An Introduction to Financial Markets

Chapter Three Elementary Theory of Interest Rates

The time value of money is one of the key ingredients in finance. We need a way to move cash flows backward and forward in time, in order to analyze and compare investment opportunities, as well as to come up with financial plans. In this chapter, we introduce the fundamental concepts related to interest rates, such as compounding frequencies, discount factors, the term structure of interest rates, and forward rates.

Interest rates are a key risk factor in the pricing of fixed-income assets, which include a multitude of securities, ranging from plain bonds to rather complicated interest rate derivatives. In this chapter, we only deal with elementary bond pricing, which can be accomplished without the need for dynamic models accounting for the uncertainty about interest rates in the future. Such advanced models shall be introduced in Chapter 11, whereas we rely here on a static picture of interest rates. Despite its (apparent) simplicity, this enables us to tackle some quite relevant problems:

• Given two bonds, how can we compare their return?
• Given a set of bond prices, how can we check whether there are arbitrage opportunities?
• How can we estimate the amount of money that we need to save each year, during our working life, in order to achieve a given target wealth at retirement?
• How can we measure the interest rate risk of a plain bond?

As an introduction to the issues involved in comparing investment opportunities, let us ...