1. [30 points] It is March 12. Apple Inc.s (AAPL) stock is currently trading at US$1203 per share and has a volatility of 40%. The stock has a dividend yield of 2.5%. The current risk-free rate of interest is 5% per annum. When solving the following problems, show each step.

1. What is the price of a European CALL option written on this stock with a $150 strike price that expires in 35 days? Price the option using the Black-Scholes model. Calculate the delta, d, of the CALL option and interpret. Calculate the elasticity of a call option, W, and interpret. What is a lower bound for the CALL option?
2. What is the price of a European PUT option written on this stock with a $150 strike price that expires in 35 days? Price the option with the Black-Scholes model. Calculate the delta, d, of the PUT option and interpret. Calculate the elasticity of the PUT option, W, and interpret. Calculate the volatility of the option. What is a lower bound for the PUT option?
3. Based on your answers to (a) and (b), verify the put-call parity holds.
4. What is the price of a European CALL option written on this stock with a $150 strike price that expires in 35 days? Price the option with a two-step binomial tree model. Would your answer change if it were an American CALL option? Show your work.
5. What is the price of a European PUT option written on this stock with a $150 strike price that expires in 4 weeks? Price the PUT option with a two-step binomial tree model. Would your answer change if it were an American PUT option? Show your work.
6. Using S_uu, S_ud, f_uu, f_ud, S₀ and f from 4.d., calculate the delta, D, and the elasticity, W, of the PUT option and the volatility of the option. Interpret your results.