Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 38. Using the Lattice Model to Value Bonds with Embedded Options, Floaters, Options, and Caps/Floors

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

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 and mortgage-backed securities.

Keywords: lattice model, recursive valuation process, option-free bond, callable bond, binomial interest rate tree, putable bond, capped floater, callable capped floater, interest rate cap, interest rate floor, step-up callable notes, range floater, option on a bond, option-adjusted spread, ...