Mathematical Techniques in Finance

CHAPTER 2Rates, Yields, Bond Math

The trade‐off between delayed versus immediate consumption and the cost of waiting is a core concept in economics and finance. Discounting the future cash flows of a financial instrument such as a stock or a bond via an appropriate rate is fundamental to their pricing. The time value of money and discounting are captured by interest rates.

2.1 INTEREST RATES

Consider an investor with $100 who invests it by depositing it in an interest‐bearing bank account for one year at an annual interest rate . In one year's time, the investor will receive the original amount deposited, $100, and the interest amount of , for a total of $104. The interest payment is in compensation for use of the money, i.e., the investor could have used the $100 for other purposes, maybe a lucrative investment, and, hence, needs to be compensated for this opportunity cost. Viewed another way, the investor is lending funds to the bank for one year and should be compensated for availing this loan.

Interest rates are generally quoted on an annualized basis, for example 4% per annum in the above case. For a loan of size , the interest amount based on the annualized interest rate ...