Term Structure of Interest Rates

I nterest rates and their dynamics provide probably the most computationally difficult part of the modern financial theory. The modern fixed income market includes not only bonds but all kinds of derivative securities sensitive to interest rates. Moreover interest rates are important in pricing all other market securities since they are used in time discounting. Interest rates are also important on corporate level since most investment decisions are based on some expectations regarding alternative opportunities and the cost of capital—both depend on the interest rates. Intuitively an interest rate is something very clear. Consider a payment of $1 which will be made with certainty at time t (throughout this article we will consider only payments made with certainty and consequently only risk-free interest rates). If the market price of $1 paid in time t from now is P0 , then the interest rate for time t can be found from the simple discount formula P0 = $1 (1+rt )t . The interest rate rt in this formula is known as the pure discount interest rate for time t. At this point a short and very incomplete review of bond terminology is in order. A standard bond has the following characteristics: