Callable Defaultable Bonds: Valuation, Hedging, and Optimal Exercise Boundaries
Posted: 20 Jan 2000
Date Written: July 21, 1999
Abstract
This paper models callable defaultable bonds, incorporating both stochastic interest rates and optimal call and default rules. We provide analytical results about valuation and optimal exercise boundaries, which we use to study hedge ratios with respect to Treasury bonds and issuer equity. Since the interest rate and equity risk of a bond depend on how close it is to call or default, the results on optimal exercise boundaries lead to new insights about durations, betas, and hedge ratios. For example, as functions of firm value, bond deltas with respect to the Treasury bond essentially inherit the shape of the exercise boundaries. It follows that a call provision can increase the duration of a defaultable bond and default risk can increase the duration of a callable bond. We also illustrate the difficulty of hedging default risk and quantify the Myers underinvestment problem for typical high grade and junk bond issuers.
JEL Classification: G12, G13, G31, G33
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