Effective duration of callable corporate bonds: Theory and evidence

This paper computes the effective duration of callable corporate bonds, using a contingent-claims model that incorporates both default risk and call risk. The model generates empirical implications regarding the cross-sectional variation and the firm-specific determinants of duration, and demonstrates that the effect of the call feature is to shorten duration (except for low-grade bonds). The effective duration is also estimated empirically for a large sample of long-term corporate bonds, using monthly bond price and interest rate data. Cross-sectional regression analysis is used to test the empirical implications of the model regarding the determinants of effective duration, and the empirical results are quite supportive of the model’s predictions.     

Are embedded calls valuable? Evidence from agency bonds

This paper examines the call option values embedded in callable agency bonds. For FHLB, FNMA, and SLMA bonds, call value estimates range from 1.23% of par to 1.47% on average, which are between those for the treasury and corporate debt securities. FHLMC bonds, on the other hand, have an average call value estimate of 2.85%. Call values are significantly larger for bonds with a longer remaining maturity and greater default risk. Most interestingly, call values in the call protection period are significantly larger than those in the callable period except for the SLMA bonds, whereas previous studies on corporate debt find no significant difference in call values between these two periods.     

Reduced-form valuation of callable corporate bonds: Theory and evidence

We develop a reduced-form approach for valuing callable corporate bonds by characterizing the call probability via an intensity process. Asymmetric information and market frictions justify the existence of a call-arrival intensity from the market's perspective. Our approach both extends the reduced-form model of Duffie and Singleton (1999) for defaultable bonds to callable bonds and captures some important differences between call and default decisions. A comprehensive empirical analysis of callable bonds using both our model and the more traditional American option approach for valuing callable bonds shows that the reduced-form model fits callable bond prices well and that it outperforms the traditional approach both in- and out-of-sample.     

Yield spreads,agency costs and the corporate bond call feature

This paper theoretically compares yields and optimal default policies for callable and non-callable corporate debt. It shows that, contrary to the conventional wisdom, it is possible for the yield spread (callable minus non-callable) to be negative. It also identifies the key determinants of the yield spread. Next, it shows that the optimal default trigger for non-callable debt is higher than the trigger for callable debt, resulting in additional default-related costs. Thus, the use of non-callable debt gives rise to an indirect agency cost of early default, which is the difference in total firm value with callable and non-callable debt. This agency cost provides a rationale for the existence of callable debt. By examining the determinants of the magnitude of this agency cost, the conditions that make callable debt more attractive (to the issuing firm) relative to non-callable debt are identified. This allows certain predictions to be made regarding the likelihood of a call feature in a corporate bond. The model's implications are supported by existing empirical studies.     

Optimal Refunding Strategies, Transaction Costs, and the Market Value of Corporate Debt

The primary purpose of this paper is to consider both qualitatively and quantitatively the effects of refunding transaction costs and interest rate uncertainty on optimal refunding strategies and the market value of corporate debt. A dynamic model of corporate bond refunding with transaction costs is developed that simultaneously solves for the optimal refunding strategy, the value of the refunding call option, the value of the bond liability to the firm, and the market (investor) value of the fixed-rate contract. We provide examples in which the price of the callable bond does exceed the call price, and we examine whether or not typical levels of refunding costs are sufficient to explain the magnitude and duration of frequently observed premiums on callable corporate bonds.     

The effects of default and call risk on bond duration

This paper examines the effects of default risk, call risk, and their interactions on bond duration. We find that call risk decreases durations of default-free bonds, while default risk alone generally decreases durations for risky bonds with only a few exceptions. The joint effect of default and call risk always results in shorter durations for corporate bonds. Controlling for the effect of default risk, call risk has a negative effect on duration, which diminishes as bond ratings decline. Finally, the effect of call risk on duration depends on bond characteristics. Empirical evidence shows that the effect of call risk is smaller for discount bonds and for deep-discount fallen angels.     

The Relation Between Treasury Yields and Corporate Bond Yield Spreads

Because the option to call a corporate bond should rise in value when bond yields fall, the relation between noncallable Treasury yields and spreads of corporate bond yields over Treasury yields should depend on the callability of the corporate bond. I confirm this hypothesis for investment-grade corporate bonds. Although yield spreads on both callable and noncallable corporate bonds fall when Treasury yields rise, this relation is much stronger for callable bonds. This result has important implications for interpreting the behavior of yields on commonly used corporate bond indexes, which are composed primarily of callable bonds.     

The effect of interest rate volatility and equity volatility on corporate bond yield spreads: A comparison of noncallables and callables

This research investigates the impact of interest rate volatility upon corporate bond yield spreads. We first consider the impact of interest rate volatility upon noncallable bond spreads. Because greater interest rate volatility likely increases the volatility of the firm's debt, we hypothesize that the relation will be positive. Given that we do find a positive relation, we thus investigate whether the positive effect of interest rate volatility on yield spreads is stronger or weaker for callable bonds. We find that the effect is weaker for callable bonds. This result indicates that there is a negative relation between default spreads and call spreads, which is consistent with the theory of Acharya and Carpenter (2002), but in contrast to the theory of King (2002). Furthermore, our results for the relationship between equity volatility and yield spread tend to support Acharya and Carpenter (2002) more than King (2002).     

Probability of call and likelihood of the call feature in a corporate bond

This paper suggests a new way of predicting the likelihood of a corporate bond being callable. We compute the probability that a bond, if callable, would actually be called within a certain period. We also hypothesize a positive relationship between this probability and the likelihood of the bond being issued with a call feature. Comparative static results yield the following empirical implications: the likelihood of a call feature should be an increasing function of coupon rate, corporate tax rate and leverage ratio, and a decreasing function of interest rate and firm risk (volatility). Tests with recently issued corporate bonds provide fairly strong support for the model’s predictions.     

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

A new characterization of the American-style option is proposed under a very general multifactor Markovian and diffusion framework. The efficiency of the proposed pricing solutions is shown to depend only on the use of a viable valuation method for the corresponding European-style option and for the transition density of the model’s state variables. Under a Gauss-Markov stochastic interest rates setup, these new American option pricing solutions are shown to offer a much better accuracy-efficiency trade-off than the approximations already available in the literature. This result is also used to price callable corporate bonds under an endogenous bankruptcy structural approach, by decomposing the option to call or default into a European put on the firm value plus two early exercise premium components.     

Callable Bonds: Better Value Than Advertised?

Callable bonds allow issuers to manage interest rate risk in the sense that if rates decline, the bonds can be redeemed and replaced with lower‐cost debt. Investors demand a coupon premium for giving issuers this option; and when deciding whether to issue callable or noncall‐able bonds, the issuing companies must determine whether it's worth paying the coupon premium. This article addresses two main questions about the structuring and refunding of callable bonds. The first concerns the value of the call option: At the time of issuance, does it make sense to accept the coupon premium for the option being acquired? The second concerns the optimal timing of a refunding: At refunding, do the cash flow savings provide adequate compensation for the option that is being exercised and hence given up? In perfect markets with no taxes or transactions costs, the average corporate issuer should be indifferent between issuing callable bonds or their noncallable equivalent. But corporate taxes, together with risk management considerations, can lead some issuers to prefer callable bonds, possibly with coupons that otherwise would be unacceptably high. Refunding decisions should be made using the concept of “call efficiency,” which compares the savings (net of transactions costs) from calling to the loss of option value. The latter should also account for any option that is built into the replacement issue. Transaction costs that occur when refunding diminish the value of the call option, and their effect should be factored in at the time of issuance. One way of avoiding such costs is to issue “ratchet” bonds—essentially one‐way floaters that automatically reset lower when rates decline, thus delivering the benefits of callable bonds while eliminating transaction costs.     

The buyers’ perspective on security design: Hedge funds and convertible bond call provisions

We provide evidence that security design reflects the interplay of capital supplier and security issuer preferences. While call provisions have historically been the default option in convertible security design, only a minority of post-2005 issues are callable. Because hedge funds dominate the market for new convertibles today and because convertible arbitrage is less risky without callability, the recent diminution in the frequency of call provisions in new convertible bond issues illustrates the importance of the preferences of the suppliers of capital in security design.     

A Duration Model For Defaultable Bonds

I extend recent theoretical work on duration and derive an improved model for the risk‐adjusted duration of corporate bonds. My ex‐ante risk‐adjusted duration is the sum of the bond's Fisher‐Weil duration and the duration of the potential expected delay in recovery caused by the default option. My main conclusion is that failing to adjust duration for default is costly for high‐yield bonds, especially those with a shorter time to maturity. For investment‐grade bonds, this cost is trivial for all maturities.     

Top management incentives and financial flexibility: The case of make‐whole call provisions

Consistent with the premise that make‐whole call provisions enhance value‐creating financial flexibility, we find that higher sensitivity of managerial wealth to stock price (delta) increases the likelihood that corporate bonds contain make‐whole provisions. Building on the results of related research, post‐issue financial performance of make‐whole callable bond issuers increases in delta. In line with prior findings that demonstrate financial flexibility can be costly to bondholders, we find that managerial equity incentives impact the incremental effect of make‐whole provisions on the pricing of corporate debt securities. Consistent with the flexibility explanation, we also find that the market response as measured by abnormal trading volume to the issuance of make‐whole callable debt varies in equity incentives. Overall, our results suggest that managerial incentives play a role in the choice, pricing, and market response to make‐whole options in corporate debt securities.     

What Is the Cost of Financial Flexibility? Theory and Evidence for Make‐Whole Call Provisions

Firms commonly incorporate make-whole call provisions in their newly issued debt, presumably to improve their ability to retire debt early if circumstances require. In return for increased financial flexibility, firms must compensate bondholders with additional (incremental) yield. To estimate theoretical incremental yields, we use and calibrate a structural model for a large sample of callable and noncallable US corporate bonds issued between 1995 and 2004. In a frictionless model where calls occur only when they are in-the-money, theoretical incremental yields average approximately 2 basis points (bp). In an extended model that incorporates taxes, transactions costs, and randomly occurring exogenous events requiring early bond retirement, incremental yields average approximately 5 bp. Empirical analysis, however, indicates that observed incremental yields are significantly greater than model-generated values, averaging between 13 and 24 bp. In the later years of our sample period, however, observed incremental yields begin to converge to model-generated values.     

The life cycle of make-whole call provisions

Perception of industry professionals is that these bonds behave no differently than non-callable bonds. However, make-whole callable bonds are almost twice as likely to be retired early as non-callable bonds. Analysis of which bonds/firms include make-whole call provisions as well as of retirement events suggests the call provision aids firms in precautionary refinancing and in paving the way for major corporate events like M&A. Detailed analysis of news reports reveals three motivating rationales: 1) to refund the debt at low current interest rates, 2) as a result of a merger or acquisition, 3) as a mechanism for paying out excess cash.     

Why firms issue callable bonds: Hedging investment uncertainty

This paper analyzes a firm's dynamic decisions: i) whether to issue a callable or non-callable bond; ii) when to call the callable bond; and iii) whether to refund it when it is called. We argue that a firm uses a callable bond to reduce the risk-shifting problem in case its investment opportunities become poor. Our empirical findings support this argument. We find that a firm facing poorer future investment opportunities is more likely to issue a callable bond than a firm facing better investment opportunities. In addition, a firm with a higher leverage ratio and higher investment risk is more likely to issue a callable bond. Finally, after a callable bond is issued, a firm with a poor performance and a low investment activity tends to call back a bond without refunding; a firm with the best performance and highest investment activity tends to call back a bond and refund its call; and a firm with mediocre performance and investment activity tends to not call its bonds.     

A sequential pricing framework for corporate securities: The case of rating-trigger step-up/-down bonds

We develop a sequential pricing framework in a continuous time cash flow model allowing for repeated valuation of different cash flow claims. One claim is valued until a prespecified boundary is hit, which is subsequently used as the new valuation starting point for the next claim. This highly flexible pricing framework is applied to the pricing of rating-trigger step-up/-down corporate bonds, the coupon payments of which depend on the issuing company’s credit rating. We present a simple closed-form pricing solution for this type of bonds including both a step-up and step-down threshold, as well as a lower default boundary.     

The issuance of callable bonds under information asymmetry

We reconsider the role of asymmetric information in motivating the issuance of callable bonds. The previous literature has emphasized a possibility that a call feature serves as a signal of issuer quality. We demonstrate that asymmetric information can motivate use of a call even when this action does not signal quality in equilibrium. We construct a matched sample of callable and non-callable bonds that permits us to control for non-informational effects on the call issuance decision. Empirical evidence from speculative grade bond markets is consistent with the hypotheses that asymmetric information motivates use of the call feature, but there is no evidence that inclusion of the call functions as a signal to the market.     

A jump to default extended CEV model: an application of Bessel processes

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.