Question

1. Consider a forward contract for one share of a stock, with T = 0.5 (6 months).
The current stock price is S0 = 50. We assume that the risk-free interest rate is r = 0.05,
and that the stock pays discrete dividends, there being exactly one dividend payment, of
size 0.75, between times 0 and T, and the payment happens at time t = 1/3 (4 months).
Calculate the price of the forward contract. Show your work. Use two decimal places in your
answer. Use sufficiently many decimals in intermediate calculations to make sure that your
two decimals in the final answer are correct.

Answer 1

Forward price is the price at which the parties agree to buy/sell specified quanitiy at specified price on predetermined date

Forward Price = Spot Price + Interest - Dividends

F = S0 + Interest - FV of dividend

= 50 + (50*0.05*0.5) - 0.75*(1+(0.5-0.33))

= $50.37

Note : As the dividend is recieved at T - 4 months, it will be invested for next 2 months hence future value at 6th month is computed