Fixed Income Securities, 4th Edition

CHAPTER 5Key‐Rate, Partial, and Forward‐Bucket '01s and Durations

The assumption in Chapter 4 that changes in the entire term structure can be described by one interest rate factor may be convenient and appropriate in certain situations, but applications with exposures across the term structure require more realistic foundations. Consider a life insurance company that has liabilities spread out over many years in the future. The insurer could make assumptions about how rates across the term structure typically vary with the 10‐year par rate and then hedge all of its liabilities by buying 10‐year bonds. But what if, over a particular period, the 30‐year rate falls and the 10‐year rate stays the same? The present value of liabilities would increase, asset value would be unchanged, and the insurer would experience a net loss in value.

Given that a one‐factor framework cannot reliably describe rate changes across the term structure, market participants have pursued three broad strategies. First, build a multi‐factor term structure model, based on a combination of data and market analysis. Many active hedge funds and asset managers, who build such models for investment purposes anyway, pursue this path for hedging as well. The Gauss+ model presented in Chapter 9 is an example of this approach. Second, hedge based on empirical analyses of relationships across rates of various terms. Examples of this approach are given in Chapter 6. Third, adopt a robust approach to hedging, which ...