Final answer:
The price of the 7% coupon bond, its modified duration, and convexity can be calculated using financial formulas. An increase in yield affects the bond's price, and this impact can be estimated using both modified duration and convexity. These measures help understand a bond’s price sensitivity and its risk profile.
Step-by-step explanation:
To answer the student's question:
a) The price of a 7% coupon bond with a 10-year maturity, a $100 face value and a yield to maturity of 8% paying semi-annually can be calculated using the present value of annuity formula for the coupon payments and the present value formula for the face value.
b) The modified duration is a measure of the bond's price sensitivity to interest rate changes. It can be calculated by using the Macaulay duration and dividing it by (1 + (y/n)), where y is the yield to maturity and n is the number of compounding periods per year.
c) The convexity of a bond measures the curvature in the relationship between bond prices and yields, or the rate of change of duration as yields change. It is calculated as the sum of the present value of the bond's cash flows times the time period squared, divided by the current bond's price times (1 + y/n)^2.
d) If the yield increases by 100 basis points, the new price based on modified duration can be calculated by the percentage change in yield multiplied by the negative of the modified duration, and then multiplied by the bond's current price.
e) The new price incorporating convexity can be estimated by adding the convexity adjustment, which is the change in yield squared times the convexity measure divided by 2, to the estimated price change from modified duration.