A flat bond is a description given to a bond being sold in a specific circumstance, namely that any accrued interest on the bond is not included in the deal. This means the flat bond is being sold at its so-called "clean price" rather than its "dirty price."
A bond is a popular type of debt security, meaning it is a tradable asset in the same way as a company stock, but the holder does not have an ownership stake in the company. Instead the company owes money to whomever owns the bond, which may not be the person who originally bought it from the company.
Both public agencies and private companies issue bonds as a way of borrowing money. Investors give the issuer money and they have the right to redeem it on a set date in the future. As a form of interest, the issuer makes a payment or payments to the holder known as the coupon. This can either be a regular payment annually, or a lump sum on the redemption date. Both the amount of interest offered and the price investors pay when trading the bonds on the open market are affected by how confident they are that the issuer will repay the bond rather than default, for example after bankruptcy.
When one investor sells a bond to another investor before it is due for redemption, she will likely want the sale price to include some compensation for the interest she has "earned" but not yet received. For example, if a bond issuer pays interest every December, a bondholder selling in June will likely want the sale price to include something close to half of the annual payment. Market prices are usually listed either as clean, meaning they are based solely on current demand for the bond without taking account of accrued interest, or dirty, meaning they are adjusted for accrued interest.
In certain circumstances, the bond being sold may not have accrued any interest, a situation described as a flat bond. There are three main reasons this could have happened, the first is that the issuer has already defaulted on making interest payments, making the sale price of such bonds usually very low. Another reason is simply that there is no interest payable on the bond; usually this means the issuer sold the bond at a discount below its face value to attract buyers. The third reason for a flat bond is that the next scheduled interest payment is to be made on the redemption date; in this case it can be argued the seller has received all the interest to which he is reasonably entitled.