Chapter 6

Empirical Approaches to Risk Metrics and Hedging

Central to the DV01-style metrics and hedges of Chapter 4 and the multi-factor metrics and hedges of Chapter 5 are implicit assumptions about how rates of different term structures change relative to one another. In this chapter, the necessary assumptions are derived directly from data on rate changes.

The chapter begins with single-variable hedging based on regression analysis. In the example of the section, a trader tries to hedge the interest rate risk of U.S. nominal versus real rates. This example shows that empirical models do not always describe the data very precisely and that this imprecision expresses itself in the volatility of the profit and loss of trades that depend on the empirical analysis.

The chapter continues with two-factor hedging based on multiple regression. The example for this section is that of an EUR swap market maker who hedges a customer trade of 20-year swaps with 10- and 30-year swaps. The quality of this hedge is shown to be quite a bit better than that of nominal versus real rates. Before concluding the discussion of regression techniques, the chapter comments on level versus change regressions.

The final section of the chapter introduces principal component analysis, which is an empirical description of how rates move together across the curve. In addition to its use as a hedging tool, the analysis provides an intuitive description of the empirical behavior of the term structure. The data ...

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