Investment Theory and Risk Management, + Website

Summary

We expand the concept of the last chapter's single discount rate to include the term structure of interest rates. The term structure then motivates the concept of the forward curve and the implications of using the forward curve and its derivatives (for example, short rates) to discount cash flows that will materialize at some future point in time. Recognizing that discount rates are now time dependent random variables, we revisit the NPV methodology as well as running PV and bootstrapping.

We then extend the immunization analysis from Chapter 2 to accommodate variable term structures, specifically, non–flat term structures that experience parallel shifts. This analysis requires modifying the concept of Macaulay duration to a variable yield curve. The analog to Macaulay is Fisher-Weil duration and the duration we use in immunization is the discrete compounding analog of Fisher-Weil given by quasi-modified duration. The analysis of immunization under parallel shifts in yield curves is a very important tool in fixed income risk management for all financial institutions having long exposure to the bond market. The tools learned in this chapter apply directly to derivative pricing models, real and financial options, and structured credit models covered in Chapters 14, 15, and 18.