Q$1)$

Consider a $9-$month dollar$-$denominated American put option on British pounds.

You are given that:

$($i$)$ The current exchange rate is $1\mathrm{.}43$ US dollars per pound.

$($ii$)$ The strike price of the put is $1\mathrm{.}56$ US dollars per pound.

$($iii$)$ The volatility of the exchange rate is $=0\mathrm{.}3.$

$($iv$)$ The US dollar continuously compounded risk$-$free interest rate is $8\%.$

$($v$)$ The British pound continuously compounded risk$-$free interest rate is $9\%.$

a$)$ Calulate $u$ and $d,$ where $u$ is one plus the rate of capital gain on the stock per period if the stock price goes up and where $d$ is one plus the rate of capital loss on the stock per period if the stock price goes down.

b$)$ Using a three$-$period binomial model, calculate the price of the put.