Survey_KW_2008

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. 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 which is determined by the default probability of the obligor. 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. We now investigate the nature of risk transfer from the underlying portfolio to tranches. This is at the heart of structured finance transactions, i.e. the pooling and reallocation of individual risks to investors. The transfer of risks is non-proportional, due to the principle of subordination of tranches. The resulting risk allocation is estimated by Monte Carlo simulation. Let us consider as base case a reference portfolio with 10’000 loans. All securities have the same characteristics: They are zero bonds with identical nominal value, 10 years to maturity, 7.63% default probability, 24.15% recovery rate, and identical exposure to the macro factor, corresponding to a correlation of ?M n = 0.15 between all securities. The applied default probability corresponds to a Baa-rating for the bonds, according to Moody’s (2005), Exhibit 17. Overall, the base case represents a realistic setting for a typical CDO transaction. The high number of loans is chosen intentionally to eliminate diversifiable risk to a large extent, giving a clear picture of systematic risk in the analysis as shown later. The evolution of individual-loan credit quality over time is simulated with 500’000 simulation runs.