Consulting Corner - March '06

A Framework for Market-Implied Defaults
by Anne Ching

In the corporate bond sector, statistical measures such as zeta scores have been used for quantifying credit and default risk for over three decades. Ten years ago Moodys KMV introduced the EDF credit measure, which represents an implied measure of default taken from market information about equity prices and respective price volatility. Also, Hull and White (2005) recently demonstrated how the future price distribution of actively traded CDOs could be implied from market quotes with the use of copulas¹. In the mortgage sector, the use of market information for forecasting expected defaults has not been widespread as in other financial sectors, but is emerging as an important methodology in mortgage analytics.

Andrew Davidson & Co., Inc. has developed a market-implied framework for estimating default probabilities for subprime transactions. The key insight underlying the framework is that market spreads for bond classes within the same transaction can be used to imply the likelihood of default of the underlying collateral. Since there are typically multiple bonds within a transaction, there are multiple data points on which to extract the likelihood of default. Moreover, if we make assumptions about the probability distribution, we can recover the distribution of defaults of the underlying collateral.

Let us consider the transaction below. Table 1.0 shows market prices for an Option One home equity loan deal (OO2006-01) as of March 23, 2006. We then compute prices for each of the bond classes using the AD&Co. OAS model. Typically in an OAS framework, one would simulate interest paths and forecast prepayment speeds for each of the paths to generate respective cash flows. One would then compute the OAS or single spread when added to each of those rate paths equates the average net present value of the cash flows to market prices. Under the market-implied framework, we introduce a dimension of default by applying a uniform default vector to each of the simulated rate paths under each scenario. We considered ten scenarios in all.

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