$1.$ The USDISK exchange rate is currently ISK $140$ per USD $1.$ The continuously compounded risk$-$free rates

in ISK and USD are $5\%$ and $3\%,$ respectively. The volatility is $15\%$ per annum.

$($a$-$b$)$ Use a five$-$step binomial tree to value an $10-$month European put option on USDISK, with a strike equal to

the $10-$month forward USDISK exchange rate.

$($c$-$d$)$ What is the price if the put is American? In which nodes are gains made by being able to exercise early?

Which nodes form the optimal exercise boundary for the holder of the put option $($i$.$e$.$ when does the holder

actually exercise the option$)?$

$($e$)$ Whatis the initial delta for the European put? What does it imply for a trader that has sold the European put

on USD$10,000$andwants to hedge that position? How does the delta change and his hedge if the exchange

rate moves up in the first step? How does the delta change and his hedge if the exchange rate moves down

in the first step? $($Please provide answers for your calculations$)$