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Call Options

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Let's discuss long call options. Data is very straightforward. It's saying that at a time in the future, we have the right to buy at a price we decide today. So let's do a little example here we have a timeline. This is your present time times zero. This is your time, the future time one.

And let's say we wanted to get this right to buy in the future. So we'll have to purchase a long call option for let's say, $1. And so what's going to happen is that in the future, we're going to have the right to buy the future asset at a price that we decided today. So what's gonna happen is we're going to receive that asset in the future in this case is $102. We're gonna have to pay the price we agreed today. This is also known as a strike price.

We should account for the price we paid for the option in the first place. And so in this example, we actually ended up with a profit. So we exercised our call option or used our call option. And that allowed us to purchase at the strike price we agreed today and receive the value of the asset in the future. But what happens if the asset in the future isn't actually higher? Well, it's a little different, because we're not going to want to exercise.

So let's walk you through this. If you were to exercise, what would happen? Well, you would receive, let's say, something that's a little bit less, you will receive the asset, but you would pay even more. So you're already ending up with a negative value of profits, that doesn't make any sense. And you're going to actually lose out more Then if you had just not exercised, if you're not decided to use your rights, you would just cut your loss at your original price that you paid for the call option. So if the value of the asset goes down, you're not going to exercise your call option, you're just going to let it go.

So let's take a look at this visually, because I find a visual representation is the way you really understand how options work. So if we were to take a look at this, we have a payoff diagram is the best way to see this. And it's where you have profits on the y axis. And you just have the value of the asset stock or bond on the x axis. And essentially it works like this. You realize what is the price you have to pay for the call option.

You figure out your strike price in this case, that was $100. And that's the time But you agreeing you can exercise your call option. So this is where you start, you realize this is your beginning point, I had to pay $1 for that call option. So this is the price that we begin at. And if the call if the value of the asset goes down, we're not going to exercise our call option. So we're going to start off with a negative profit of $1.

But if the price of the asset goes up, we're just going to make profit. And in this case, our break even point will be the price of the stock with the asset plus whatever you had to pay for your call option, so in this case, $101 is that breakeven number in this example, and anything greater than that is just pure profit. So this is how you can visualize What a call option is going to do with a payoff diagram. Now, there are actually several different kinds of options out there, there's many types. Let's take a look at a few of them. The simplest one is the American call option.

And that's where essentially you're saying that between now and in the future, if you have a call option, you can use it, you can exercise it at any time between now and a specific future date. Let's say this is February 5. anytime between today and February 5, you can use your call option. European option is a little different. It's saying that only on that specific day, in the future, you're allowed to use the call option, you're not allowed to use it on any other day. A B muting option is saying that you can use it on any of these few selected specific dates. So that's going to depend on your contract.

Of course. And then on any of those days, you can exercise your call option. Exotic options get a little bit crazy because you might not always have the right to buy, you might on a certain day have the right to sell. You can have exotic options working the other way as well where someone else might have the right to buy from you or the right to sell Do you call options on specific dates. And Asian option is quite a different principle. It's saying that we're looking at not the specific price of an asset on any given day.

Rather, we're going to look at the average price of a stock a bond over time. And that average is what we're going to compare to at the end of the day. So when we were looking at our earlier example, right now, we might have a strike price of $100 that we agree on today. And this average we're not looking at any specific point We don't care about these little points, we'll only care about the average, if the average went up to let's say, $102, then we get to exercise and receive that value. So that's quite a different way of looking at or looking at behavior over time. And the digital call option or auction is also known as a binomial option.

And if we had a payoff diagram again, you're able to see that a digital option is instead focusing on instead of unlimited profit where we earlier had our example, it just goes up forever. What we're instead we're going to say is, you can only make a certain amount of profit, but you make all that profit. So let's say if we were looking at our original strip recreation of 100. You're going to exercise and you immediately make a certain amount of money but you don't make anything more. You just always make that same amount of money. So binomial option looks a little bit like this, when you see a payoff diagram, you make a specific amount of money, but only that amount of money and you make that all or you make nothing.

So these are the different types of options that you have available. And now you understand the different combinations that you can have, how you draw them and how they work.

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