Consider the following binomial tree. The numbers in squares are stock prices. The numbers in circles will be option prices (# numbers are the exercise numbers to answer your calculation).

Today, the stock is at 100 and can go up and down over the next week, and then again up and down from there. We are pricing a call struck at 93.

#25 Call Value =

Hint: Here, we are at expiry. The stock price is in the square. The strike price is 93. What is the payoff?

#26 Call Value =

Hint: Here, we are at expiry. The stock price is in the square. The strike price is 93. What is the payoff?

#27 Call Value =

Hint: Here, we are at expiry. The stock price is in the square. The strike price is 93. What is the payoff?

#28 Call Value =

Hint: Here, we are one week prior to expiry. We apply the recursive formula: C = q C_u + (1-q) C_d.

#29 Call Value =

Hint: Here, we are one week prior to expiry. We apply the recursive formula: C = q C_u + (1-q) C_d.

#30 Call Value =

Hint: Here, we are two weeks prior to expiry. We apply the recursive formula: C = q C_u + (1-q) C_d. to the up and down circle values from the middle layer.

31.

Compute and interpret the delta. If you sell a call option on one thousand shares, the delta hedge will require you to buy _________ shares of stock (how many?).

Hint: Look where Node #30 can lead to. Apply the formula Cup - Cdn divided by Sup - Sdn. That gives you the delta per share; times 100 shares, and you get the delta number of shares you need to buy.