Survey_KW_2006

Abstract

We apply a firm-value model to capture the occurrence of obligor default. More precisely, we apply a structural one-factor correlated default model. The driving factor is a market factor, and company value is modeled as the interplay of the market factor and a company specific, idiosyncratic risk factor. This market model approach is the model of choice in most corporate finance applications. We model company value Vn,t of each obligor n ? {1, 2, ..., N} at any time t before maturity as being driven by a generalized macroeconomic factor Y Mt that is common to all securities, and an idiosyncratic component n,t. In the implementation, we do not need to apply simplifying assumptions to determine the loss distribution of the underlying portfolio. Instead, we are able to fully profit from the Monte Carlo Simulation procedure. Analytical approaches often rely on limiting assumptions, e.g. that the portfolio is composed of an infinite number of securities with identical characteristics. Thus, analytical models to some extent may be suitable for sensitivity analyses, but Monte Carlo Simulation is more appropriate for real-world applications. All individual securities in the portfolio can be accounted for by their specific exposure size, recovery rate, default probability, and maturity. Furthermore, Monte Carlo Simulation allows to differentiate between obligors and individual securities. The occurrence of joint obligor defaults is modeled by accounting for the sensitivity of each individual obligor to the common factor. The loss distribution is simulated in 5 steps: First, a realization of the macro factor is simulated until maturity. Subsequently, default scenarios are generated for all individual obligors in the portfolio. Default occurs, if the simulated firm value of an obligor, based on realizations of the macro factor and an idiosyncratic term, falls below the default boundary. The default boundaries correspond to cut-off values denoting the maximum default probability allowed for a tranche of a particular seniority. In the third step, individual loan losses are obtained by applying a recovery rate to loan default. Fourth, portfolio loss is given as the sum of realized individual loan losses. This corresponds to one realization in the simulation. Fifth, many simulation runs yield the loss distribution of the entire portfolio.