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

• Published date: 01 August 2022
• Author: Liang‐Chih Liu,Tian‐Shyr Dai,Lei Zhou,Hao‐Han Chang
• Date: 01 August 2022
• DOI: http://doi.org/10.1002/fut.22359

Received: 21 February 2022

|

Accepted: 19 May 2022

DOI: 10.1002/fut.22359

RESEARCH ARTICLE

Analyzing interactive call, default, and conversion policies

for corporate bonds

Liang‐Chih Liu

1

|Tian‐Shyr Dai

2,3

|Lei Zhou

2

|Hao‐Han Chang

2

1

Department of Information and Finance

Management, National Taipei University

of Technology, Taipei, Taiwan

2

Department of Information Management

and Finance, National Yang Ming Chiao

Tung University, Hsinchu, Taiwan

3

Risk and Insurance Research Center,

National Chengchi University, Taipei,

Taiwan

Correspondence

Liang‐Chih Liu, Department of

Information and Finance Management,

National Taipei University of Technology,

No. 1, Sec. 3, Zhongxiao E. Rd., Taipei

106, Taiwan.

Email: lcliu@ntut.edu.tw

Abstract

This paper studies the timings of interactive call and conversion decisions

made by bond issuers and holders, respectively, due to the presence of

different embedded options. We develop a risk‐neutral‐valuation‐based game

option model featuring bondholder–stockholder conflicts of interest. The

presence of conversion (call) options possessed by the bondholders (issuers)

accelerates the call (conversion) decisions. Granting bondholders additional

put options further hastens call decisions and hence conversion decisions in

response to call accelerations. Our empirical studies are consistent with past

call policy research and support our interactive exercise analyses that explain

the rationales behind early call and conversion phenomena.

KEYWORDS

call policy, conversion policy, corporate bond with embedded options, game option, risk‐

neutral valuation

JEL CLASSIFICATION

G12, G13, G31

1|INTRODUCTION

A corporate bond is an important financial instrument for a firm to raise capital to finance business expansions and

repay debts. The Securities Industry and Financial Markets Association reports that the corporate bond issuance

volume in the US market grew from 337.4 billion in 1996 to 2280.5 billion dollars in 2020.

1

Bonds with call provisions

also increased from 14% of the total issuance volume to nearly 88% in 2020, perhaps because callable bonds not only

provide financial flexibility for borrowing firms (Banko & Zhou, 2010; S. Brown & Powers, 2020; Elton & Gruber, 1972)

but also elicit better investment decisions benefiting both stockholder and bondholder (Alderson et al., 2017; Z. Chen

et al., 2010; Schall & Siegel, 2016; Thatcher, 1985). Thus the prevalence of call provisions makes it important to

investigate provision designs (Powers, 2021; Tewari et al., 2015) and optimal call policies. Pioneered by the seminal

work of Brennan and Schwartz (1977), the optimal call policy for a default‐free callable bond (abbreviated as a

Chereafter)

2

is to redeem the bond once its market value equals its effective call price. This at‐the‐money (ATM) call

policy maximizes stockholders' value by minimizing the corresponding bondholders' value in a frictionless market.

J Futures Markets. 2022;42:1597–1638. wileyonlinelibrary.com/journal/fut © 2022 Wiley Periodicals LLC.

|

1597

1

See http://www.sifma.org/research/statistics.aspx.

2

For conciseness and ease of identification, each type of option‐embedded bond will be represented by an abbreviation (see Table A1 in Appendix A

for explanations) in the typewriter font. The abbreviations of three moneyness statuses for embedded options defined in Table A2 will be represented

in sans serif type in this paper.

Acharya and Carpenter (2002;AC) then shed light on the in‐the‐money (ITM) call policy when a bond issuer is granted

the option to announce default on its callable bond (i.e., callable defaultable bond, CD). Since exercising the call option

simultaneously terminates the CD and eliminates the default option, the issuer postpones its call timing (compared

with the ATM call policy) to preserve the value of the default option. Similarly, the issuer delays its announcement of

default on the CD compared with that on an otherwise identical noncallable bond (i.e., a D). The interactive call and

default decisions are empirically consolidated by Jacoby and Shiller (2010) and Kim and Stock (2014).

While the delay of bond issuers' call decisions due to the presence of their default options are well studied as above,

studies of how the presence of bondholders' embedded options influences issuers' call decisions are rare. This paper

fills this gap by studying the timings of interactive call and conversion decisions made by bond issuers and holders

3

;we

construct a game option model by extending the AC framework. Our model is based on Merton's (1974) structural

credit‐risk model; thus, all bonds and their embedded options are viewed as contingent claims on their issuers' assets

and the stochastic short‐term interest rate.

4

In addition to the aforementioned CD, we focus on three popular types of

convertible bonds: a noncallable convertible defaultable bond without call and put provisions (abbreviated as a CVD),

and convertible CD with put provisions (a PCVCD and a CVCD).

5

Each bond is decomposed into an otherwise identical

default‐free straight bond plus a game option granting both the bond issuer and holder the right to terminate the bond

early (Kifer, 2000). Instead of exogenously specifying a default or a forced‐conversion boundary as in Sîrbu and Shreve

(2006) and Finnerty (2015), we prove the existence of endogenous default and call (conversion) boundaries that

maximize stockholders' (bondholders') benefits. The continuation region of the game option and hence the optimal

timing to declare default, call, or conversion are derived to analyze interactive exercise timings.

How our game option analyses feature bondholder–stockholder conflicts of interest are described as follows. If

either one of the call, default, or conversion options embedded in a CVCD is exercised, the host bond is terminated and

the other two options cease to exist. This implies that exercising the call option grants a CVCD issuer extra benefits to

eliminate the value of the conversion option belonging to the CVCD holder. Increments (decrements) in the conversion

option value accelerate (decelerate) the timing of a CVCD call to diverge from (converge to) that of an otherwise

identical CD call. In response to the acceleration in call timing, the conversion decision is also hastened to preserve the

conversion value; thus the timing of a CVCD conversion should be earlier than that of an otherwise identical CVD

conversion. This explains the diminishing number of recently issued convertible bonds with call provisions (Grundy &

Verwijmeren, 2018), since call acceleration could significantly raise the risk for convertible arbitragers. Although

granting bondholders additional put rights can further hasten issuers' call decisions as inferred in our above interactive

analyses, the impact on conversion timings is mixed in theory. On the one hand, similar to AC's argument on the

interactive call and default decisions, a PCVCD holder postpones her conversion decision to preserve her put option.

On the other hand, she could convert the bond earlier in response to the issuer's call acceleration. Our empirical

evidence reveals that the latter cases are significantly more common than the former.

To empirically confirm our theoreticallyderived interaction effect, we collect dollar‐denominated corporate bonds that

are allowed to be called and converted anytime within their call and conversion periods from the Mergent Fixed Income

Securities Database (Mergent FISD). Focusing on bonds with continuous call schedules allows us to fairly compare their

call timings without disturbance by vastly diverse call frequencies.

6

Moreover, to fairly compare the timings of calls

(conversions) of bonds with vastly different lengths of call (conversion) periods, we utilize a normalized indicator, the

ratio of time span (abbreviated as RatioTS), defined as the ratio of the time length between the option exercise date and

3

Recent convertible bond research focuses mainly on the rationale for issuance decisions (Batten et al., 2021; Dorion et al., 2014), the presence and

impact of convertible arbitrage (S. J. Brown et al., 2012; De Jong et al., 2013; Van Marle & Verwijmeren, 2017), the design of bond contracts (Grundy

& Verwijmeren, 2016,2018; Verwijmeren & Yang, 2020), and the conversion policy (Jensen & Pedersen, 2016). A detailed review of convertible bond

financing can be found in Dutordoir et al. (2014).

4

The structural credit‐risk model is widely adopted for pricing convertible bonds, such as Sîrbu and Shreve (2006), Liao and Huang (2006), and

N. Chen et al. (2013), to name a few. Though pricing convertibles with default risk can also be handled via Jarrow and Turnbull's (1995) reduced‐

form 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. In addition, according to the statistics recorded in Finnerty (2015), about 49.44% of investment‐grade,

84.44% of speculative‐grade, and 68.99% of nonrated callable convertibles are putable.

6

While around half of CDs collected from Mergent FISD have discrete call schedules, almost all callable convertibles have continuous ones. In

addition, almost all convertible bonds can be converted anytime in their conversion periods.

1598

|

LIU ET AL.

maturity date tothe length of the time span allowed to exercise the option.

7

Clearly, the greater RatioTS is, the earlier the

bond is terminated during the period allowed to exercise the option. RatioTS is estimated by regressing the dummy

representingthe presence or absence of different embedded options and other bond‐and firm‐level controls. We find that

the presence of conversion (call) optionshastens the issuers' call (holders' conversion) decisions.

Although put provisions can be widely found in callable convertibles (Verwijmeren & Yang, 2020), until this paper,

the impact of embedding put provisions on call timings has not been studied. In our collected data, around 49% of the

PCVCDs were redeemed when their call options were out‐of‐the‐money (OTM) whereas only around 29% of CVCDs

were. In addition, around 9% of our callable convertible bonds were converted when their conversion options were

OTM, and all of them were PCVCDs. Our regression analyses also reveal that granting bondholders additional put

rights further accelerates call timings. The conversion timings are significantly earlier due to the presence of put

provisions to echo the further precipitation of call decisions. To our knowledge, this interactive call policy has never

been addressed by a long strand of empirical studies of call policies for callable convertibles, such as Bechmann et al.

(2014), King and Mauer (2014), and Grundy and Verwijmeren (2016).

Our proposed interactive exercise policies also help explain one of the rationales

8

behind widely observed OTM

calls of convertible bonds (Cowan et al., 1993): valuable conversion options hasten call decisions to preempt imminent

conversions and equity dilutions (Bechmann et al., 2014).

9

Associated with the OTM calls hastened by conversion

rights, bondholders also convert their bonds earlier to prevent impending calls from curtailing their values. Thus, we

can attribute early conversion decisions to the presence of call provisions in addition to the presence of market

frictions, such as short‐sale costs (Jensen & Pedersen, 2016). In addition, the interactive exercise policies can explain

Grundy and Verwijmeren's (2016) finding that calls of dividend‐protected convertible bonds are earlier. This is because

the values of their conversion options are protected against dividend payments to hasten call decisions.

Our model also contributes to the modeling of callable convertible bonds via the game option framework. Yan et al.

(2015), Zhu et al. (2018), and Du et al. (2021) consider a default‐free callable convertible bond, whereas Yagi and

Sawaki (2005) and Sîrbu and Shreve (2006) focus on a CVCD. However, as they adopt exogenous default boundaries

when evaluating the CVCD, their models fail to feature the empirically consolidated interaction between call and

default decisions. The model proposed by Bielecki et al. (2008) also suffers from this problem, since the defaults are

exogenously determined via a default indicator process. Though endogenous defaults are considered in N. Chen et al.

(2013) and Leung et al. (2015), their model merely focuses on a perpetual CVCD without clarifying how the presence or

absence of one bond‐embedded option influences the policy for exercising another embedded option. To fully uncover

interactive exercise policies, we generalize the AC framework by simultaneously considering the tradeoff between call

and default decisions as well as bondholder–stockholder conflicts of interest. Our model further elucidates how the

presence of put provisions influences the interactive call and conversion decisions.

10

The remainder of this paper proceeds as follows. Section 2presents the models of a bond issuer's asset value, the

short‐term interest rate, the bond values, and the embedded option values adopted in AC and in this paper. Section 3

extends the AC framework to analyze the exercise policies for bonds with game options. We compare the exercise

boundaries of different embedded options and show how these exercise policies are influenced by the market factors

and the presence of other embedded options. To confirm our proposed interaction, Section 4presents the evidence on

7

Although moneyness is widely adopted to measure the exercise timings in the literature, it is improper to compare the timings among different bond

types. This is because the definition of moneyness differs according to the bond‐embedded options (see Table A2). For example, the moneyness of the

call option embedded in a convertible bond is measured by the size relationship between the conversion value and its effective call price according to

Ingersoll (1977a). However, the moneyness of the same option embedded in a CD compares the size relationship between the bond market value and

the effective call price. Note that conversion value is not applicable to a CD.

8

In addition, OTM calls could also be announced to replace busted convertibles with cheaper bonds as the interest rate level declines (Bechmann

et al., 2014; Bhattarcharya, 2012) or to preempt imminent default (N. Chen et al., 2013; Sarkar, 2003).

9

Bechmann et al. (2014) provide an example of an antidilution argument upon a call announcement in a footnote:

Several out‐of‐the‐money call announcements explicitly mention the “avoid‐dilution arguments”as the main reason for the call. For

example, on November 5, 1997, BancTec Inc. made an out‐of‐the‐money convertible bond call. In the call announcement, the firm

said “the call will be funded with internal capital and existing lines of credit and should allow the company to avoid dilution of 1.5

million shares,”which should be compared to the 21.1 million shares outstanding.

10

Instead of analyzing interactive call and conversion decisions given the presence or absence of put provisions, Finnerty (2015) models exercise

decisions with exogenously specified put and forced‐conversion barriers. Feng et al. (2015) evaluate PCVCDs with exogenously specified call, put,

and default barriers.

LIU ET AL.

|

1599