Put options

Hello, could anyone help me with this exercise?:
"You bought a put option on a stock with a strike price of $5. Suppose that the stock is currently traded at $6 per share, what is the payoff your put option position?"
Thank you!!

Reply 1

DataVenia

Volunteer Team, Clearing and Applications Advisor

A put option represents the right (but not the obligation) to sell the underlying stock at a specified price (the strike price) on or before a specified date (the exercise date).

The question says that the stock is currently trading at $6 per share, but doesn't tell us whether we've yet reached the exercise date. (European options can only be exercised on the exercise date, whilst American options can be traded on or before the exercise date). I guess we'll have to assume that exercising the option today is valid (either because today is the exercise date or because this is an American option).

If we exercise the option, and sell the stock at $5 per share we're actually making a $1 per share loss - because the stock is currently trading at $6 per share (and we could just sell the stock at $6 per share on the open market instead). In reality we wouldn't exercise this option (it's a right, not an obligation) and would simply let the option expire. So the payoff is $0. (Note that the question might be assuming that you always exercise the option - even if you'd make a loss - and so might want an answer of -$1 per share. I think that's unlikely though.)

The question doesn't talk about the premium we'll have paid to buy the put option, which will have been non-zero. So, in reality, we've lost money even if we don't exercise the option.