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March 3 Math Colloquium

Albert Cohen, Michigan State

Pricing Bonds and Swaps with Recovery

The classical Merton model (R.C. Merton, "On the pricing of corporate debt: The risk structure of interest rates", The Journal of Finance
29.2, 449-470, 1974.) assumes that default and post-default recoverable values are driven by a common stochastic factor, that of
the firm's asset value. However, a single factor for pricing such bonds assumes that bond and equity returns are perfectly correlated,
which need not be true.

New methods, (A. Cohen and N. Costanzino, "Bond and CDS Pricing with Recovery Risk I and II", available as SSRN preprints) address the entanglement of
recovery risk with default risk in the pricing of defaultable bonds. The authors show that this mixture can lead to errors in estimating
the total risk that investors in these bonds have undertaken. The approach taken also considers related instruments such as CDS's and
equity as well as solving the related boundary value problems for bond price.

In this talk, we review these new methods and we also present a transform for a multifactor bond-pricing model that represents the partial information
available to firm managers about recoverable value. We recover a version of the ubiquitous Wang Transform in the classical Merton model, and will
calculate the transformed default probability in two other related structural models. The effect of this extra uncertainty about post-default recovery, we will see, can be observed through the distortion of the original
default risk.

Three examples are used to illuminate the approach, including a model that incorporates short-term credit spreads into asset and recovery value evolution. Finally, market data is used to calibrate the first example and return predictive measures of the
company analyzed.

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