# Forward Price with Dividends

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?

• Just keep in mind that no-arbitrage means that that if you borrow $100$ at $6\%$ on January $1$, buy the stock, hold it for one year, and sell at the forward price, you break even. Then just write out all the cash flows.
– lulu
Commented May 30, 2017 at 17:34

$S_0 = 100$
$F_{No-Aribitrage} = S_0e^{0.06} - 4e^{0.75*.06} - 4e^{0.5*0.06}-4e^{0.25*0.06}-4e^{0} =89.82$
$S_0 = 105$
$F_{No-Aribitrage} = e^{0.5*.06}*S_0 - 4e^{0.25*0.06} -4e^{0} =100.13$