Corporate Bonds: Valuation, Hedging, and Optimal call and Default Policies

Abstract

This paper studies the valuation and risk management of callable, defaultable bonds when both interest rates and firm value are stochastic and when the issuer follows optimal call and default policies. Since interest rate sensitivity is low when call is imminent and firm value sensitivity is high when default is imminent, characterizing the issuer's call and default policies is essential to understanding corporate bond risk management. We develop analytical results on optimal call and default rules and use them to explain the dynamics of a hedging strategy for corporate bonds using Treasury bonds and issuer equity.

To clarify the interaction between the issuer's embedded call and default options, we compare the callable defaultable bond to its pure callable and pure defaultable counterparts. Each bond's embedded option is a call on a riskless, noncallable host bond, distinguished only by its strike price. This generalized call option perspective generates intuition for a variety of results. For instance, spreads on all bonds, not just callables, narrow with interest rates; a decline in rates can trigger a default; a call provision can increase the duration of a risky bond; a call provision increases equity's sensitivity to firm value, mitigating the underinvestment problem identified by Myers (1977).