Encyclopedia of Financial Models I

Using the Lattice Model to Value Bonds with Embedded Options, Floaters, Options, and Caps/Floors

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

ANDREW KALOTAY, PhD

President, Andrew Kalotay Associates

MICHAEL DORIGAN, PhD

Senior Quantitative Analyst, PNC Capital Advisors

Abstract: In principle, the valuation of a financial instrument is straightforward: It is the present value of the expected cash flow. For fixed income securities, the expected cash flow, ignoring the possibility of default, is the periodic interest payments and the maturity value. The interest rates used to discount the expected cash flows are obtained from an appropriate benchmark spot rate curve. When a fixed-rate or floating-rate bond has an interest-sensitive embedded option such as a call option, put option, or a cap in the case of a floater, the expected cash flow will be dependent on future interest rates. To value fixed income securities with embedded options, the lattice framework is the standard tool in practice. The same lattice-based framework is also used to value interest-sensitive derivatives such as options, caps, and floors.

We will demonstrate in this entry how the lattice framework provides a robust means for valuing fixed-rate and floating-rate bonds and interest rate derivatives. In addition, we extend the application of the interest rate tree to the calculation of the option-adjusted spread, as well as the effective duration and convexity of a fixed income ...