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5.2 A FEW FUNDAMENTAL CONCEPTS OF THE BOND WORLD

5.2.1 Par

The price of a bond is expressed as 100 times the percentage of its principal value. The principal value is the amount the investors will receive at maturity: this means that 100 is taken to be the full amount. When the price Bt of a bond is equal to 100 we say that the bond is worth par. We have already encountered the concept of par when dealing with swaps and we have already mentioned how, only mathematically though, a bond is similar to the leg of a swap.

Bonds tend to be issued at par, that is, an investor pays the amount that he is expecting to receive at maturity. We already see how this means that at the issue date one of the variables of Equation 5.1 is fixed: B0 = 100.

If the price is given and the discount factors Di are known, then would all issuers in one currency issue bonds of similar maturity with the same coupon simply chosen so as to lead to 100 when discounted? Of course not.

Within the Euro zone, for example, we know very well that the coupon on a German bond will be much smaller than the coupon on a, say, Spanish bond. This is because we have not considered yet the element of credit.

A further issue with the price of a bond is the concept of accrued interest. Accrued interest is the amount accrued by the coupon between the last coupon date and now. We call the price given by Equation 5.1 clean price and the price given by the clean price plus the accrued interest is called the dirty price. On coupon dates the two prices will be equal, otherwise the dirty price is, of course, always higher: this is to compensate the seller of a bond for the missed coupon payments. If one investor sells on March 1 a bond that pays every first day of December and June, the investor who buys the bond, on the following June 1, will receive the full coupon although he will only have held the bond for half of the accrual period: to compensate the seller he pays the dirty price.

 
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