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# Put payoff diagram

Video transcript

We have company ABCD trading at $50 a share Let's draw a payoff diagram for a put option with a $50 strike price trading at $10 So once again we get to draw two types of payoff diagrams One type that only cares about the value of the option at expiration. This is what you tend to see in academic settings like business schools or textbooks. And the other one will actually draw a profit and loss based-on that option position, so incorporate the price you actually paid for the option. You tend to see this more in practice. So you have a put option. Remember, this is the right to sell the stock at $50. So the stock let's say at expiration. All of these are at expiration. At expiration the stock is trading at $0, the company went bankrupt. Now it's worthless. What is the put option worth? You would now go on the market, buy it for almost $0 , and then you would exercise your put option and then you would sell it for $50. So you would definitely excerise it, and you'd make a lot of money the underlying stock can be bought for $0, the put option is now worth $50, because you can buy it for 0 and sell it for 50 dollars. if you have the put option. If the underlying stock price is $10, then you could still go to buy the stock for $10. If you had the option, you would excercise the option to sell it for $50, so you would make $40. So, the option would be worth $40. And anyone who's holding the option would make instant $40. So, the value of the option becomes less and less, as the value of the stock becomes more and more, up until you you get to $50. At $50 you wouldn't really care you have the right to sell something at $50, which you could buy for $50. So, it's kinda worth nothing. The value of the put option could start at $50, because you have the right to sell something worthless at $50, if the stock's going bankrupt After $50, it becomes the option. You don't really doesn't have any value anymore. And if the stock goes anything above %50, it's still worthless. If the stock is $100 or something like that, there's no way you could exercise the option. because why would you excercise the right to sell something at $50, while in the open market you can sell it at $100. Let's do the same thing for the profit/loss version. So, the stock is worth nothing, you can buy it for nothing, and then if you have the option, sell it for $50. But, we have to incorporate the fact that you paid 10 dollars for the option. So, instead of the option is worth $50, we would say it's worth 50 minus this So, it'd be worth $40. And this is all the way you would exercise the option all the way until the option is worth $50 But at $50, instead of saying it's worthless, you have to remember, if the stock is 50$, you wouldn't exercise the option. But you did pay $10 for it. So, you wouldn't exercise something that you paid $10 for so you would have to take a $10 loss. so the option started at 50, and it'd become less and less, all the way to the point that if you don't exercise it, you would took the loss of paying for the option. not exercising it. And any stock price above that, you just took a $10 loss.