$1)$ The following American option prices were observed for CBA Inc. on

August $5$th$.$ The share price at that time was $$75\mathrm{.}80.$ CBA does not pay

dividends.

Note: In your answers to this question use $365$ days per year. You should use

continuous interest compounding in any calculations that you think require it$.$

For example, the $10-$day continuously compounded risk$-$free rate is $8\mathrm{.}15\%$ per

year.

a$)$ What is meant by the intrinsic value of an option? Provide a brief

explanation. Use the September $80$ call option and September $80$ put option

to illustrate your answers.

b$)$ As an option trader, you suspect that the August $75$ call option is underpriced relative to the August $75$ put option. Using an appropriate noarbitrage bound on the price of the call option, demonstrate how this bound

is violated, leading to an arbitrage opportunity. Outline how you would set

up a trade to generate risk$-$free arbitrage profits.

$\backslash$table$[[,$Calls,,,Puts,,$],[$Strike$,,$Aug,Sep,Nov,Aug,Sep,Nov$],[$x$,15^($th $),19^($st $),13^($th $),15^($th $),19^($st $),13^($th $)],[75,3\mathrm{.}4500,7\mathrm{.}5500,9\mathrm{.}2000,3\mathrm{.}2500,5\mathrm{.}9500,7\mathrm{.}7500],[80,1\mathrm{.}2000,4\mathrm{.}2500,7\mathrm{.}1000,6\mathrm{.}4500,8\mathrm{.}5000,9\mathrm{.}1000],[$T $($days$),10,45,100,10,45,100],[$r$^($c$)($T$),0\mathrm{.}0815,0\mathrm{.}0850,0\mathrm{.}0890,0\mathrm{.}0815,0\mathrm{.}0850,0\mathrm{.}0890]]$

$3)$ Explain the relationship between the value of a call option and time to expiry