Consider a stock whose stock price is 100 on January 1st. This stock pays a dividend of 4 at the end of every quarter. You are Holding a Forward contract with delivery date of one year. Assume the interest rate is 6% compounded continuously.
a) What is the no-arbitrage Forward Price for the above Forward contract?
b) If you want to sell your Forward contract on July 1, 2016, what no- arbitrage price will you be able to get, if the stock price is 105 on that day.
For part a, how do I account for the dividends being paid quarterly?
Part I
$S_0 = 100$
$F_{No-Aribitrage} = S_0e^{0.06} - 4e^{0.75*.06} - 4e^{0.5*0.06}-4e^{0.25*0.06}-4e^{0} =89.82 $
Part II
$S_0 = 105$
$F_{No-Aribitrage} = e^{0.5*.06}*S_0 - 4e^{0.25*0.06} -4e^{0} =100.13$