Consider a two$-$step binomial tree, where a stock that pays no dividends

has a current price of $100,$ and at each time step can increase by $10\%$ or

decrease by $5\%.$ The annually compounded interest rate is $7\%.(30$ pts$)$

$($a$)$ Plot the binomial tree to describe this problem.

$($b$)$ Calculate the price of a two$-$year $101-$strike European call using a replication argument. $($Using a different method will deduct all the points$)$

$($c$)$ Calculate the price of a two$-$year $101-$strike European call using riskneutral pricing. $($Using a different method will deduct all the points$)$

$($d$)$ What is the price of a two$-$year $101-$strike European put?