There are three ways to buy bonds: premium purchase, that is, the purchase price is greater than the face value; Buying at a discount means that the purchase price is less than the face value; Equivalent purchase means that the purchase price is equal to the face value. If the coupon rate of the bond is equal to the market interest rate when the bond is actually issued, the bond should be issued at parity (the issue price is equal to the face value of the bond); If the coupon rate is higher than the market interest rate when the bond is actually issued, the bond should be issued at a premium (the issue price is higher than the face value of the bond), and the premium part will be used as compensation for the issuer to pay more interest according to the coupon rate than the market interest rate in the future; If the coupon rate is lower than the market interest rate when the bond is actually issued, the bond should be discounted according to at discount (the issue price is lower than the face value of the bond) as the price at which the issuer will pay less interest according to coupon rate than the market interest rate in the future.
Bond premium or discount is essentially to balance the interest income of bond investors and the interest expenditure of bond issuers. According to the pre-adjusted interest income and expenditure to protect the interests of both parties, any price has the same impact on investment enterprises. For premium, parity and discount bonds, the faster the interest payment frequency of discount bonds, the lower the bond value, which is negatively correlated; The interest-paying frequency of parity bonds changes, and the bond value remains unchanged; The faster the audit frequency of premium bonds, the higher the value of bonds, that is, there is a positive correlation. As the maturity date approaches, the value of premium bonds will gradually decrease to the face value of bonds; The value of discounted bonds gradually increases to the face value of bonds, while the value of parity bonds remains unchanged. With the shortening of the term, the change of discount rate (which can be understood as market purchase cost) will have less and less influence on the bond value, that is to say, the bond value will become less and less sensitive to the specific change of discount rate.