Put writer payoff diagrams

If I were to buy a put option with a fifty dollar excercise price and if I were to buy it for $10.00, then the value of my position the payoff for that put option, at the maturity or at the expiration I should say. At the expiration of the option. Depending on what the stock price is, and expiration would look like this: if the stock price is worth, if the stock price goes to zero then the put option is worth fifty because I could buy the stock at zero and excercise my option to sell at fifty. At "putting" the stock to someone else at fifty dollars. All the way to if the stock becomes worth fifty then my put option, I wouldn't need to excercise it because why would I? It's worthless to have the option to sell something at fifty where you can just sell the actual stock in the open market or buy the stock at fifty. So then the put option becomes worthless for a stock price above that. Now, this is the payoff diagram. And this is when we just think about the value and expiration. If we think about the actual profit and loss at expiration, it would look like this It would just be shifted down by ten dollars because we have to pay $10 to get this value. So if the stock is worth zero, the put option is worth $50, but I spent $10 dollars to get it, so the profit is going to be $40 dollars. And so then at $50, I wouldn't excercise the put option so I've lost the $10 dollars I spent on the option so my payoff diagram would look like, I'm gonna draw it, relatively neatly. My payoff diagram would look like this Once again, this payoff diagram just incorporates the price of the option So it's the actual profit. This is just the value at expiration, depending upon what the value of the stock is at expiration. Now this is just a situation if you were to buy an option but there has to be someone on the other side of the contract someone who's holding, agreeing to buy the option for you So you could actually have the writer, you could actually have the writer, of the put the payoff diagram we just showed is the person who owns the put, but someone else had to have created the put. They said, "Oh, you know what, I will give you the right. "I will give you the right to sell, to sell me the stock at $50, up to some expiration date." So what does their payoff diagram look like? Well if this guy is going to be able to make $50, this guy over here the writer of the put, the writer of the put is going to lose $50. He's going to have to essentially go out he's actually going to have to buy that $50 put or buy that $50 stock from this person because he has to uphold his side of the transaction but he's buying something for $50 that's worthless because based over, at this end of the axis, the stock would be worth nothing so he's taking a $50 loss, all the way to him not having to do anything because the put holder won't actually excercise their options if their stock price is $50, so their payoff diagram is going to look like this So you can see it's actually the mirror image of the payoff diagram of this person on the other side of the contract And if you were to add these two payoff diagrams, you would be neutral, because all of the money is exchanging hands between the buyer and the seller of the put. If you look at the actual profit or loss if the put is not excercised then the writer of the put essentially just got a free $10 He sold the put, he sold the put to this guy for $10 He created the put and sold it to that guy for $10 the put is not excercised, he gets to keep that $10. But then if the stock goes down and he's forced to buy the stock from the owner of the put he has to buy it because that's his side of the deal then all of a sudden he loses money So he would go, if all the way down if the stock is worth nothing, He is forced to buy something for $50 that is worth nothing He would take a $50 loss, but he paid the $10 on the actual price of the option so it would be a negative $40 profit So his profit and loss would look like this But once again, these are the mirror images of each other.