CDO Valuation: Term Structure, Tranche Structure, and Loss Distributions
by Michael B. Walker of the University of Toronto
January 19, 2007
Abstract: This article describes a new approach to the risk-neutral valuation of CDO tranches, based on a general specification of the loss distribution, and the expected loss at zero default, for the reference portfolio. The new approach can describe tranche termuctures, and the generality with which the basic distributions are specified allows it to be perfectly calibrated to any set of market prices (for any number of tranches and maturities) that is arbitrage-free. Also, given a set of arbitrage-free market prices, arbitrage-free interpolated term structures (plots of tranche price versus maturity for a given tranche) and tranche structures (plots of tranche price versus tranche for a given maturity), as well as implied loss distributions, can be obtained, allowing bespoke tranches to be priced. The marking to market of tranche prices, and the establishment of forward-start premiums for the index are discussed. An efficient linear programming approach to valuation, essential to the implementation, is also described. The article also makes use of a new, simple yet general, approach to the problem of unequal notionals, and of random, time-dependent, risk-neutral, recovery rates.
Keywords: collateralized debt obligations, risk-neutral.
Previously titled: CDO Models -- Towards the Next Generation: Incomplete Markets and Term Structure