Question $4$: Contains four parts, $($a$),($b$),($c$),$ and $($d$).$

Consider the following potentially relevant information. Assume that all rates given are

continuously compounded and are risk$-$free.

$S_{\text{U}\text{S}\text{D}}=$$$1\mathrm{.}30$ CAD

$r_{\text{U}\text{S}\text{D}}=0\%$

$r_{\text{C}\text{A}\text{D}}=2\%$

${}_{\text{U}\text{S}\text{D}}=0\mathrm{.}20$

Question $4($a$)$ : Using the Black$-$Scholes$-$Merton model find the price of a $3-$month

European call option to purchase a US dollar at a strike price of $$1\mathrm{.}25$ in Canadian

funds.

Question $4($b$)$ : Calculate the Delta $\frac{ac}{d5}$ of the same call option.

Question $4($c$)$ : Calculate the Gamma $\frac{de{l}^{2}C}{del{s}^2}$ of the same call option.

Question $4($d$)$ : Calculate the Vega $\frac{\text{d}\text{e}\text{l}\text{c}}{\text{d}\text{e}\text{l}}$ of the same call option.