After-Tax Bond Yields When Tax and Coupon Payments Are Not Simultaneous

Typical after-tax bond yield-to-maturity calculations do not accurately reflect the timing of tax payments for the cash basis tax payer. The best of the methods gives reasonable yield estimates when the first coupon payment date is around May 15. As payment dates vary from May 15, bond values are affected by tax deferrals relating solely to the non-simultaneity of coupon interest and tax payments. These valuation effects, which are not measured by conventional bond models, can be significant, as demonstrated by model simulation and empirical tests which show that the bond market does price the coupon timing tax deferrals predicted by the model.     

Bond indenture provisions and the risk of corporate debt

This paper examines the effect of alternative bond indenture provisions on the allocation of risk among the firm's claimants. The approach taken here differs from that of earlier studies in that risk allocation is examined while the firm's leverage (in market value terms) is held constant. In this context, four indenture provisions are examined: (1) the time to maturity, (2) the promised payment schedule, (3) financing restrictions and (4) priority rules. It is concluded that risk is transferred from stockholders to bondholders as the time to maturity and promised payment increase appropriately. Furthermore substitution of longer-term debt for an equal amount of shorter-term debt also increases the risk to bondholders while decreasing the risk to stockholders. The analysis shows that a coupon bond can be represented by a unique discount bond with the same risk and value. This permits the characterization of the effective maturity of a risky debt issue, a concept analogous to the stochastic duration of a default-free coupon bond. These results are shown to be independent of the means used to finance the debt issue. Finally, it is concluded that the relative risk associated with different bonds issued by the same firm cannot be determined by the structure of priority rules alone. It is also necessary to consider the timing of the promised payments compared to that of the other debt issues in the firm's capital structure.     

Default Risk and the Duration of Zero Coupon Bonds

This paper applies a contingent claims approach to examine the duration of a zero coupon bond subject to default risk. One replicating portfolio for a default-prone zero coupon bond contains a long position in the default-free asset plus a short position in a put option on the underlying assets. The duration of the bond is shown to be a weighted combination of the duration of the default-free bond and the put option. The duration is less than maturity and is not an immunizing duration. The technique is then extended to subordinated debt.     

Bond durations: Corporates vs. Treasuries

We compare the durations (the percentage price sensitivity with respect to the default-free short rate) of corporate and Treasury bonds in the reduced-form, intensity-based credit risk modeling framework. In a frequently used intensity-based model for corporate bond valuation we provide an example showing that, given the parameter estimates found in empirical studies, the duration of a corporate coupon bond may very well be larger than the duration of a similar Treasury bond. This finding contrasts with conclusions of previous studies. In a general, intensity-based recovery of market value framework we provide a simple sufficient condition for when the duration of a corporate bond will be smaller than that of a similar Treasury bond. We also provide an upper bound on the duration of the corporate coupon bond.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stochastic durations,the convexity effect,and the impact of interest rate changes

This article shows that the equilibrium models of bond pricing do not preclude arbitrage opportunities caused by convexity. Consequently, stochastic durations derived from these models are limited in their ability to act as interest rate risk measures. The research of the present article makes use of an intertemporal utility maximization framework to determine the conditions under which duration is an adequate interest rate risk measure. Additionally, we show that zero coupon bonds satisfy those equilibrium conditions, whereas coupon bonds or bond portfolios do not as a result of the convexity effect. The results are supported by empirical evidence, which confirms the influence of convexity on the deviation of coupon bond returns from equilibrium.     

基于多项式样条函数的我国零息票收益率曲线构造

零息票收益率曲线是利率期限结构理论分析的基础,在金融估价和风险管理中发挥着重要作用。提出基于多项式样条函数构造零息票收益率曲线的过程及改进方法:考虑国债采样日位于付息日之间、年付息次数可变的情形,使分析更具一般性;针对多项式样条函数拟合时回归系数不显著的问题,采取剔除不显著变量的方法进行改进;讨论比较了两种样条值确定方法在我国的适用性,并研究了模型的稳定性。选取上交所国债进行的实证研究表明,在现阶段我国国债样本数据较少、结构不甚合理的情况下,采用剔除不显著变量的三段三次样条函数可以较好地构造我国的零息票收益率曲线。     

ILLIQUIDITY RISK,PROJECT CHARACTERISTICS,AND THE OPTIMAL MATURITY OF CORPORATE DEBT

I derive the optimal maturity period for corporate debt used to finance a specific project, when costly financial distress is triggered by the inability to meet coupon obligations. My model predicts a negative relation between bond risk and maturity, and it explains why high-grade bonds show greater maturity dispersion than low-grade bonds, as observed in U.S. corporate bond markets. The major determinant of bond maturity is project duration for low-risk bonds and project risk for high-risk bonds. Other determinants of bond maturity are debt burden, reorganization costs, corporate tax rate, interest rate, and project growth rate.     

A contingent claims analysis of the interest rate risk characteristics of corporate liabilities

This paper provides a contingent claims analysis of the interest rate risk characteristics of corporate liabilities by identifying Merton's (1973) option pricing model with Vasicek's (1977) mean reverting term structure model. Only a non-zero positive range of duration values for the firms' assets is shown to be consistent with the previous empirical evidence on the interest rate sensitivity of corporate stocks and bonds. Chance's (1990) duration measure is shown to be biased downward under empirically realistic conditions. Theoretical conditions are derived under which the duration of a default-prone zero coupon bond can be either higher or lower than the duration of the corresponding default-free bond. The duration of the default-prone bond of a firm with high (low) interest rate sensitive assets is shown to be an increasing (decreasing) function of the bond's default-risk.     

OPTIONS ON U.S. TREASURY COUPON ISSUES

Pricing models for options on default-free coupon bonds are developed and tested under the assumption that the bond prices, rather than interest rates, are the underlying stochastic factors. Under the assumption that coupon bond prices, excluding accrued interest, follow a generalized Brownian bridge process, preference-free, continuous-time pricing models are developed for European put and call options, and a discrete-time model is developed for American puts and calls. The empirical validity of the models is assessed using a six-moth sample of daily closing prices.     

The Pricing of Default-free Interest Rate Cap,Floor, and Collar Agreements

The paper focuses on the valuation of caps, floors, and collars in a contingent claim framework under continuous time. These instruments are interpreted as options on traded zero coupon bonds. The bond prices themselves are used as the underlying stochastic variables. This has the advantage that we end up with closed form solutions which are easy to compute. Special attention is devoted to the choice of the stochastic process appropriate for the price dynamics of the underlying zero coupon bonds.     

Tax Shields,Sample-Selection Bias,and the Information Content of Conversion-Forcing Bond Calls

The information content of conversion-forcing bond calls depends on the after-tax cash flow to bondholders. If the dividend after conversion exceeds the after-tax coupon but is less than the before-tax coupon, the call reveals unanticipated decreases in dividends and/or earnings that reduce the tax shield from interest payments. In contrast, a call when the dividend is less than the after-tax coupon reveals the timing of an anticipated shift from exceptional firm-specific positive growth to the industry norm. Efforts to document properties of convertible calls are subject to sample-selection bias because calls are disproportionately associated with positive pre-call firm-specific growth.     

Differential taxation and the equilibrium structure of interest rates

Equilibrium coupon bond pricing relationships given differential taxation are derived under uncertainty assuming that both corporate and municipal bonds were originally issued at par but are currently selling at a discount. The impact of differential taxation upon the term structure and coupon structure of interest rates is investigated, while the tax structure of interest rates is uniquely characterized. Differential taxation substantially alters the prevailing equilibrium structure of interest rates.     

Pricing interest rate options in a two-factor Cox-Ingersoll-Ross model of the term structure

Solutions are presented for prices on interest rate optionsin a two-factor version of the Cox-Ingersoll-Ross model of theterm structure. Specific solutions are developed for caps onfloating interest rates and for European options on discountbonds, coupon bonds, coupon bond futures, and Euro-dollar futures.The solutions for the options are expressed as multivariateintegrals, and we show how to reduce the calculations to univariatenumerical integrations, which can be calculated very quickly.The two-factor model provides more flexibility in fitting observedterm structures, and the fixed parameters of the model can beset to capture tie variability of the term structure over time.     

Bond Selection for Managed Portfolios

Abstract:   Investors in coupon bonds evaluate them based upon financial considerations such as coupon rate, time‐to‐maturity, callability, convertibility, and financial condition of the issuer. These investors regard promised yield as only a rough measure of the reward a bond offers to compensate them for the pure time‐value‐of‐money and the financial risks to which they are exposed. Hence, they need a more meaningful measure of reward to facilitate comparisons among coupon bonds. The purpose of this paper is to describe an alternative heuristic approach to the task of making such comparisons. The approach produces a simple ordinal measure of reward, called the 'indifference spread,' that considers implicitly the potential sources of return to, as well as many of the risks associated with, investment in coupon bonds. For any coupon bond, the indifference spread method permits assessment of relative reward offered for the combined exposures to price and call risks, while also reasonably accommodating possible sale anytime prior to maturity. Once an investor (e.g., money manager) identifies indifference spreads for all bonds under consideration as of any moment in time, he/she can then draw conclusions regarding their relative values at that time based, in large part, on these spreads.     

The Optimal Write-Down Coefficients in a Percentage for a Catastrophe Bond

Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. When the aggregate catastrophe loss exceeds a specified amount by the maturity, the CAT bond is triggered and the future bond payments are reduced. This article first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal write-down coefficients in a percentage, implemented by Monte Carlo simulations, which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal write-down coefficients in a percentage help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it demonstrates how the number of coupon payments, loss share, retention level, strike price, maturity, frequency, and severity parameters of the catastrophe loss process and different interest rate models affect the optimal write-down coefficients in a percentage with numerical examples for illustrations.     

The Valuation of Semiannual Bonds between Interest Payment Dates: A Correction

This note provides a correction to Taylor's 1988 work on the valuation of semiannual coupon bonds between interest payment dates. It shows that the discrepancy in values between Taylor's model and the standard Wall Street pricing formula is much smaller than indicated by Taylor and is unlikely to generate opportunities for arbitrage profits.     

信用债流动性视角下的货币政策传导效果

企业债券是社融存量规模中仅次于贷款的一个重要组成部分,其利率的变化直接关系到实体经济的融资成本,文章通过实证研究指出,近年来基准利率与信用债二级市场成交收益率和一级市场发行票面利率相关性逐步提升,反映出通过债券路径的货币政策传导效果在逐步增强,而债券市场成交活跃度提升是其重要推手。文章进而提出进一步提升市场流动性的相关政策建议。     

An International Study of Tax Effects on Government Bonds

It is shown that coupon bonds alone are not sufficient to span time-dated claims on ordinary income, capital gains, and non-taxable wealth. In an incomplete bond market where the pure dated claims are not spanned by existing bonds, marginal rates of substitution between present consumption and pure dated claims on ordinary income, capital gains income, and non-taxable wealth, respectively, can differ across bondholders. However, the relative pricing of coupon bonds in each of these countries is shown to be consistent with the tax status of the major (non-tax-exempt) holders of government debt.     

Forward-neutral valuation relationships for options on zero coupon bonds

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds.