Question

The current price of a dividend-paying stock is $40. The risk-free rate of interest is 2.0% per annum with continuous compounding. The stock is supposed to pay dividends in six months from now. (a) If the dividend amount is known to be $2, then the one-year forward price should be $__________ if there is no arbitrage opportunities. (b) If the dividend amount is known to be 4% of the stock price in six months, then the one-year forward price should be $__________ if there is no arbitrage opportunities.

Answer 1

a)

Forward price = (Stock price - Dividend * e^{-(risk free rate * (6 months / 12 months))}) * e^{risk free rate * time to expiry}

Forward price = ($40 - ($2 * e^{-(2% * 0.5)}))* e^{(2% * 1)}

Forward price = $38.79

b)

Dividend = 4% * Stock price

Dividend = 4% * $40

Dividend = $1.6

Forward price = (Stock price - Dividend * e^{-(risk free rate * (6 months / 12 months))}) * e^{risk free rate * time to expiry}

Forward price = ($40 - ($1.6 * e^{-(2% * 0.5)} )) * e^{(2% * 1)}

Forward price = $39.19