Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation, Second Edition

CHAPTER 7

Valuation of Bonds with Embedded Options

In Chapter 4, we discussed the valuation of option-free bonds. These are bonds where neither the issuer nor the investor has the option to alter a bond’s cash flows. In this chapter we will explain how to value bonds with embedded options.

OVERVIEW OF THE VALUATION OF BONDS WITH EMBEDDED OPTIONS

To develop an analytical framework for valuing a bond with an embedded option, it is necessary to decompose a bond into its component parts. Consider, for example, the most common bond with an embedded option, a callable bond. A callable bond is a bond in which the bondholder has sold the issuer an option (more specifically, a call option) that allows the issuer to repurchase the contractual cash flows of the bond from the time of the bond’s first call date until the maturity date.

Consider the following two bonds: (1) a callable bond with an 8% coupon, 20 years to maturity, and callable in five years at 104 and (2) a 10-year 9% coupon bond callable immediately at par. For the first bond, the bondholder owns a 5-year option-free bond and has sold a call option granting the issuer the right to call away from the bondholder 15 years of cash flows five years from now for a price of 104. The investor who owns the second bond has a 10-year option-free bond and has sold a call option granting the issuer the right to immediately call the entire 10-year contractual cash flows, or any cash flows remaining at the time the issue is called, for ...