1. Todays price of Shake Shack (SHAK) is $40. SHAK does not pay dividends. One year from today, there are two possible states. In the u state, the economy is good and the price of SHAK is $60. In the d state, the economy is bad and the price of SHAK is $10. The c.c. risk-free interest rate is zero percent. Assume there is no arbitrage. What is the price of a call option on SHAK with a strike of $40 and a maturity of one year?

1a. What is the price of a put option on SHAK with a strike of $40 and a maturity of one year?.

2. Todays price of Capital One Financial Corporation (COF) is $50. COF does not pay dividends. One year from today, there are two possible states. In the u state, the price of COF is $100. In the d state, the price of COF is $25. The c.c. risk-free interest rate is zero percent. Assume there is no arbitrage. A power derivative has payoffs X_u = S_u² and X_d = S_d². What is the price of a power derivative on COF?

2a. A fraction derivative has payoffs X_u = S_u/10 and X_d = S_d/10. What is the price of a fraction derivative on COF?