Question

A European put option on the common stock of XYZ Ltd. is currently selling for a price of $2 per share. The expiration date of the put is 3 months from now. The relevant interest rate is 4% per annum. The exercise price of the put $30 per share and the size of one put is 100 shares.

Suppose Ms. Parker sells 20 of these puts now, find her profit (loss), assuming the spot price of the stock on the expiration date to be equal to either (i) $15 or (ii) $40.

Secondly, find the break-even level of the spot price of the stock on the expiration date.

Answer 1

Given the current price of the put option is $2 per share

We know that the when we buy a put option we have a right to sell and when we sell a put option we have an obligation to buy.

Here Ms. Parker sold 20 put options hence total amount he has received is 20*2*100 = 4000

Now when we invest these initial sale proceeds for a period of 3 months we get 4000 + 4000*0.04 * 3/12 = 4040

Now when spot price at expiration is $15 -

We have the exercise price as $30

Now since we have an obligation we have to check if the other party will exercise or lapse his right

Accordinlgy when the other party has right to sell at 30 and in the market it is $15 he will exercise the option

Hence loss to Ms. Parker will be 15 per share

Total Loss will be 15*20*100 = 30,000 for all the 20 puts with underlying 100 shares

Now we have earned some intial income by selling the put and also interest on it which is equal to 4040

Hence net loss = 30,000 -4040 = $25960

Now when spot price at expiration is $40 -

the other party has right to sell at 30 and in the market it is $15 he will lapse the option

Hence the profit on the put option will be initial income plus the interest earned on investment = $4040.

Break Even level of spot price

THis is the point where we will have no profit and loss

That means our loss will be equal to initial income plus interest earned by investing the sale proceeds

Let Loss = X

X *20 *100 = 4040

X = 2.02

Hence the share price should be below exercise price of 2.02 inorder to break even

That is break-even spot price is 30-2.02 = $27.98

Note- Since interest has been given we have taken the investment interest income to calculate various items like profit/(loss) and break even .