 A bond price is the current price of its copons and principal repayment that occurred over its entire life till its maturity. Formerly bond price is the price that a one is willing to pay at present for future coupon and principal repayment on the bond. So we can say that basically the bond price is the present value of its copons and the present value of its repayment. Now to determine these present values we used a certain discount rate. This present value is then depends upon the market interest rate and that market interest rate is used as the discount rate. For risky bonds the discount rate may carry certain additional specific characters like default risk, liquidity risk and other attributes like the call risk etc. Now how to compute the bond price? We have an example where the value of an 8% 30 years bond with power value of 1000 dollars if the discount rate is 7%, 8% and 9%. Then what this bond will be valued? We use the present value formula of determining the price of the bond. If we put into the formula values at 7%, 8% and 9%, we get 1125 dollars for 7% discount rate, 1000 at 8% discount rate and that discount rate is equal to our coupon rate 897 dollars at 9% discount rate. So we see that as we increase our discount rate the price of the bond goes on falling. Now what is convex tree with reference to the bond? Convexed tree is basically the relationship between the bond prices and the bond yield. It is a property of a bond prices because the bond price curve is convex with reference to the interest rate that is used to discount the bond. The curves shape implies an increase in the interest rate resulting in the price decline. In the following picture if we see at the horizontal level or the x axis if we see that our interest rate goes on decreasing, it goes from left to right then at the vertical axis or the y axis we see that the price goes on increasing, it goes on decreasing. So with the increase in our discount rates the price of the bond goes on decrease and that relationship is the convex tree of the bond. We see also that the following curve shows inverse relationship between the bond price and the discount rates. What is the difference between the bond prices and the yields? The prices of any outstanding bond may fluctuate inversely with the market interest rate in the secondary markets. A bond's maturity determines its price sensitivity to the fluctuations in the interest rates. This means that longer the bond's maturity greater the price sensitivity to changes in the interest rates. This means that we have greater discounting power in the bond's valuation. So we can say that short term tables are taken as the safe and less sensitive to changes in the interest rates in the secondary market.