5 - Interest-rate models II

Abstract

This chapter explores multi-factor and whole yield curve models. In a whole yield curve, the dynamics of the entire team structure are modeled. The Ho–Lee model is a simple type of whole curve model, which allows random parallel shifts in the yield curve. Another model is the Heath–Jarrow–Morton (HJM) model, which is more commonly used than the Ho–Lee model. One-factor models describe only a single kind of change that may occur to the curve, including non-parallel (pivotal) shifts and changes in the slope of the curve. Certain two-factor and multi-factor models have been developed that seek to describe the different type of yield curve shifts. As far as the assessment of these models is concerned, in assessing the value of the different models that have been developed and the efficacy of each, what is important is how they can be applied in the market, rather than any notion that multi-factor models are necessarily “better” than the one-factor models. What is required is a mechanism that efficiently prices bonds and interest-rate options; a term structure model attempts to accomplish this by describing the dynamics of the interest rate process and generating random interest-rate paths. The generated paths are then used to discount the cash flows from the fixed income instrument.