundamental financial variables, such as asset and liabilities to determine the default time. In particular, following the first structural model by Merton (1974), the default happens when equity is below the debt.
Let be a random variable, whose distribution is unknown, but assume that it is possible to compute its first moments . Then it is possible to choose a known random variable moments, and replace by . The random variable with the same has to be chosen such that it is strictly linked to the unknown random variable . The MM approach has several application in the financial field. The most common example is the approximation of the sum of log-normal random variables (whose sum is not log-normal distributed) with a lognormally distributed proxy.
322. 34 are independent for any . 1 Copulas Basics Modeling default of several obligors implies modeling the default probability of the single obligor as well as the dependence structure between obligors. A general distribution function, in our example a distribution function of a portfolio of several obligors, contains information about both marginal obligor distribution and their correlation structure. However these two parts are implicit in it. A copula function is a tool, allowing a way of isolating the description of such dependence structure.
Collateralized Debt Obligations: A Moment Matching Pricing Technique based on Copula Functions by Enrico Marcantoni