The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

LATTICE MODEL

The first complication in building a model to value bonds with embedded options is that the future cash flows will depend on what happens to interest rates in the future. This means that future interest rates must be considered. This is incorporated into a valuation model by considering how interest rates can change based on some assumed interest rate volatility. Given the assumed interest rate volatility, an interest rate “tree” representing possible future interest rates consistent with the volatility assumption can be constructed. Since the interest rate tree looks like a lattice, these valuation models are commonly referred to as lattice models. It is from the interest rate tree (or lattice) that two important elements in the valuation process are obtained. First, the interest rates on the tree are used to generate the cash flows taking into account the embedded option. Second, the interest rates on the tree are used to compute the present value of the cash flows.

For a given interest rate volatility, there are several interest rate models that have been used in practice to construct an interest rate tree. An interest rate model is a probabilistic description of how interest rates can change over the life of the bond. An interest rate model does this by making an assumption about the relationship between the level of short-term interest rates and the interest rate volatility as measured by the standard deviation. A discussion of the various interest rate ...