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In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyze the market signaling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders’ belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyze pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signaling equilibrium of our game option model under information asymmetry. We analyze how the callable feature may lower the adverse selection costs in convertible bond financing. We show how low quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high quality firm.

We develop a generic method for constructing a weak static minimum variance hedge for a wide range of derivatives that may involve optimal exercise features or contingent cash flow streams to provide a hedge along a sequence of future hedging dates. The optimal hedge is constructed using a portfolio of pre-selected hedge instruments, which could be derivatives with different maturities. The hedge portfolio is weakly static in that it is initiated at time zero, does not involve intermediate re-balancing, but hedges may be gradually unwound over time. We study the static hedging of a convertible bond to demonstrate the method by an example that involves equity and credit risk. We investigate the robustness of the hedge performance with respect to parameter and model risk by numerical experiments.

This paper provides an overview of the main results of the literature on pricing convertible bonds. It covers simple convertible bonds which are non-callable and can be converted only at maturity as well as more complicated callable and puttable convertible bonds under stochastic interest rates. The paper also reviews the main results in the literature on why firms issue convertible bonds. The two most often cited rationales for issuing convertible bonds - as delayed equity, and to sweeten debt - are discussed in the context of both asymmetric information and agency models of capital structure. Finally, the paper provides some thoughts on incorporating strategic issues into the pricing of convertible bonds.