The current price of a non$-$dividend$-$paying biotech stock is $$140$ with a volatility of $25\%.$ The risk$-$free rate is $4\%.$ For a three$-$month time step:

$($a$)$ What is the percentage up movement? $(2$ marks$)$

$($b$)$ What is the percentage down movement? $(2$ marks$)$

$($c$)$ What is the probability of an up movement in a risk$-$neutral world? $(2$ marks$)$

$($d$)$ What is the probability of a down movement in a risk$-$neutral world? $(2$ marks$)$

$($e$)$ Use a two$-$step tree to value a six$-$month European call option and a six$-$month

European put option. In both cases the strike price is $$150.(12$ marks$)$