Coupon Bonds Research Articles

A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds

This paper introduces a more general modeling world than available under the classical no-arbitrage paradigm in finance. New research questions and interesting related econometric studies emerge naturally. To explain in this paper the new approach and illustrate first important consequences, we show how to hedge a zero coupon bond with a smaller amount of initial capital than required by the classical risk neutral paradigm, whose (trivial) hedging strategy does not suggest to invest in the risky assets. Long dated zero coupon bonds we derive, invest first primarily in risky securities and when approaching more and more the maturity date they increase also more and more the fraction invested in fixed income. The conventional wisdom of financial planners suggesting investor to invest in risky securities when they are young and mostly in fixed income when they approach retirement, is here made rigorous. The main reason for the existence of less expensive zero coupon bonds is the strict supermartingale property of benchmarked savings accounts under the real world probability measure, which the calibrated parameters identify under the proposed model. We provide intuition and insight on the strict supermartingale property. The less expensive zero coupon bonds provide only one first example that is indicative for the changes that the new approach offers in the much wider modeling world. The paper provides a strong warning for life insurers, pension fund managers and long term investors to take the possibility of less expensive products seriously to avoid the adverse consequences of the low interest rate regimes that many developed economies face.

Evaluation of Corporate Bond Market Performance in Bangladesh

Bond market plays a vital role in economic development of a country. Bond market provides long term finance to issuers by creating alternative source of finance through stock market, besides providing stable source of income to investors against volatile stock market. However, Bangladesh corporate Bond market is at very initial stage. Hence, it is needed to make an analysis of investors’ attitude towards corporate bonds in Bangladesh for determining investors finding on the issue. The study is limited to performance evaluation of three corporate bonds in corporate bond market in Bangladesh and investigate investors attitude towards it. We have collected secondary information from DSE web site and processed through SPSS to make performance analysis and collected primary data from investors of some brokerage houses in Chittagong metro through questionnaire survey for analyzing investors’ attitude towards corporate bond market. The study has found that price stability of ACI zero coupon bond is more than IBBL Perpetual Mudaraba Bond and BRAC subordinated convertible bond and it is also found that only 5% of respondents prefers to invest in corporate bonds due to lack of supply of corporate bond, lack of investors’ awareness, inadequate market regulations etc.IIUC Studies Vol.10 & 11 December 2014: 127-144

Forecasting the US Term Structure of Interest Rates Using Nonparametric Functional Data Analysis

In this paper we consider a novel procedure to forecasting the US zero coupon bond yields for a continuum of maturities by using the methodology of nonparametric functional data analysis (NP‐FDA). We interpret the US yields as curves since the term structure of interest rates defines a relation between the yield of a bond and its maturity. Within the NP‐FDA approach, each curve is viewed as a functional random variable and the dynamics present in the sample are modeled without imposing any parametric structure. In order to evaluate forecast the performance of the proposed estimator, we consider forecast horizons h = 1,3,6,12… months and the results are compared with widely known benchmark models. Our estimates with NP‐FDA present predictive performance superior to its competitors in many situations considered, especially for short‐term maturities. Copyright © 2016 John Wiley & Sons, Ltd.

Pricing Coupon Bond Options and Swaptions under the One-Factor Hull–White Model

In this article, the authors propose an alternative approach for pricing bond options and swaptions under the one-factor Hull–White model. Their proposal differs from the existing models used to evaluate these type of instruments when the evolution of the term structure of interest rates is modeled by short-rate models. Assuming that the forward price of a coupon bond is a martingale under the forward risk-neutral measure, the proposed model involves deriving the volatility of the coupon bond as a function of its stochastic duration. Once the volatility function is defined, the price of options on coupon bonds can be derived by simply applying the standard no-arbitrage pricing theory in the context of the one-factor Hull–White model. Given the equivalence between the price of a coupon bond and the price of the corresponding swaptions, this approach can be adopted to calibrate the parameters of the one-factor Hull–White model using swaptions quoted in the market. The new solution proposed for the calibration can be considered as an alternative with respect to the existing approaches proposed in the literature and used currently by practitioners. Numerical results are provided in order to analyze the features of the proposed model for calibration purposes. <b>TOPICS:</b>Fixed income and structured finance, derivatives applications, quantitative methods

Interest Rate Term Structure Decomposition at the Issue Level: Model and Implications

The paper builds on and expands Barnard (2015). A relationship between the portfolio term structure and issue term structures is defined, such that the portfolio term structure is no longer directly decomposed. Rather, issue term structures are decomposed, and the portfolio term structure is derived from the issue term structures. When decomposing term structures at the issue level, minimizing the difference between modelled price and market price is replaced by an alternative objective: minimizing co-variance between issue term structures and the portfolio term structure. The model is specifically targeted at vanilla bond portfolios, or mixed bond portfolios comprising of vanilla and zero coupon bonds. It may be applied to both risk-free and risky portfolios. In particular, it should be able to adapt better to risky portfolios, known to have greater spread variance across individual issues, viz-a-viz the portfolio.The theoretical framework to accomplish issue level decompositions is subsequently delineated. The issue of negative forward rates is further examined. The model is applied to a sample of risk-free bonds, and the implications in terms of risk data are noted.

Determination of zero-coupon and spot rates from treasury data by maximum entropy methods

An interesting and important inverse problem in finance consists of the determination of spot rates or prices of the zero coupon bonds, when the only information available consists of the prices of a few coupon bonds. A variety of methods have been proposed to deal with this problem. Here we present variants of a non-parametric method to treat with such problems, which neither imposes an analytic form on the rates or bond prices, nor imposes a model for the (random) evolution of the yields. The procedure consists of transforming the problem of the determination of the prices of the zero coupon bonds into a linear inverse problem with convex constraints, and then applying the method of maximum entropy in the mean. This method is flexible enough to provide a possible solution to a mispricing problem.

SHORT RATE FORECASTING BASED ON THE INFERENCE FROM THE CIR MODEL FOR MULTIPLE YIELD CURVE DYNAMICS

In this paper, we propose a strategy to extract the information on the market participants’ expectation of the future short rate from the cross-sectional zero coupon bond prices. In line with the current market practice of building different yield curves for different tenors, we construct multiple one-factor short rate processes to pin down the salient features of the yield curve at different tenors. We represent this information in the form of the Cox–Ingersoll–Ross model implied parameters, and show that this information can be used to forecast the future short rate. This approach of representing the information on the market participants’ consensus in the form of implied model parameters and using these implied parameters for forecasting purposes resembles the approach of representing the market expectation of the underlying asset volatility reflected by stock option prices in the form of implied volatility, and using it to forecast the realized volatility. We illustrate the implementation of this method using historical US STRIPS prices and effective Federal Funds rate.

Optimal retirement planning with a focus on single and joint life annuities

We optimize the asset allocation, consumption and bequest decisions of a couple with an uncertain lifetime. The asset menu consists of zero coupon bonds and pure endowments with different maturities, whole life annuities and stocks. The pure endowments pay either fixed or variable benefits, and, similarly to the whole life annuities, are contingent on either a single or a joint lifetime. We model the stock returns and the parameters for the term structure with a vector autoregressive model, thus considering time-varying investment opportunities. To find the optimal solution we use a multi-stage stochastic programming approach, which allows for including complex surrender charges on pure endowments and annuities, as well as transaction costs on stocks and bonds. Our findings indicate that despite high surrender charges, households should invest in a wide combination of life contingent products with different maturities and underlying financial risk.

Sharing of Real Risks by the Financial Sector

My previous article "Heads I Win Tails You Lose Double" SSRN ID 269467) deals with the role of the financial sector in capitalist economies In short, its contribution is the transfer of funds from surplus units to the units with deficit of funds. Because of the importance of its role, the New Classical School (NCS) advocates that financial sector should be free to innovate and introduce new activities as much as it please. On the other hand,a large group of economists criticize the financial sector for creating business cycles and financial crises. To deal with the some of the pros and the cons related to this sector, we have advocated that financial companies should be required to share to a higher degree the risks they deal with in the real sector. This suggestion is a difficult one to implement because of the variety of existing financial deals, and imposes a serious challenge to research in the area of financial economics. Available at SSRN: http://ssrn.com/abstract=269467.In this article we deal with a very simple case of risk sharing; the case where a financial firm (usually a bank) facilitates the issue of bonds to finance a project proposed by a firm in the real sector. Assume the management of the firm has decided that the optimal way to finance the project is to issue a number of zero coupon bonds, and the financial firm has undertaken to handle the issuing of these bonds.It is proposed that before the issue of bonds the production firm and the financial one are obliged to make an agreement that is not transferable. The purpose of the agreement is to determine the division of the anticipated future returns of the project between the production firm and the financial institution.The partners are required to estimate and agree on the probability distribution of profits at the end of the project if no such agreement was required. In addition they are required to determine the profits of similar projects in the market are anticipated to earn on the average. This figure can be estimated from the evaluation of the financial firm with the overall market conditions, and its experience with other ongoing projects of similar type. Finally, they are required to agree that in the "up" case the financial firm will receive a given ratio of the "higher than normal" profits, and in the "down" case will pay the firm the same ratio of the "less than normal" profits This ratio (which is derived in the text) must make the agreement fair, in the sense that today the expected benefits from the agreement are, for both agents, the same as those of the "no agreement" case. The text justifies these requirements on the basis market conditions, expectations, and the experience of the financial firm.It is shown that in the "up" case the production firm will earn less profits (and in the "down" case more profits), than in the "no agreement" case. The question is: does either firm prefer an agreement of this type? The answer depends on their attitude to risk, as is discussed in the text. The significant part of this suggestion is that regulations that impose such deals are fair for the whole society, and force the financial sector to undertake some of the real economy risks (and the benefits) that deals with.

Recovery Rate in the Event of an Issuer’s Insolvency — Empirical Study on Implications for the Pricing of Credit Default Risks in German Corporate Bonds

According to the Jarrow–Turnbull model, coupon bonds are valuated as a portfolio of zero-coupon bonds that, in the event of insolvency, pay a recovery rate at the end of their term. However, when it comes to valuations, the German insolvency law differs in certain respects. To find out whether a model adapted to the German insolvency law will prove to be more empirically robust, an empirical study of 103 corporate bonds was carried out over more than 800 trading days.

The Integrity Effect on Municipal Bonds

We study whether the integrity of local governments has effects on municipal bond coupon rate. We conjecture that higher integrity is associated with lower bond coupon rate. One of proxies for the integrity is the integrity index which Anti-Corruption and Civil Rights Commission of Korea announces annually. The high degree of the index implies high integrity. We also use the number of crimes by local government officials as the integrity measure. Empirical results show that Increasing a unit of integrity is equivalent to decreasing 0.34% of municipal coupon bond. The sensitivity of the integrity to municipal bond coupon rate is stronger before 2007-2008 financial crisis, when the coupon rate was higher, than after the crisis. Overall, our results imply that local governments could save financing cost by improving the integrity of the governments.

Is a pure TIPS strategy truly risk free?

A Treasury Inflation-Protected Security (TIPS) is virtually risk free. As an obligation of the U.S. Treasury, it is mostly free of default risk. As an inflation-indexed security held to maturity, it is risk free in terms of purchasing power. However, investing in a TIPS-only portfolio for retirement is not risk free. This paper presents the results of a simulation analysis designed to evaluate the performance of a portfolio of inflation-indexed Treasury coupon bonds. This study demonstrates that significant shortfall risk exists for TIPS-only portfolios across a range of savings plans and the securities selection rules.

Partial Durations: The Case of Fixed and Floating Rate Bonds

Floating rate bonds are coupon-paying instruments generally indexed to interest parameters. At the trading date, the payment dates and indexation rules are known, while the value of future coupons is uncertain. In this perspective, floating rate bonds are generally seen as a portfolio of zero coupon bonds. Therefore, at each coupon payment date, the bond should be quoted at face value and its duration should match the maturity of the replicating zero coupon bond. However, the empirical evidence based on historical prices of real floating rate bonds shows that such an instrument is not systematically quoted at parity and its market risk profile could differ from that of the replicating zero coupon bond. The aim of this work is to study the duration of a floating rate bond using a partial modified duration approach after decomposing the floating rate bond into its main building blocks. The final goal is to capture the effective risk factors of these instruments in real financial markets in order to define synthetic risk measures that should be able to reflect the instrument’s effective risk profile.

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.

Forecasting of the Convexity Adjustment and the Short Rate Based on the Inference from the CIR Model

We propose a strategy to extract the information on the market participants' expectation of the future short rate from the cross-sectional zero coupon bond prices. In line with the current market practice of building different yield curves for different tenors, we construct multiple one-factor short rate processes to pin down the salient features of the yield curve at different tenors. We represent this information in the form of the Cox-Ingersoll-Ross model implied parameters. We show that this information can be used to forecast the future short rate. This resembles representing the market expectation of the underlying asset volatility reflected by stock option prices in the form of implied volatility, and using it to forecast the realized volatility. We illustrate the implementation of this method using historical US STRIPS prices and effective Federal Funds Rate.

A novel partial integrodifferential equation-based framework for pricing interest rate derivatives under jump-extended short-rate models

Interest rate derivatives under jump-extended short-rate models have commonly been valued using lattice methods. Unfortunately, lattice methods have pitfalls, mainly in terms of accuracy, efficiency and ease of programming. This paper proposes a much faster and more accurate valuation method based on partial integrodifferential equations (PIDEs). Spatial differential and integral terms are discretized by fourthorder finite differences and Simpson's rule, respectively. For the time-stepping, we investigate a Crank-Nicolson scheme, an implicit-explicit (IMEX) scheme and an exponential time integration scheme. We demonstrate our method by pricing bonds as well as European and American options on both zero-coupon and coupon bonds under jump-extended constant-elasticity-of-variance processes. Through a variety of test problems, we demonstrate that our PIDE-based approach is remarkably superior to lattice methods in terms of accuracy, speed and ease of implementation. By way of example, pricing a one-year zero-coupon bond under the Vasicek model extended with exponential jumps, our method attains an accuracy of 104 in 0:09 seconds with the IMEX scheme, whereas a truncated tree takes 78 seconds to reach the same accuracy.

Immunization and Hedging of Longevity Risk

Pension funds and life insurers offering annuities hold long term liabilities linked to longevity. Risk management of life annuity portfolios aims to immunize or hedge both interest rate and mortality risks. Standard fixed interest duration-convexity hedging must be adapted to allow for both interest rate and longevity risk. We develop an immunization approach along with a delta-gamma based approach allowing for both risks incorporating models for mortality and interest rate risk. The immunization and hedge effectiveness of fixed-income coupon bonds, annuity bonds, as well as longevity bonds, is compared and assessed using simulations of portfolio surplus outcomes for an annuity portfolio. Fixed-income annuity bonds can more effectively match cash flows and provide additional hedge effectiveness over coupon bonds. Longevity bonds, including deferred longevity bonds, reduce risk significantly compared to coupon and annuity bonds, reflecting the long duration of the typical life annuity and the exposure to longevity risk. Longevity bonds are shown to be effective in immunizing surplus over short and long horizons. Delta gamma hedging is shown to only be effective over short horizons.

The Bond Coupon's Impact on Liquidity

Corporate bond investors are compensated for liquidity and counter-party risk in the yield received in excess of the credit premium and risk-free rate. This paper shows that the liquidity premium as a hedge against uncertain future states is determined by the ratio of excess coupon payments after paying for credit protection to the capital gain realized after hedging interest rate risk. The liquidity premium increases with the time that investors must wait for compensation. The results suggest that the way in which investors receive compensation for liquidity risk is a more significant determinate of the liquidity premium than turnover.

Consumption and Asset Prices with Homothetic Recursive Preferences

When preferences are homothetic, utility can be expressed in terms of current consumption and a variable that captures all information about future opportunities. We use this observation to express the differential equation that characterizes utility as a restriction on the information variable in terms of the dynamics of consumption. We derive the supporting price system and returns process and thereby characterize optimal consumption and portfolio decisions. We provide a fast and accurate numerical solution method and illustrate its use with a number of Markovian models. In addition, we provide insight by changing the numeraire from units of consumption to units of the consumption process. In terms of the new units, the wealth-consumption ratio (which is closely related to the information variable) is the value of a coupon bond and the existence of an infinite-horizon solution depends on the positivity of the asymptotic forward rate.

Credit Risk and LGD Modelling

Abstract This paper deals with the methods for estimating credit risk parameters from market prices, e.g. Probability of Default (PD) and Loss Given Default (LGD). Precise evaluation of these parameters is important not only for bank to calculate their regulatory capital but also for investors to price risky bonds and credit derivatives. In this paper, we introduced reduced-form analytical methods for the calculation of LGD to pricing Credit Default Swaps. Reduced-form credit risk models were introduced as a reaction to structural approach, especially trying to decrease informational difficulty when modelling credit risk. In the reduced-form approach, the market value of defaulted bonds is the same as in the fraction recovered from the exposure at default. We use the face value convention, which Hull & White (2000) presented in their model which extended recovery of face value convention for coupon bonds.