Question

Suppose that you own a call option on a non-dividend paying stock with a strike price of $40 that will expire in three months. The current stock price is $60, and the three-month risk-free rate of interest is 4% with continuous compounding. Suppose that you short the stock and invest the proceeds for three months. What is the value of your combined position in the call, the stock, and the investment in three months if the stock price is greater than $40? What is the value of your combined position as a function of the stock price in three months if the stock price is less than $40?

Answer 1

Suppose the stock price after 3 months happens to be $50. So the call is excersised in the favour of the buyer, i.e. the buyer can now buy the stock at $40 (strike price).

After 3 months the profit to the buyer is as follows :

Settle the long position in the option by buying the stock : ($40)

Deliver the stock to close the short position : $0

Recieve investment proceeds 60 *(1.04)^3/12 :        $ 60.59 (approx)

Therefore profit to the buyer = $20.59 (60.59 - 40)

Suppose the stock price after 3 months happent to be $35. The call is lapsed and the buyer can buy the stock from the market at $35.

After 3 monts the profit to the buyer is as follows :

Buy the stock from the market and close the short position : ($35)

Recieve investment proceeds 60 *(1.04)^3/12 : $ 60.59 (approx)

Therefore profit to the long = $25.59 (60.59 - 30)