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

Chapter 37. Yield Curves and Valuation Lattices

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: The complication in valuing bonds with embedded options and option-type derivatives is that cash flows depend on interest rates in the future. Academicians and practitioners have attempted to capture this interest rate uncertainty through various models, often designed as one- or two-factor processes. These models attempt to capture the stochastic behavior of rates. In practice, these elegant mathematical models must be implemented numerically in order to be useful. One such model is a single factor model that assumes a stationary variance, or volatility.

Keywords: interest rate lattice, yield curve, one-factor model, binomial interest rate tree, recursive valuation

An often used framework for the valuation of interest rate instruments with embedded options and interest rate option–type derivatives is the lattice framework. Effectively, the lattice specifies the distribution of short-term interest rates over time. The lattice holds all the information required to perform the valuation of certain option-like interest rate products. First, the lattice is used to generate the cash flows across the life of the security. Next, the interest rates on the lattice are used to compute the present value of those cash flows. ...