$($a$)$ Consider a four$-$month call option on the British pound. Suppose that the current exchange rate is USD$/$GBP $1\mathrm{.}6,$ the exercise price is USD$/$GBP $1\mathrm{.}6,$ the riskfree rate on the USD is $8$ percent p$.$a$.,$ the risk$-$free rate on GBP is $11$ percent p$.$a$.,$ and the volatility of the spot rate $($and the forward rate$)$ is $10$ percent.

Required

Use Black$-$Scholes model to estimate the price you would pay for the call option $(14$ marks$)$

$($b$)$ Using a pay$-$of diagram, distinguish the following currency put options;

$($i$)$ Out of the money marks$)$

$($ii$)$ At the money

$(2$ marks$)$

$($iii$)$ In the money

$(2$ marks$)$