Consider the binomial problem below

Annual risk free rate is equal to 12%. Current stock price is equal to $75 per share. The stock could goes up by 22% or goes down by 10% at the end of the year. You want to evaluate a European option on this stock with the maturity of one year.

 

a) Price a call option on this stock with the exercise price X = 80.

 

b) Price a put option on this stock with the exercise price X = 80.

 

c) Verify if the results you get from a) and b) satisfy put-call parity?