Question

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).

120 #25 110 #28 100 100 #26 #30 90 #29 0 #27

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.

Use the computed q to sweep back through the tree to fill the call values in circles. For #28 - #30 use the option terms, then for nodes #28 - #30 use the recursive formula:   C = q C_u + (1-q) C_d. Ignore interest.

#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.

Answer 1

Q25. Payoff on the call option = Max [ stock price - exercise price , 0 ]

Call value = Max [ (120-93 ) , 0 ] = 27

Q26

Call value = Max [ (100-93 ) , 0 ] = 7

Q27.

Call value = Max [ (80-93 ) , 0 ] = 0