A bond will trade at a discount when it offers a coupon rate that is lower than prevailing interest rates. Since investors want a higher yield, they will pay less for a bond with a coupon rate lower than the prevailing rates—the upfront discount makes up for the lower coupon rate.
#1 – Distressed Bond Trades at a significant discount to face value, Such bonds may or may not make interest payments. Or the timings of payment might be delayed. Hence investors in such bonds are speculating.
A bond rating agency may lower the credit rating of an issuer. The lower rating means increased risk, so the bond will trade at a discount to compensate investors for the additional risk.
When selling a bond at a discount the interest lowers below the coupon rate. This causes the bond's price to rise above its par value.