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.

Analyzing interactive call, default, and conversion policies for corporate bonds

“…Determinants that were verified to significantly influence the call timings in the literature are controlled. Specifically, increments in coupon rates, decrements in Treasury rate levels, average call prices, Treasury rate volatility, and stock return volatility hasten the call decisions (Bechmann et al, 2014;King & Mauer, 2000, 2014Sarkar, 2003). The signs for the coefficients on these explanatory variables in our regressions are generally consistent with the literature.…”

“…Though pricing convertibles with default risk can also be handled via Jarrow and Turnbull's (1995) reducedform credit-risk model, such as Chambers and Lu (2007) and Wang and Dai (2017), adopting structural models facilitates the analyses of option exercise policies in terms of the bond issuer's asset value and interest rate. A detailed review of convertible bond pricing models can be found in Batten et al (2014), Kwok (2014), and Batten et al (2018). 5 According to data collected by Grundy and Verwijmeren (2018), a majority of convertible bonds issued before 2000 are callable; noncallable convertible issues became popular after 2003.…”

Game options with gradual exercise and cancellation under proportional transaction costs

“…Game options have proved to be important not only in their own right, but also because they underpin the theory for other traded derivatives such as convertible bonds or callable options; see e.g. Kallsen and Kühn [KalKuh05], Kühn and Kyprianou [KuhKyp07], Bielecki et al [Bie08], Wang and Jin [WanJin09], or Kwok [Kwo14].…”