Explaination of Long Put Option Trading with example. Payoff Function of Long Put Option Explained with example
In our previous series, we had covered Trading Long Call Option and then we also covered the Trading Short Call Option with Payoff Functions.
In this series we cover the Long Put Option which we will explain with an example and payoff function diagrams of Long Put Options.

Long Put Option Trading Strategy

To begin with, a Long Put Option position is one in which you take a BUY position of a PUT option. So say for example, you buy a Put option on Microsoft with a strike price of $30 and you pay $5 for buying the put option. At the time of buying, suppose that the actual Microsoft stock (i.e. the underlying) is trading at $29.
Now, since you BOUGHT a Put Option, hence you have a LONG position, that's why it is called a LONG PUT option position.
Have a look at the payoff function of the Long Put Option Position which is as follows.

Payoff Function for Long Put Option

For the time being, ignore the price ($5) you paid for buying the put option. So theoretically, you have the PINK colored payoff function for Long Put option at the strike price of $30. It will give you profit only when the stock price of the underlying (i.e. Microsoft stock price), goes below stike price of $30. So if the unerlying stock price ends at $25, you get a profit of $5 ($30 - $25 i.e. Strike Price - Underlying Price).
However, that is theoretical as we did not consider the price of $5 you paid for buying the Put Option.

Break Even Point for Long Put Option Position
Considering the $5 price you paid, the payoff function needs to be adjusted for that and since you PAID $5, it will be taken as negative and hence the theoritical PINK colored payoff function will shift down by that amount ($5) and then we will have the RED colored payoff function, which actually shows profit and loss considering the price paid for options.
Hence, if the price of the underlying microsoft shares ends at $25, then as per the Red payoff function, you are at No Profit, No loss. The reason is that theoritically, your profit is (Strike Price - Underlying Price = $30 - $25 = $5). However, you already paid $5 for purchasing the option. So even though you get $5 on the expiry day, your profit and loss is zero since you had paid $5 upfront for taking this put option.
This therefore becomes the break even point for your Long Put Position.
Break Even Point for Long Put Position = Strike Price - Put Option Premium Paid

Step by step video explanation for trading Long Put option See Video - Long Put Option Trading explained with Example