Exercise 4 [20 points] We consider a 2-year binomial model for a stock S valued at $100 at t=0. The risk free rate is 2%, u = 1.1 and d = u1 . Question 1 [5 points] Compute at t=0 the and the of a European put option P on S, with strike K = $100 expiring at t=2. Question 2 [4 points] Create at t=0 a replicating portfolio, constituted of cash and stock, for P. Question 3 [4 points] We consider a European call option C on S, with strike K=$100expiringatt=2. Att=0,theofCis0.04andtheofCis0.05. Create a -neutral portfolio using P, C and a short position ot two units of the stock S. Question 4 [4 points] Compute at t = 0 the value of an American option Pa on S, with strike K = $100 expiring at t=2. Question 5 [2 points] Compare at t=0 the value of P and Pa. How do you interpret the difference ? Question 6 [1 points] Is there a node in the tree where the early exercise of Pa is optimal ?

Exercise 4 (20 points] We consider a 2-year binomial model for a stock S valued at $100 at t=0. The risk free rate is 2%, u = 1.1 and d=1 Question 1 [5 points] Compute at t=0 the A and the I of a European put option P on S, with strike K = $100 expiring at t=2. Question 2 (4 points] Create at t=0 a replicating portfolio, constituted of cash and stock, for P. Question 3 (4 points] We consider a European call option C on S, with strike K = $100 expiring at t=2. At t=0, the A of C is 0.04 and the T of C is 0.05. Create a AT-neutral portfolio using P, C and a short position ot two units of the stock S. 0 the value of an American option Pa on S, Question 4 (4 points] Compute at t with strike K = $100 expiring at t=2. Question 5 (2 points] Compare at t=0 the value of P and Pa. How do you interpret the difference ? Question 6 [1 points] Is there a node in the tree where the early exercise of Pa is optimal ? Exercise 4 (20 points] We consider a 2-year binomial model for a stock S valued at $100 at t=0. The risk free rate is 2%, u = 1.1 and d=1 Question 1 [5 points] Compute at t=0 the A and the I of a European put option P on S, with strike K = $100 expiring at t=2. Question 2 (4 points] Create at t=0 a replicating portfolio, constituted of cash and stock, for P. Question 3 (4 points] We consider a European call option C on S, with strike K = $100 expiring at t=2. At t=0, the A of C is 0.04 and the T of C is 0.05. Create a AT-neutral portfolio using P, C and a short position ot two units of the stock S. 0 the value of an American option Pa on S, Question 4 (4 points] Compute at t with strike K = $100 expiring at t=2. Question 5 (2 points] Compare at t=0 the value of P and Pa. How do you interpret the difference ? Question 6 [1 points] Is there a node in the tree where the early exercise of Pa is optimal