A stock, currently priced at $$10,$ is modelled by means of a recombining binomial tree

with $u=1\mathrm{.}1,d=0\mathrm{.}9$ and a discrete time step of $3$ months. The stock does not pay

dividends. The continuously compounded constant risk$-$free rate is assumed to be $4\%$

per annum. Consider a European call option on the stock, with time to maturity of $6$

months and a strike price of $$11.$

$($a$)(10$ points$)$ Use the risk$-$neutral pricing method to calculate the current price of the

option.

$($b$)(5$ points$)$ Calculate the current price of a European put option on the same stock,

with time to maturity of $6$ months and strike price $$11,$ using call$-$put parity