Survey_Jobst_2002

Abstract

In the course of proper asset pricing of structured finance transaction with a defined credit event, such as loan securitisation, extreme events enter very naturally, and as such, understanding the mechanism of loss allocation and the security design provisions governing them becomes essential. In absence of historical credit default data, we propose a Mertonbased (1974) credit risk pricing model that draws on a careful simulation of expected loan loss based on parametric bootstrapping through extreme value theory (EVT). Given the number of stochastic variables and the complexity of the relationships no closed form solution for calculating the needed risk measures is available. Thus, the analysis is undertaken with a Monte Carlo simulation model. In this way we simulate and measure credit risk, i.e. collateral default losses, of a loan portfolio for the issuing process of securitisation transactions under symmetric information. The loss distribution function stems from portfolio-level statistics derived from deterministic assumptions about asset-specific properties as to the contribution of expected/unexpected credit loss by individual loans. The allocation of periodic losses in proportion to the various constituent tranches, their evolution over time and their bearing on the pricing of the CLO tranches for risk-neutral investors and in comparison to zero-coupon bonds will be the focus of this examination. Hence, the suggested model serves as a blueprint for the adequate valuation of CLO transactions, if we render the value of contingent claims dependent on the totality of expected periodic credit loss of a multi-asset portfolio allocated to the tranches issued. The resulting tranche spreads are indicative of the default pattern of CLOs, which causes excess investor return expectations in view of information asymmetries. By assuming a uniform portfolio and a corresponding distributional approximation of stochastic loan losses (without taking into consideration prepayments and early amortisation triggers most common to CLOs), the analysis illustrates the dichotomous effect of loss cascading as the most junior tranche of CLO transactions exhibits a distinctly different default tolerance compared to the remaining tranches. Finally, we explain the rationale of first loss retention as credit risk cover on the basis of our simulation results for pricing purposes. As an extension to this paper, we propose to test the viability of the model by comparing simulated credit risk to historical probabilities of portfolio credit default, aside from the presented comparison of simulated risk-neutral returns on tranches and analytical bond prices.In simulation of the interest rate , we need to distinguish between two cases: (i) a variable (stochastic) risk-free interest rate based on the fitted distribution of observed LIBOR rates and (ii) a constant risk-free rate, which is the average value of the stochastic interest rate across time. In this section we allow for a varying risk-free interest rate per period. Due to the regression of the United Kingdom from the European exchange rate system (European Monetary System (EMS)) on 16.09.1992 (JORION, 2001),14 we restrict the database of interest rates to 12-month LIBOR rates quoted at the daily market’s closing from 04.00.1993 to 02.10.2001 in order to avoid a “change point” in the time series of observed daily interest rates.15 The observed data points do not display significant historical bias (“momentum effect”) and heteroscedasticity is low, such that they can be safely regarded independent and identically distributed. Since only the first 1,000 observations contain 460 zero returns, the simulation of stochastic interest rates for the given investment horizon in the presented model requires the transformation of daily LIBOR rates to end-of-the week quotes. This methodology does not harm the statistical validity of extrapolating future interest rates, as the intra-week rates do not fluctuate, so that a particular end-of-week effect of daily 12-month LIBOR rates can be confidently ruled out. After this conversion of daily rates will are still left with 447 observations to substantiate the simulation.