actuarial science

A coupon bond has a spot price of $900. The bond will pay coupons of $50 in 6 months and in one year. The risk free rates are 8% (per year continuously compounded) for 6 month maturity and 10% for one year maturity.

(a) Find the delivery price for a one year forward contract on the bond, with delivery immediately after the coupon payment.

(b) Suppose that immediately after the first coupon is paid, the continuously compound risk-free rate of interest is 9% for 6 month maturity, and the spot price of the bond has risen to $950. Determine the value of the short position in the original forward contract entered at time 0.