Game option models of convertible bonds: Determinants of call policies

Abstract

The interaction of bondholder's conversion and issuer's call in a convertible bond leads to a game option model between the two counterparties. Like typical pricing models for corporate debts, the fair value of a convertible bond is highly dependent on issuer's credit risk, tax benefits of coupons and other structural features. The convertible bond pricing models in the literature can be categorized into two approaches: (i) structural firm value models that incorporate dilution effect in the issuer firm's corporate structure upon conversion; and (ii) reduced form models that price convertible bonds based on calibration with market liquid instruments. We review and comment on various pricing formulations of convertible bonds and effectiveness of different numerical schemes for solving the associated optimal stopping problems. Empirical studies on issuers' optimal call policies have revealed discrepancies between the optimal decision rule derived from pricing models and actual market practices. The more refined model formulation of a convertible bond should include corporate finance considerations in the determination of the optimal call policies.