The current price of a non$-$divided$-$paying stock is $$140$ with a volatility of $25\%.$ The risk$-$free interest rate is $4\%$ per annum compounded continuously.

$($a$)$ For a three$-$month time step, calculate $u,d,$ and $p.$

$($b$)$ Use a two$-$step tree to value a six$-$month European call option with a strike price of $$150.$

$($c$)$ Use a two$-$step tree to value a six$-$month European put option with a strike price of $$150.$