Suppose that Bigco is currently trading for $100 per share. We are offered a European call option to purchase one share with an expiration date in one year. We know that on the expiration date Bigco stock will sell for either $120 per share (a “good day”: probability = 80%) or for $80 per share (a “bad day”: probability = 20%). No other prices are possible. The stock will not pay any dividends during the year. The riskless interest rate is zero, so a bond can be purchased (or sold) for a face value of $100 and has a certain payoff of $100 in one year. Stocks, bonds, and options can all be bought or sold, long and short, without any transactions costs.
What is call premium (value of call) with strike price of $100?