Why does bond price tend to 100?

Question

For example: if a bond got a 1% coupon, and tomorrow is the maturity date, so tomorrow I will have 101.

So, in my opinion a bond price should tend to notional+coupon, because today I want this amount of money to be at par. Where I am wrong?

Answer 1

There’s two prices for a bond:

1. Invoice or dirty price: what you actually pay; and
2. the clean price, which is the dirty price less accrued interest.

In market convention, the clean price is the quoted price.

Accrued interest starts off at \$0 at a coupon date, and then rises (roughly) linearly each day until it matches the value of a coupon at the coupon date. The exact formula is a fixed schedule that depends upon market convention.

If you buy a 1% annual coupon bond one day before maturity, you will probably have a clean price very close to \$100. The accrued interest will be very close to \$1, and so the dirty price would be close to \$101.

The deviation of the clean price from \$100 would depend on the deviation from 1% for the yield you bought it at. The exact accrued interest will depend on the daycount convention in the market.

In any event, people use the clean price precisely because there is a “pull to par,” we do not have to worry about the coupon when thinking about the bond price.