Time is money. A dollar today is better than a dollar tomorrow. And a dollar tomorrow is better than a dollar next year. But just how much is that time worth — is every day worth the same or will the price of money change from time to time?

The interest rate market is where the price of money is set — how much does it cost to have money tomorrow, money in a year, money in ten years? Previously we made the modelling assumption that the cost of money is constant, but this isn't actually so. The price of money over a term depends not only on the length of the term, but also on the moment-to-moment random fluctuations of the interest rate market. In this way, money behaves just like a stock with a noisy price driven by a Brownian motion.

The uncertainty of the market opens up the possibility of derivative instruments based around the future value of money. Bonds, options on bonds, interest rate swaps, exotic contracts on the time value of different currencies, are all derived from basic interest-rate securities, just as stock options are derived from stocks in the market. In nominal cash terms, the market for such interest-rate derivatives far outstrips that for stock market products. Fortunately we shall still be able to calculate the prices of these contracts on exactly the same risk-free hedging basis as before.