Question

Suppose Amazon stock is trading for $ 535 per​ share, and Amazon pays no dividends.

a. What is the maximum possible price of a call option on​ Amazon?

b. What is the maximum possible price of a put option on Amazon with a strike price of $ 590​?

c. What is the minimum possible value of a call option on Amazon stock with a strike price of $ 500​?

d. What is the minimum possible value of an American put option on Amazon stock with a strike price of $ 605​?

Answer 1

Solution:

a.

The maximum possible price of the call option is the current market price of such security as on today, which is $ 535.

b.

The maximum possible price of the put option is the exercise price (strike price) as on today of such security, which is $ 590.

Note: In the absence of any rate in the question, assuming the value of strike price is the strike price as on today.

c.

The formula to calculate the minimum possible value of the call option of the security as on today is as follows:

Minimum value of call option of security = Maximum {(Current market price as on today – Strike price as on today), 0}

                                                                   = Maximum {($ 535 – $ 500), 0}

                                                                   = $ 35

Hence, the minimum possible value of the call option as on today is $ 35.

d.

The formula to calculate the minimum possible value of the American put option of the security as on today is as follows:

Minimum value of American put option of security = Maximum {(Strike price as on today – Current market price as on today), 0}

                                                                                   = Maximum {($ 605 – $ 535), 0}

                                                                                   = $ 70

Hence, the minimum possible value of the American put option as on today is $ 70.

Note: The formula to calculate the strike price as on today is as follows:

Strike price as on today = Strike price * e-rt

r is the rate of interest on per annum.

t is the time period.