Question: find the price to be written in a forward contract for delivery of the

Question

Question: find the price to be written in a forward contract for delivery of the bond at t=1

2. (10 points) A bond is being considered as possible investment. The bond has two years to run, and in two years will pay the face value of 10,000 dollars. The bond pays yearly coupons of 500 dollars. A coupon has just been paid to the current owner, so if you purchase the bond your first coupon will be one year from now. Suppose the current term structure of interest rates is: (s1,20.04,0.05). The first rate is for funds to be lent for one year, starting now. The second rate is for funds to be lent for a period of two years, starting now, compounded annually Let doj be the discount factor for the period from now to j years from now: cash receivedj years from now is multiplied by doj to determine the present value of the cash. The discount factors do,j and do.2 are determined by the term structure of interest rates given above.

Explanation / Answer

Given: I1=0.04 and I2=0.05

Since we need to find the present value of an amount to be received in the future discount factors

d0,1=1/(1+i1)=1/1.04 = 0.9615 and d0,2=1/(1+i2)2 =1/(1.05)2 = 0.9070 at time t=0

at time t=1 , d11=1/(1+i2) =1/1.05 =0.9524

Thus at t=0

NPV of the bond = 500(d0,1+d0,2)+10000d0,2=500(0.9615+0.9070)+0.9070*10000 = 10004.25

At t=1

NPV of the bond = (500+10000)d1,1 =10500*0.9524 = 10000.2

Thus the Forward contract had to be priced atleast at $10,000.2 at t=1 (and $10,004.25 at t=0 which must be the least price the owner has brought for.)

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