There is a 400-day forward contract on a 8% U.S. Treasury bond (making semiannual coupon payments) with face value of $2000 and spot price of $2,180. The Treasury bond will make next coupon payment in 80 days, and another coupon payment in 262 days. The annual risk-free rate is 5%. Assume there are 365 days in a year and continuous compounding.

 

(a)  Calculate the no-arbitrage forward price of this contract.

(b)  Assume the forward price in the contract is equal to the no-arbitrage price you computed in (a). After 100 days, the value of the bond is $2,150. Calculate the value of this forward contract to the long position and short position. Suppose now the annual risk-free rate is still 5%.