Consider a zero coupon bond with face value F, maturity date T, and yield y. Calculate the bond's value, duration, and convexity under continuous compounding. Consider n different fixed-income securities with prices P1, P2, ..., P, and convexities C1, C2,...,Chi, respectively. Assume that all securities have the same yield. Prove that the convexity C of the portfolio consisting of these securities is given by C= where P = P. You have an obligation to pay 2,000 in exactly 2 years from now. There are three different bonds in which you can invest (short selling is allowed). Relevant data about these bonds is provided in the table below. Find the portfolio that immunizes the obligation against first and second order changes in yield if continuous compounding is used. 2 Obligation Bond 1 Bond 2 Bond 3 Face Value 2,000 100 100 100 Coupon Rate 0% 0% 0% 0% Maturity Date 13 Yield 10% 10% 10% 10% Hint: In addition to matching the prices and durations, you should also match the convexities. Consider a zero coupon bond with face value F, maturity date T, and yield y. Calculate the bond's value, duration, and convexity under continuous compounding. Consider n different fixed-income securities with prices P1, P2, ..., P, and convexities C1, C2,...,Chi, respectively. Assume that all securities have the same yield. Prove that the convexity C of the portfolio consisting of these securities is given by C= where P = P. You have an obligation to pay 2,000 in exactly 2 years from now. There are three different bonds in which you can invest (short selling is allowed). Relevant data about these bonds is provided in the table below. Find the portfolio that immunizes the obligation against first and second order changes in yield if continuous compounding is used. 2 Obligation Bond 1 Bond 2 Bond 3 Face Value 2,000 100 100 100 Coupon Rate 0% 0% 0% 0% Maturity Date 13 Yield 10% 10% 10% 10% Hint: In addition to matching the prices and durations, you should also match the convexities