Question

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 $ 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: k=M ck) Hint: F, = dom) - Sk=1 dík,M) S = 920 M = 2 d(0,M) = .924 d(1,M) = 1 d(2,M) = 1 c(k) = 80 current value of contract = -100.324

Answer 1

The current value of the forward contract is $173.92.

Step-by-step explanation:

To calculate the current value of the forward contract, we first need to find the current forward price (Ft) of the bond. Using the provided formula for Ft, we can plug in the given values:
k = 2 (since there are two coupon payments before maturity)
c(k) = $80 (the coupon payment)
d(0,M) = 0.924 (discount factor for 6 months)
d(1,M) = 1 (discount factor for 1 year)
d(2,M) = 1.00 (discount factor for 2 years)

Now we can calculate:
Ft = $920 - ($80 × 0.924) - ($80 × 1)
Ft = $920 - $73.92 - $80
Ft = $766.08

The current value of the forward contract can be calculated using the present value formula:
Current value = (Delivery price - Forward price) × d(1,M)
Current value = ($940 - $766.08) × 1
Current value = $173.92