Question

The price of a stock is $60. The price of a one-year European put option on the stock with a strike price of $45 is quoted as $10.5 and the price of a one-year European call option on the stock with a strike price of $75 is quoted as $7.5. Suppose that an investor buys 100 shares of stock, shorts 100 shares of call options, and buys 100 shares of put options.

(a) Show the profit (loss) table for the combined position (long stock, long put, and short call) if ST $75.

(b) Draw the profit (loss) graph for (a), illustrating how the investor’s profit or loss varies with the stock price over the next year.

Answer 1

Solution:

In the given case investor has bought share at $60. So if share price rise investor gains and if falls investor looses. further he has also sold call option for $7.5 at a strike price 75. this means if stock price rises above $75 he has pay money to the buyer of call, but at the same time he will gain in stock appreciation so the loss will be nullified. Futher he buyed put option at $10.5 at a strike price of $45, this means if price goes below strike price he will receive money from seller of put, but again this profit will be nullified by fall in stock price.

Here is the table showing pay off and profit at stock price of 75

Stock prices in Future	Pay off from Share bought at price $60	Pay off from call option sold at $75	Pay off from call option buyed at $45	Net Premium paid	Profit
75	15	0	0	-3	18

   

Here I am showing graphically how profit will move with the changes in stock price. here I will show profit at vertical axis and prices at the horizontal axis. It will be clear from the graph that Maximum profit= $18, Maximum loss=$12