Suppose the price of a stock is today is $100. We would like to use the binomial pricing model to price a call option on this stock with exercise price 8100 and expiring in one year. We break the year into two 6-months consecutive periods. We know that after the first 6-month period the price of the stock will have evolved with either a multiplying factor of 0.8 or a multiplying factor of 1.2. From that point, after the next 6-months the price of the stock will have evolved with either a multiplying factor of 0.8 or a multiplying factor of 1.2. Suppose risk-free interest rate is 2 percent.
- Find the possible prices for the stock after one year.
- Find the payoffs of the call option after one year.
- Find the price of the call option today.