A forward contract for 4 months is entered into when a stock index is at 1000. I

Question

A forward contract for 4 months is entered into when a stock index is at 1000. If the risk free interest rate is 3% per year (with continuous compounding) and the dividend yield on the index is 2% per year, what is the futures price?

After 1 month the index price is 980, what is the value of the futures agreement assuming the risk free rate with continuous compounding is now 5% (but the original dividend rate remains 2%) and the contract price is equal to $50 times the index value?

Please answer both parts, the forward/futures price at 4 months and the value of the futures agreement after 1 month.

Explanation / Answer

1)future price= spot price*e^(r-a)*t
r=risk free rate
a=dividend yield
t=time to maturity
=1000*e^(3%-2%)*(4/12))
=1003.34
value of difference between new forward price and prior aggreement at the discounted rate
=(spot*e^(-q*t))-(k*e^(-r*t))
=(908*e^(-2%*0.25))-1003.34*e^(-5%*0.25)
=-15.76
loss in dollars=50*-15.76=788.15

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