Consider a long position in a 6-month forward contract on a 1-year coupon bond w

Question

Consider a long position in a 6-month forward contract on a 1-year coupon bond with a 8% quarterly coupon. (Note: The bond has 1-year to maturity as of t=0). Assume a face value of $1 million. Use the discount factors for August 15, 2000 in Table 5.9 to find the forward price at t=0. Assume delivery would occur just after the coupon at t=0.5 has been made. Now assume that 3-months have gone by (i.e. it is now November 15, 2000).See table 5.9 for the Nov. 15th discount factors. What is the value of the original forward contract now?

Table 5.9
Maturity z(0,t)
0.25 0.9844
0.50 0.9690
0.75 0.9531
1.00 0.9386

Please show all calculations

Explanation / Answer

Value of forward contract (t=0.5)=P.V of Face value at delivery-P.V of remaining coupon

Value of forward contract(t=0.5)=1000000*0.9690-(0.08*100000/4)*0.9690-(0.08*100000/4)*0.9844

Value of forward contract (t=0.5) = 965093.2

Value of forward contract after 0.25(3 months have passed) =P.V of Forward value-P.V of remaining coupons

Value of forward contract after 0.25= 965093.2*0.9844-(0.08*100000/4)*0.9844

Value of forward contract after 0.25(3 months have passed) =948068.9461

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