Problem $4.($Forward curves, $\backslash (8^\{\backslash$prime$\}\backslash ))$ The risk$-$free interest rate is $\backslash (3\backslash \%\backslash )$ annualized and continuously compounded. Assume the market is frictionless. When you plot the forward curves below, you may choose to either $($i$)$ use the analytical expression of the forward curve to plot it accurately and smoothly, or $($ii$)$ find forward prices for $\backslash (\backslash$mathrm$\{$T$\}=0,0\mathrm{.}25,0\mathrm{.}5,0\mathrm{.}75,1\backslash ),$ and linearly interpolate between adjacent points.

$($a$)$ Plot the forward curve for stock forward contracts with the underlying stock paying no dividends. The current underlying stock price is $\backslash (\backslash$$ $10\backslash )$ per share. $(3\text{'})$

$($b$)$ Plot the forward curve for currency forward contracts with a constant foreign interest rate of $\backslash (5\backslash \%\backslash ),$ annualized and continuously compounded. The current price of foreign currency is $\backslash (\backslash$$ $8\backslash )$ per unit. $(\backslash (\backslash$left$\mathrm{.}3^\{\backslash$prime$\}\backslash$right$)\backslash )$

$($c$)$ What do the shapes of forward curves in $($a$)$ and $($b$)$ tell you about how the underlying asset prices will change in the future? Discuss. $(2\text{'})$