Option-free Bonds Research Articles

First Duration, Then Convexity, Then What? Tilt?

Standard treatments of the impact of interest rate changes on bond prices include duration and convexity. These concepts derive from the first and second derivatives of a Taylor series expansion of an option-free bond price as a function of interest rates. Does the third derivative matter? This paper derives the formula for the third derivative- based term, which we call tilt, and explores its properties. Tilt tells how quickly the convexity changes. Similar to the properties of duration, a higher yield reduces tilt, a longer maturity increases tilt, and a higher coupon reduces tilt, ceteris paribus. Tilt adds little to the accuracy of the impact of small interest rate changes for default-free option-free bonds. Tilt becomes interesting for bonds with embedded options such as callable bonds and mortgage-backed securities. Such bonds can experience rapidly changing convexity and price under certain interest rate regimes.

Pricing Fixed-Income Derivatives Under Increasing and Decreasing Interest Rate Cases Using a Skewness-Adjusted Binomial Interest Rate Tree

There are two general approaches to modeling stochastic interest rate movements using a binomial model—the equilibrium model and the calibration model. Both models assume that the interest rate’s logarithmic return is normally distributed. However, a number of empirical studies have provided evidence that the return distributions of a number of securities exhibit persistent skewness. In modeling interest rate patterns, the existence of skewness in a binomial process impacts not only the values of the up and down parameters, but also the probabilities of the underlying rate increasing or decreasing each period. In this paper, we present empirical evidence showing the significance of skewness when interest rates are increasing and decreasing. We next illustrate how the Johnson, Pawlukiewicz, and Mehta skewness-adjusted binomial model can be used to calibrate a binomial interest rate tree for increasing and decreasing interest rate cases in which the end-of-the period distribution is characterized by skewness. Using the skewness-adjusted binomial equilibrium model, we then compare the prices of option-free bonds and bond derivatives under stable, increasing, and decreasing rate scenarios.

Cash management using multi-stage stochastic programming

We consider a cash management problem where a company with a given financial endowment and given future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal wealth. We formulate the optimization problem as a multi-stage stochastic linear program (SLP). The company can choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment, and rebalances the portfolio at every stage. The uncertainty faced by the company is reflected in the development of interest rates and equity returns. Our model has two new features compared to the existing literature, which uses no-arbitrage interest rate models for the scenario generation. First, we explicitly estimate a function for the market price of risk and change the underlying probability measure. Second, we simulate scenarios for equity returns with moment-matching by an extension of the interest rate scenario tree.

Quantitative Analysis for Investment Management.

(NOTE: Each chapter concludes with a Summary, Suggestions for Further Reading, Problems and Questions, and Appendices.) I. ANALYSIS OF INDIVIDUAL SECURITIES. 1. Fixed Income Security Prices and Yields. 2. Option-Free Bonds: Measuring and Managing Interest Rate Risk. 3. The Term Structure of Interest Rates. 4. Equities: The Discounted Cash Flow Approach. 5. Principles of Option Pricing. 6. Fixed Income Securities with Call and Prepayment Options. 7. Other Options Embedded in Bonds and Equity. 8. Forward and Futures Contracts. II. ANALYSIS OF PORTFOLIOS OF SECURITIES. 9. Investor Preferences and Attitudes Toward Risk. 10. Fundamentals of Portfolio Analysis: The Generic Portfolio Problems. 11. Capital Market Equilibrium and the Pricing of Securities. 12. Active Portfolio Strategies. 13. Performance Evaluation and the Organization of Portfolio Management. Index.

Duration, Convexity, and Time as Components of Bond Returns

Duration and convexity measures have been used to approximate bond returns when small yield changes take place. Chance and Jordan explain that the approximations require yield changes to occur instantaneously. In many applications, the more important issue is the change in bond values as yields change with the passage of time. Using realistic hypothetical yield changes and the mathematical relationship between bond returns and the components of bond returns, they show that convexity adds little to the explanation of returns for option-free bonds when yields change over time. They argue that theta, which measures the impact of the passage of time on bond prices, provides a better explanation of returns than does convexity.