1)The current stock price is $100, the strike price of American call and put is $110, the present value of the strike price is $105, the time to maturity of both options is 1, and the price of the American call is $4. Which of the following is a possible price of the American put and satisfies the put-call parity?

A. 4

B. 8

C. 12

D. 16

E. 20

2. In above problem, if the stock is a dividend paying stock, which of the above given choices for the price of the American put satisfies the American put-call parity?

A. 4, 8, 12

B. 12, 16, 20

C. 8, 16, 20

D. All of the above

E. None of the above

 

Answer:

1.) C. 12

2.) B. 12, 16, 20

Step-by-step explanation

1.) For American non-dividend paying stock, put-call parity is...

S0 - K < C - P < S0-PV of K

where S0 = Spot price = $100

K = Strike price = $110

C = Call premium = $4

P = Put premium = ?

PV of K = Present value of strike price = 105

Putting all the value in call put parity equation. We can get -10 < 4-P < -5

By solving this we can get Value of P between 9 and 14.

So, among given option only possible value between this two is $12.

2.) While for Dividend paying American option call put parity can be derived as...

S0 - D - K < C - P < S0-PV of K

where S0 = Spot price = $100

D = Dividend (D>0)

K = Strike price = $110

C = Call premium = $4

P = Put premium = ?

PV of K = Present value of strike price = 105

Putting all the value in the call put parity equation. We can get -10-D < 4-P < -5

By solving this we can get the Value of P between 9 and 14+D.

Considering the value of D up to 6 only one pair satisfies the put-call parity. Which are 12, 16, and 20.

If we have any information that the value of the dividend is Less than $6 then none of the above pair can satisfy the put-call parity.