Bonds: It′s All About Discounting
Before we delve into all the good stuff (swaps and options), let us review some fixed income basics.
TIME VALUE OF MONEY: FUTURE VALUE, PRESENT VALUE
Following the classical fixed income gospels, we remember that the Future Value, FV, on a horizon date of an investment PV at an annual interest rate of r , compounded m times a year, for N whole compounding periods is
For example, if m = 1, we have annual compounding FV = PV(1 + r )N, and N is the number of years until the future horizon date. If m = 2, we have semiannual compounding (standard for U.S. Treasury securities) FV = PV(1 + r /2)N, and N = 2T is the number of whole semiannual periods until the horizon date (T years from now).
The above formula can be easily generalized to incorporate horizon dates that are not a whole number of compounding periods away. We compute T as the number of years between the investment date and the horizon date, according to some day count basis, and come up with:
From college math courses, we recall that as you increase the compounding frequency, the above, in the limit, becomes
is then referred to as the continuous
An alternative to using compounded rates is to use simple or noncompounding interest rates:
where T is the number of years (can be fractional) to the horizon ...