Explain Option Trading: Farmer Fred invents the option
Now you know the basics about what an option is and the terminology used by option traders. There is one neat little tool you should be familiar with which we will look at now: The PAY-OFF DIAGRAM.
A Pay-off diagram is a graph that gives you an overview of the option. We will make a graph of how the value of the option depends on the price of the underlying. Let’s use the example of the call option that Gus wrote to Fred. It’s important to be clear about from who’s point of view we’re looking at the option. After all, any loss that Fred makes means that Gus makes a profit of the same size. You will see when we have drawn the pay-off diagrams for both Fred and Gus that they are the mirror images of each other.
Try to draw this diagram yourself. Your learning becomes much more solid from working with these things than from reading. On the X-axis we’ll have the price of the underlying. I our case the price of fuel. On the Y-axis we’ll put the pay-off. Let’s start with the pay-off for Farmer Fred. Fred has a call option with a strike price of 10$. From previously we know that Fred will exercise his option if the price of the underlying goes to 11$. Being able to buy from Gus at 10$ when the market price is 11$ means that Fred got a 1$ pay-off from making the deal with Gus. We also know that if the underlying price goes to 9$ Fred throws his option away and buys the fuel in the market instead (or from Gus at 9$). Fred has gained nothing from his agreement with Gus and thus the pay-off is zero.
The two outcomes we have considered are marked in the pay-off diagram above. We continue calculating Fred’s pay-off for different prices of the underlying and connect the dots. The result is the graph below.
Continuing with Gus’ pay-off, we already know that Fred will not exercise the option if the market price is 10$ or below. If the price is 11$ per gallon Fred will exercise the option and Gus will have to sell fuel to him for 10$. If Gus had not written the call option to Fred he could have sold this gallon to someone else, or to Fred, for 11$. There fore Gus’ pay-off at a market price of 11$ is -1$. Calculating Gus’ pay-off for other market prices gives this diagram.
This diagram makes sense but how can there be two different pay-off diagrams for the same option? Both diagrams are call options after all. That’s because one is the diagram for the writer/seller of the call and the other is the diagram for the buyer/owner of the call. In trading terms to own something is to be LONG. To owe something, or have a negative position is to be SHORT. In this terminology Fred is long a call and Gus is short a call. A long and short position in the same instrument (option, future, forward or stock for example) are always mirrors of each other and the pay-off diagrams are mirror images.
To check that we got everything right we can sum Fred’s and Gus’ pay-offs for all prices of the underlying. Before doing the calculations and drawing the diagram for their combined pay-offs, what would we expect it to be? Yes, Zero off course. Any money Fred makes is a loss for Gus and the other way around. No money is coming in to Fred and Gus’ agreement and no money is going out. It’s a zero-sum game. Of course in reality there would be at least one more party, the IRS, and the option would no longer be a zero-sum game but that is another story.