Valuation, Liquidity, and Net Income
Chapters 6 through 9 introduced modern multifactor interest rate models of Heath, Jarrow, and Morton (HJM). In this chapter, we introduce some of the key issues for the practical application of the HJM concepts. We spend the rest of the book addressing these issues in great detail, but we start here with an overview of the most important topics.
HOW MANY RISK FACTORS ARE NECESSARY TO ACCURATELY MODEL MOVEMENTS IN THE RISK-FREE YIELD CURVE?
In Chapters 6 and 7, we implemented a one-factor model of yield curve movements in the HJM framework. We extended that to a two-factor model in Chapter 8 and a three-factor model in Chapter 9. This begs the question, How many risk factors are necessary to accurately model the movements of the forward rates (zero yields, and zero prices) of the risk-free curve? There are two answers. The most important is the perspective of a sophisticated analyst whose primary concern is accurately reporting the risk that his or her institution faces. The second perspective is that of a sophisticated regulator. We address these both in turn.
We start with a perspective of a sophisticated risk manager whose primary concern is accuracy in modeling. There are two conditions for determining the risk number of risk factors driving the yield curve: