An Incomplete-Market Model for Collateralized Debt Obligations
by Michael B. Walker of the University of Toronto
October 27, 2005
Abstract: This article describes a model that appropriately treats the incomplete-market aspects of collateralized debt obligations (CDO's). The model is a termucture model that can be calibrated so that it precisely reproduces, in terms of a single set of model parameters, the market values of the prices of contracts on a number of different tranches and having a number of different maturities for each tranche. The calibrated model gives arbitrage-free ranges of prices for derivatives when this is appropriate, as is the case in the pricing of an unmarketed tranche. In this case, risk-neutral pricing is only a first step in the pricing process, which is completed by negotiation in the market. Thus, within a certain price range, tranche prices are market prices that are determined by investor perceptions as influenced by analysts' reports, etc (and not by the predictions of a particular copula model). A related conclusion is that the Black-Scholes type hedging of changes in tranche value with time is not appropriate, and this is illustrated with reference to the effects of the downgrade of Ford and General Motors in May 2005. By way of contrast, definite prices for certain other derivatives are found when this is appropriate, as in the case of the pricing of forward-start CDO's.
Keywords: CDO, forward-start CDO, collateralized debt obligation, incomplete market, default risk.
Previously titled: An Incomplete-Market Termucture Model for Collateralized Debt Obligations