2. Two-step Binomial Tree (15 points) Step: n=0 n=1 n=2 Consider the above two-step binomial tree, with each step being three months, =0.25. The stock price is shown on the tree. The annual risk-free rate is 5%. u= Su/St=1.05, d=1/u. There is no dividend from the stock. 1) Consider an at-the-money European call option (S=K) with six-month maturity a) What is the payoff to this call option at the expiration date at each possible stock price? b) Calculate the call option fair value today. 2) Consider a European put option with six-month maturity and a strike price of $90. a) What is the payoff to this put option at the expiration date at each possible stock price? b) Calculate the put option fair value today. (Bonus question, 10 points) Calculate at-the-money American call option (S=K) with six-month maturity St=100 Su=105 Sd=95.23 Suu=110.25 Sud=Sdu=100 Sdd=90.70

2. Two-step Binomial Tree (15 points) Consider the above two-step binomial tree, with each step being three months, t=0.25. The stock price is shown on the tree. The annual risk-free rate is 5%. u=Su/St=1.05,d=1/u. There is no dividend from the stock. 1) Consider an at-the-money European call option (S=K) with six-month maturity a) What is the payoff to this call option at the expiration date at each possible stock price? b) Calculate the call option fair value today. 2) Consider a European put option with six-month maturity and a strike price of $90. a) What is the payoff to this put option at the expiration date at each possible stock price? b) Calculate the put option fair value today. (Bonus question, 10 points) Calculate at-the-money American call option (S=K) with six-month maturity