Consider a European call option on a non$-$dividend$-$paying stock where the stock price is $$40,$

the strike price is $$40,$ the risk$-$free rate is $4\%$ per annum, the volatility is $30\%$ per annum,

and the time to maturity is $6$ months.

$($a$)$ Calculate u$,$ d$,$ and p for a two$-$step tree.

$($b$)$ Value the option using two$-$period risk$-$neutral valuation. You are not required

to draw the tree.