Question

Now suppose Stock A is dividend-paying, with $1 dividend paid for each 3 months. The spot price of a Stock A is $5, and the risk-free rate of interest is 8% per annum with continuous compounding. (d) What are the main differences between forwards and futures? (e) What are the forward price and the initial value of a one-year forward contract on one share of Stock A? (f) Four months later, the price of the stock is $6 and the risk-free interest rate is still 8%. What are the forward price and the value of the forward contract?

Answer 1

d) Forward contract is similar to Futures contract except that Forward contracts are specific and tailor made to the needs of the parties, are more costly , are traded Over the Counter (OTC) and have default risk whereas Futures contract have fixed specifications, less costly , traded on the exchange and do not have default risk.

e) Forward price = (Spot price - present value of dividends) * exp (r*t)

where r is the continuously compounded risk free rate

and t is the time till maturity in years

Assuming that a dividend has just been paid

Present value of dividends = 1*exp(-0.08*3/12)+1*exp(-0.08*6/12)+1*exp(-0.08*9/12)+1*exp(-0.08*12/12) = $3.81

So,  Forward price = (5-3.81)*exp(0.08*1)

=$1.29

Initial value of the forward contract= present value of benefits

Since the forward contract is entered into at the theoretical price of $1.29 , the initial value is 0

f)  Present value of remaining dividends = 1* exp(-0.08*2/12)+1* exp(-0.08*5/12)+ 1* exp(-0.08*8/12) = $2.90

Forward price after 4 months = (6-2.90)*exp(0.08*8/12) = $3.27

Value of the forward contract to the buyer of the forward = (3.27-1.29)*exp(-0.08*8/12) = $1.87

(Value to the seller of the forward contract will be -$1.87)