Fixed Income Mathematics

Chapter 20: Variable and Uncertain Cash Flows

OVERVIEW

In this chapter, we apply the probability concepts studied in Chapter 18 and the spot rate curve concepts studied in Chapter 19 to learn how to evaluate flows of funds that vary in size, are uncertain, or both. Like the previous chapter, this represents a change in our viewpoint from the earlier chapters. Previously, we assumed that all payments would be made in full, when due, and based all the calculations on that assumption. We now change that to allow for the chance that a payment may not be made. This represents a change, just as in the previous chapter we introduced the idea of differing interest rates for different bond payments. We used varying interest rates, another change from the early part of the book.

We first look at a series of examples, using a simple flow of funds. You should be able to expand this to longer and more complicated fund flows without any real problem.

We apply a single interest rate to evaluate a varying flow of funds. We then apply the probability concepts to this varying flow of funds and compute the value of the flow. We apply varying interest rates to the variable flow of funds and then apply a combination of varying interest rates and probabilities to the same variable flow of funds.

We apply the results to several different business applications, including insurance and project analysis.

Mostly, this chapter, and the next two chapters, don t introduce new concepts but rather apply concepts...

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