Question

You buy a European call option for a stock. The premium paud for this put option is $15. The pricd is $200. You are now at the maturity of this option.

(a) If the price at maturity is $210, what is the optimal decision? Calculate and explain possible choices.

(b) What are the profits/losses for the seller of this option? Explain.

(c) What is the breakeven point? Explain.

Answer 1

Call Option is a contract that gives the owner (buyer) the right but not the obligation to purchase an underlying security at a predetermined price (strike price) at a specified time in the future.

Premium is the price paid by the buyer to the seller of the call option for the reservation of the right to purchase at a predetermined price(strike price). The owner (buyer) of the option should pay the premium upfront, which is the price (cost) of the option. Note that even if the option is exercised or not the premium is retained by the seller.

Exercising the right by the buyer will depend on the actual price of the underlying security at the time of maturity.

• If the price of the security is above the strike price, the option will be exercised by the buyer paying the strike price.
• If the price of the security is below the strike price the buyer will not exercise the option and loses the premium paid upfront to the seller.

A European call option is a type of call options which can be exercised only at the maturity or at the expiration date of the contract. Unlike American option which can be exercised any time during the contract.

a.

• Premium (P) : $15
• Strike Price (S) : $200
• Price at Maturity (M) : $210

Assuming 'n' number of stocks are purchased.

The buyer would exercise the call option even though Option cost is more than the total Option value. Because it would help him to minimise his loss.

Option cost : Premium * n = 15n

Option value : (M-S) * n = 10n

Case 1: If option not exercised

Buyer bears the loss that is the cost of the option, 15n. (premium paid to the seller upfront)

Case 2: if option exercised

Buyer only makes a net loss of 5n. That is Option value minus Option cost:10n - 15n.

Case 2 is more preferable to the Buyer compared to Case 1. Hence the decision is made to exercise the option.

b.

Net profit for the seller per unit of the stock at expiration is = P - Max(M-S, 0) = 15 - (210-200) = 5

Total profit = 5n

At maturity, the price of the stock settles above the strike price which would mean a loss to the seller. But here, in this case, as the per-unit premium charged is more than the per-unit loss the seller makes a net profit of [P - Max(M-S, 0)] * n.

c.

Break-even condition: Max [ M - S, 0] = P.

It is the situation where both the parties, seller and buyer makes neither profit nor loss. For this to hold true above condition need to be satisfied.

In this particular case, if the premium is equal to $10 then at strike price $200 and Maturity price $210, the buyer and seller would be at break-even.