Question

(A bond forward) A certain 10-year bond is currently selling for $920 A friend of yours owns a forward contract on this bond that has a delivery date in 1 year and a delivery price of s 940. The bond pays coupons of $ 80 every 6 months, with one due 6 months from now and another just before maturity of the forward. The current interest rates for 6 months and 1 year (compounded semiannually) are 7% and 8%. respectively (annual rates compounded every 6 months). What is the current value of the forward contract? First solve for the current forward price Ft of the bond:
Hint Ft d,M) に1 d(k,M) S=920 d(0, M)- d(2, M) c(k)- 80

Answer 1

Answer: -$100

Explanation:

Value of forward contract = Selling price - Forward price on bond

Forward price = Present value of cashflows + Present value of bond

Periodic rate = 7%/ 2 = 3.5% per semi annum

= 8% / 2 = 4%

3.5% will be used to discount the payment 6 months from now as that is the 6 month rate. The rest will be 4%.

= (80 / (1 + 3.5%) ) + ( 80 / ( 1 + 4%)²) + (940 / ( 1 +4%)²)

= $1,020.342

= $1,020

Value of forward contract = 920 - 1,020

= -$100