Valuing and Analyzing Bonds with Embedded Options

This chapter introduces the analysis and valuation of bonds with embedded options. For callable bonds, it discusses their unique reinvestment risk and negative convexity. For both callable bonds and puttable bonds, the chapter introduces two additional measures to gauge their risk: yield-to-call and yield-to-put, respectively. The chapter reviews the application of the spot rate curve in bond valuation and introduces the Z-spread to measure bond-specific risk more accurately. To model interest rate risk, the chapter builds a binomial interest rate model and calibrates it with on-the-run Treasury issues. The option-adjusted-spread (OAS) is introduced to measure the bond-specific risk excluding the option effect. The difference between Z-spread and OAS represents the option effect. Common measures of convertible bond risk and value are discussed including the possibility of valuating a convertible bond using option-pricing models and its drawbacks.

Why Callable Bonds Are not Called When the Market Price Reaches the Call Price: A Duration Argument

It is a fact that firms do not call callable bonds when bond prices reach for the first time the call price. This paper provides an original explanation for this behavior by resorting to duration analysis. It is known that, ceteris paribus, a bond with a higher coupon, or a higher yield, has a lower duration that a bond with a lower coupon, or a lower yield. This implies that the bond that is to be called has a lower duration than the bond that replaces it. A lower duration signifies a lower interest rate risk. The firm with a callable bond will wait for market interest rates to fall further in order to equalize durations and bear the same risk. The underlying assumption is that by equalizing durations the firm keeps facing the same financial risk. In this case, it is the same amount of interest rate risk. Consequently, there are no changes in the capital structure, no redistribution effects on other debt claims, and financial leverage is unaffected. The paper provides illustrations on this active law by considering four callable bonds, with different remaining maturities, and each one with a set of two different call prices.