A stock sells for $100 today. Over each of the next two years the stock will either increase in value by 10% or decrease in value by 5% with probabilities of 70% and 30% respectively. This means, for example, that in one year the stock will sell for 100 ×1.10 = 110 with 70% probability or for 100 × 0.95 = 95 with 30% probability. (Please note that these probabilities are "physical" probabilities, NOT the risk-neutral ones!) The stock then increases or decreases in price from these points over the following year. The one-period risk-free rate in each period is 2%. 

(a) Consider a European call option on the stock where the option has two-years to maturity and is currently at the money (exercise price of $100). 

What should be the price of this option? 

(b) Suppose that the option in 5a is selling for $8. Could you take advantage of this price? If so, how?