Fixed Income Analysis, Second Edition

CHAPTER 9

VALUING BONDS WITH EMBEDDED OPTIONS

I. INTRODUCTION

The presence of an embedded option in a bond structure makes the valuation of such bonds complicated. In this chapter, we present a model to value bonds that have one or more embedded options and where the value of the embedded options depends on future interest rates. Examples of such embedded options are call and put provisions and caps (i.e., maximum interest rate) in floating-rate securities. While there are several models that have been proposed to value bonds with embedded options, our focus will be on models that provide an “arbitrage-free value” for a security. At the end of this chapter, we will discuss the valuation of convertible bonds. The complexity here is that these bonds are typically callable and may be putable. Thus, the valuation of convertible bonds must take into account not only embedded options that depend on future interest rates (i.e., the call and the put options) but also the future price movement of the common stock (i.e., the call option on the common stock).

In order to understand how to value a bond with an embedded option, there are several fundamental concepts that must be reviewed. We will do this in Sections II, III, IV, and V. In Section II, the key elements involved in developing a bond valuation model are explained. In Section III, an overview of the bond valuation process is provided. Since the valuation of bonds requires benchmark interest rates, the various benchmarks are ...