FM for Actuaries

6
Bonds
and Bond Pricing
A bond is a contract/certificate of debt for which the issuer promises
to pay the holder a sequence of interest payments over a specified
period of time, and to repay the principal at a specified terminal date.
There are various types of bonds with different features: couponpaying
bonds, zero-coupon bonds, inflation-indexed bonds, callable
bonds, etc. Different risks are involved in investing in different types
of bonds.
In a bond transaction the investor determines the price in order to
achieve a fair rate of return to compensate for the risks. We introduce
three formulas for pricing a bond, namely, the basic formula, the premium/discount
formula, and the Makeham formula. Bonds are loans
from bondholders to issuers. Analogous to the concept of loan amortization,
methods of constructing bond amortization schedules are
discussed. When bonds are traded between two coupon-payment
dates we need to extend the pricing formulas to include the accrued
interest. We distinguish between the quoted price and the purchase
price of a bond, with the difference being the accrued interest.
We will also discuss the pricing of a callable bond, which is a complex
problem due to the uncertainty about the call event. Finally, while
much of this chapter assumes a flat term structure for the purpose
of pricing a bond, we show how to extend the pricing formula to the
case of a known but nonflat term structure.