Question

A Stock currently trades at a price of S0=100 and is scheduled to pay the following dividends:

At time 0.2, a cash dividend of $8 per share will be paid. 2. From time 0.25 to time 0.75, dividends are paid continuously at a rate proportional to its price. The dividend yield is 6%. 3.At time 0.8, a cash dividend of $6 per share will be paid. 4.The continuously compounded risk-free interest rate is 5%.

Find the price of a one-year prepaid forward contract on stock ABC.

Answer 1

Spot Price = 100 | At t = 0.2, D = 8 | At t = 0.25 to 0.75, Div Yield = 6% | At t = 0.8,D = 6 | Rate = 5%

Forward Price formula = Spot Price * e^{(R - Div Yield)*T} - Dividend * e^R(T-t)

Since continuous dividend is paid for 0.75 - 0.25 = 0.5 period, hence, we will compound Spot Price with (R -Div Yield) for 0.5 period and remaining will be at R.

Forward Price = 100 * e^0.5*5% * e^{0.5*(5% - 6%)} - 8*e^5%*0.8 - 6*e^5%*0.2

Solving the above equation, we will get the price of one year forward contract.

Forward Price = 87.6333 or 87.63

Hence, price of the forward contract is $ 87.63