Chapter 4

Fixed Income Mathematics

The Basic Tools

In the first three chapters, we discussed measures of risk and return in a general way. We have discussed the Jarrow-Merton put option as a measure of risk along with more traditional measures of risk, such as the sensitivity of net income to changes in risk factors and the sensitivity of the net market value of a portfolio (i.e., the value of equity in the portfolio) to changes in risk factors.

In the rest of this book, we discuss implementation of these concepts in a detailed and practical way. Implementation requires accurate and efficient modeling of market values of every transaction in the portfolio both at the current time and at any date in the future. Valuation and multiperiod simulation also require exact knowledge of cash flow dates and amounts, recognizing that these amounts may be random, such as an interest rate on a floating-rate mortgage, early prepayment on a callable bond, or payment on a first to default swap. We turn to that task now.


The concept of present value is at the very heart of finance, and yet it can seem like the most mysterious and difficult element of risk management analytics even eight decades after the introduction of Macaulay’s duration in 1938. It is safe to say, though, that no self-respecting finance person in a large financial institution should look forward to a pleasant stay in the finance area if he or she is uncomfortable with the present value concept ...

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