Question $4$

Consider a one$-$year forward contract on a stock that will pay dividend $$4$ in six months

from now. The current stock price is $$40,$ and the annual risk$-$free rate is $1\mathrm{.}5\%.$

a$)$ Derive the forward price according to the no$-$arbitrage condition.

b$)$ Suppose the borrowing risk$-$free rate is $3\mathrm{.}5\%$ while the saving risk$-$free rate is still $1\mathrm{.}5\%.$

Derive the minimum upper bound and maximum lower bound of the forward price given no

arbitrage.