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Consider a 3-year bond with face value $1000 and annual coupon rate 4%. The coupon is paid semi-annually. a) Suppose the yield-to-maturity is 3%, derive the current bond price, and its duration and convexity. b) Suppose the yield-to-maturity increases from 3% to 3.1%, derive the corresponding bond price. Question 3 Suppose the yields of five zero-coupon bonds with maturity from 1 year to 5 years are y1=9%,y2=9.25%,y3=9.9%,y4=10.5%,y5=11% a) Is the yield curve upward sloping or downward? b) calculate the one-year to four-year forward rates, i.e., f1,f2,f3,f4 ? Consider a one-year forward contract on a stock that will pay dividend $4 in six months from now. The forward price is $40, and the annual risk-free rate is 3%. Derive the current stock price according to the no-arbitrage condition. Question 5 Consider a one year forward contract whose underlying asset is a coupon paying bond with maturity date beyond the expiration date of the forward contract. Assume that the bond pays coupon at the end of every June and December and the annual coupon rate is 10%, and the face value of the bond is $1000. Suppose now it is March 1st and the current market price of the bond is $950. Taking the annualized risk-free rate as 10%, find the forward price of this bond forward