A central problem in finance is answering the simple question: How much is this contract worth? For example, Bob might say he’ll give me $102 in a year, and I want to know how much I should pay him for that guaranteed money. If I figure out that the value of the contract is a $100, then I’m saying that the guaranteed $102 in a year is worth $100 today. This means I get a 2% interest on my $100 investment. This is called the one-year spot rate, and there are similar rates for all sort of different time frames. Taking 1/ (1+.02) gives me the discount rate and multiplying this by the $102 payment gets me to the $100 value of the contract.
The next step is that I may want to know how much $102 two years from now is worth next year. So instead of figuring out what it is worth today, I want to know what it will be worth in a year. To figure this out, I need something called the forward rate, which tells me the annual interest rate one year in the future, in this example.
With the forward rates, I can take a complex series of future payments and find the value of all of those payments today, but also the value at different points in the future. The complexity is that depending on when I want to value them to and the timing of the payment I need to use different sets of forward rates and that’s the application I’ll walk through below.
That is a novel use of the “table in a cell” technique.