Convertible Debt: Corporate Call Policy and Voluntary Conversion

This paper examines why, in contrast to the predictions of finance theory, firms do not call convertible debt when the conversion price exceeds the call price. The empirical results suggest that the principal reason is because some firms enjoy an advantage of paying less in after-tax interest than they would pay in dividends were the bond converted. This cash flow incentive is the inverse of an investor's incentive to convert voluntarily if the converted dividends are greater than the bond's coupon. Because of taxation, however, the decisions by investors and firms are not symmetric, and there exist bonds which the firm may not call and an investor will not convert. The results also find that voluntary conversion is significantly related to both the conversion price and the differential between the coupon and the dividends on the converted stock.     

Coupon and tax effects on new and seasoned bond yields and the measurement of the cost of debt capital

A model of the tax structure of interest rates is developed and simple approximate expressions relating yield to coupon are derived. The effect on these simple expressions of alternative assumptions about holding period length, expectations of future interest rates, and other factors, is evaluated. It is shown that with recent U.S. yield averages the new-seasoned yield spread varies with the new-seasoned coupon spread as the theory prescribes. It is concluded that new issue yield averages should provide a more reliable measure of the cost of debt capital than is provided by seasoned yield averages.     

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.     

Actuarial pricing of deposit insurance

Using a pricing formula for options on coupon bonds (Jamshidian [1989], El Karoui and Rochet [1990]) we are able to compute the actuarial pricing of deposit insurance for a commercial bank. Our formula takes into account the maturity structure of the bank's balance sheet, as well as market parameters such as the term structure of interest rates and the volatilities of zero coupon bonds. The relation with asset liability management methods is explored.     

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.     

Valuation of companies and projects under differential personal taxation

This paper develops formulae for the valuation of companies and projects where there is both differential personal taxation of dividends and interest arising from dividend imputation, and differential taxation of interest and capital gains. The former has been addressed in the literature. This paper represents an extension to recognize both phenomena. It is also shown that valuation errors from ignoring these phenomena are all significant, with the errors from ignoring the interest/capital gains tax differential being at least as great as those from ignoring imputation. Thus, a valuation formula that allows for both phenomena is indicated.     

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.     

HOW CHANGES IN BOND CALL FEATURES AFFECT COUPON RATES

In April 1998, Level 3, a telecommunications company, sold $2 billion of 9.19%, ten-year bonds to finance the building of a fiber-optic network. Like most below-investment-grade issues, as well as many investment-grade issues, the Level 3 issue contained an embedded call option that gave the company the right to repurchase the bonds after five years at par value plus the (semi-annual) coupon rate, with the call price declining to par two years before maturity.
Because issuers must pay for the call provision in the form of a higher coupon rate, the choice of whether or not to include a call option can be a difficult one. And, once management decides to include a call option, it must then decide how to structure the call. The most important call structure decisions are how long to make the call protection period and how to set the call price—both of which can have a significant impact upon the coupon yields required to attract investors. Using a well-known option pricing model, the authors of this article summarize their recent research on how variations in bond call features can be expected to affect par coupon yields of new issues under different market circumstances—circumstances that include market conditions relevant to option valuation such as the shape of the term structure and the volatility of interest rates.     

Distortionary Taxation, Debt, and the Price Level

This paper compares the determinacy of equilibria under exogenous interest rates in an economy with a cash constraint, in which taxation is lump-sum or distortionary. Under passive fiscal policies lump-sum taxes generate nominal indeterminacy, while with distortionary taxes indeterminacy can be real, but not purely nominal. In general, under distortionary taxation uniqueness of the equilibrium allocation depends on monetary and fiscal policy interactions through taxes, debt, and interest rates. To illustrate this principle, we consider balanced-budget policies under distortionary income taxation and show that a unique equilibrium allocation prevails if interest rates are set consistent with long-run deflation. A separate section extends the analysis to endogenous interest rates.     

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.     

Debt Management under Corporate and Personal Taxation

The presence of long-term debt in a corporation's capital structure is shown to give rise to a valuable tax-timing option that can be exercised by the firm on behalf of its shareholders. This option, which is not available if the firm is fully equity financed, implies that leverage will have a positive tax effect on total firm value even if there is no such effect associated with the tax deductibility of the coupon interest payments on debt. The more volatile interest rates and bond prices are, the more valuable the tax-timing option and the larger the favorable impact of debt on shareholder wealth.     

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。     

A Long‐Term Perspective on the Determinants of Treasury Bond Stripping Levels

We examine the proportion of individual Treasury bonds held as strips over the entire history of the STRIPS program. First, we document a secular decline in the Treasury bond stripping levels from 1985 to 2010, coincidental with the long‐term decline in the interest rates. This pattern suggests that investors purchase strips to avoid reinvestment risk and to lock in the high interest rates in the 1980s and 1990s. Second, higher coupon and longer maturity bonds are shown to be more heavily stripped. Third, the suspension of new issues of 30‐year bonds from 2001 through 2006 created a gap in the maturity structure of Treasury bonds and induced heavy stripping of 30‐year bonds issued post 2006. Our findings suggest that stripping is motivated by several factors, including interest rate risk management, tax concerns and market completion.     

SERIAL ISSUE EVIDENCE FOR THE RELATION BETWEEN THE RISK STRUCTURE AND MATURITY: A DECOMPOSITION METHODOLOGY

The risk structure of the interest rates literature shows that coupon effects can cause changes in yield spreads as maturity lengthens. These effects make it difficult to empirically isolate the default risk component of the spread for coupon-paying bonds. Attempts to calculate zero-coupon risk structures suffer from the relative scarcity of zero-coupon corporate bonds. We show that yield spreads for coupon-paying bonds that are identical except for default risk decompose into a relative duration component, a premium discount coupon component, and a default component. We present closed-form solutions for measuring the first two components so that the default risk portions can be isolated as residuals. We further present an empirical application of the decomposition metrics for sixteen exchange-traded serial issues and nonparametrically examine the relation between the default premia and maturity. We find various maturity relations.     

EXACT FORMULAS FOR PRICING BONDS AND OPTIONS WHEN INTEREST RATE DIFFUSIONS CONTAIN JUMPS

I develop Heath‐Jarrow‐Morton extensions of the Vasicek and Jamshidian pure‐diffusion models, extend these models to incorporate Poisson‐Gaussian interest rate jumps, and obtain closed‐form models for valuing default‐free, zero‐coupon bonds and European call and put options on default‐free, zero‐coupon bonds in a market where interest rates can experience discontinuous information shocks. The jump‐diffusion pricing models value the instrument as the probability‐weighted average of the pure‐diffusion model prices, each conditional on a specific number of jumps occurring during the life of the instrument. I extend the models to coupon‐bearing instruments by applying Jamshidian's serial‐decomposition technique.     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

When can you immunize a bond portfolio?

This paper presents a condition equivalent to the existence of a Riskless Shadow Asset that guarantees a minimum return when the asset prices are convex functions of interest rates or other state variables. We apply this lemma to immunize default-free and option-free coupon bonds and reach three main conclusions. First, we give a solution to an old puzzle: why do simple duration matching portfolios work well in empirical studies of immunization even though they are derived in a model inconsistent with equilibrium and shifts on the term structure of interest rates are not parallel, as assumed? Second, we establish a clear distinction between the concepts of immunized and maxmin portfolios. Third, we develop a framework that includes the main results of this literature as special cases. Next, we present a new strategy of immunization that consists in matching duration and minimizing a new linear dispersion measure of immunization risk.     

CREDIT SPREADS AND THE ZERO‐COUPON TREASURY SPOT CURVE

We examine the relation between credit spreads on industrial bonds and the underlying Treasury term structure. We use zero‐coupon spot rates to eliminate the coupon bias and to allow for a consistent study both within and across the different credit ratings. Our results indicate that the level and slope of the Treasury term structure are negatively correlated with changes in the credit spread on investment‐grade corporate bonds. We also find that the relation between credit spreads and the Treasury term structure is relatively stable through time. This is good news for value‐at‐risk calculations, as this suggests that the correlations among assets of different credit classes are stable; therefore use of historic correlations to model spread relations can be valid.     

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.     

Trading strategies based on term structure model residuals

The term structure of interest rates is an important input for basically every pricing model and is mostly calibrated on coupon bond prices. Therefore, the estimated interest rates should accurately explain the market prices of these bonds. However, nearly all empirical papers on interest rate estimation, e.g. Svensson, L.E.O. 1994. Estimating and interpreting forward interest rates: Sweden 1992–1994, IMF Working Paper, International Monetary Fund, report significant pricing errors in their sample. So an important question is what drives these pricing errors of the bonds. One simple explanation would be different tax treatment or different liquidity, but most papers on this research topic, e.g. Elton, E., and T.C. Green. 1998. Tax and liquidity effects in pricing government bonds. Journal of Finance 53: 1533–62, cannot fully explain the observed pricing errors. Therefore, these errors must be at least partially caused by either model misspecification or by the deviation of particular bond prices from general market conditions, i.e. mispricing revealing insufficient market efficiency. We provide empirical evidence for the German government bond market that risk-adjusted trading strategies based on bond pricing errors can yield about 15 basis points p.a. abnormal return compared to benchmark portfolios. Furthermore, the abnormal returns are continuously achieved over the whole time period and not randomly on a few days and show a relation to changes in the level and the curvature of the term structure of interest rates. Therefore, pricing errors contain economic information about deviations of bond prices from general market conditions and are not exclusively caused by model misspecification and/or differences in liquidity and tax treatment of individual bonds.