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How to Price and Trade Options with Robinhood

Hello guys. So a friend and I, we had a discussion about options and I thought of making a video to explain how they work. I'm uniquely qualified to do that because I know very little about it. The more I know on a subject, the more difficulties for me to explain. So probably I'm just in the sweet spot that I know just enough, but not a lot. So I can probably explain still. Why somebody would bother about options. As I explain in my cashflow video, if options make sense or not for you, depends on which phase of your life you are. If for example, you don't have lots of assets and you don't want value retention, you have some disposable income every month and what you want is capital gains. Putting for example, $1,000 in a stock and waiting for a year and if the year is really good you get 20% returns, which means that you just got $200 out of it.

You know, is this going to make a difference? Probably not really. On the other hand, you might decide to use leverage and if there are crazy swings on the price, you might lose your money overnight without actually being wrong just because of volatility. So this might also not be really good, but with options you have a limited downside if you're buying options and you can make money if the stock goes up or if the stock goes down. And this money can potentially be disproportionally a lot. So it looks like a leveraged product. So yeah, I think it's really cool to know how to use those as well. And this might be quite attractive and it reminds a lot of cryptos that you buy a coin and there is volatility and all you can lose is the money you put into the coin. But it has the potential to go up.

So somebody who's used on trading cryptos might find options more familiar than trading stocks. So I'm going to show you with the example of Apple how this works. Options weren't really accessible to people, but our good friend Robert Hood made them accessible to everyone. So actually you have a stock like Apple and then you go trade and trade options and it is that simple. And here on the top you can find expiry dates and I will explain what that is and you can see there are long term options, like even for January, 2025 that are available, they have prices. There's the center point where it's the current price of the stock and then there are different price points that you can have and you have two main options, call and put and you can buy and sell them. Probably you should never sell

because this has the potential of unlimited loss. every option has a price. For example, this 140 put for January 17, it costs $25. So you can click on that and then you can buy for example, 10 of those and they will cost you $25,000. Now if you click here, there is this diagram that shows how much you will earn or you will lose at different price points of the stock. This is the payoff at the expiry date. So if at the expiry date, the price is exactly the same as it is today, $138. Actually you see that I lose 25,000. So I use the entire amount. If it is 115, so it dropped quite a bit, then it becomes zero. My payoff, and this is the break even point. So up to the break even point, you don't make money, you actually lose money but a bound amount of money and beyond that you start making money.

When you buy a put option, it's like you are shorting the stock and you can see there the max profit is 115,000. In order to do that with traditional stocks, you would have to short 831 shares of apple and that would be pretty expensive, especially if one day the price of apple go to thousands of dollars, you would have to cover that with the option. the maximum you can lose is bound and you can get all the upside for your position. And if the market moves your way for a couple of days and you're actually profitable, you can sell it on spot and get the profit. If you have a call option, then you get reverse this diagram. So actually it's a little bit like being long on the stock, believe it will go up and the break even point is in this case 173.

So you start making money there. So this might explain a little bit how trading practically works in Robin Hood, but the question is still how do we know if a price is relatively high or low? We don't have lots of intuition about the prices we get here. What we know now is that on the expiry dates, either we are going to have a valuable option or the value of the option is going to be zero, which effectively means that we lost money. But those options, we cannot just trade them today or at the expiry date. We can trade them at any point in time and the prices change dramatically, especially if we are far away from the expiry date or if we are close to the expiry date and the strike price of the option is very close to the price of the underlying asset. So we have to have a way to think about pricing options.

The Bible for options is options, features and other derivatives from Hull. It's a technical book, it has lots of equations and it explains everything in detail and I'm going to use a few ideas from there. So an option is not a stock, it's a derivative. This means that its price depends on the price of an underlying asset. So in the case of stock options, this would be the price of a stock. An option gives you the right to buy or to sell at a specific price at some point in the future. A call option of $150 for March 17th allows you to buy at 150. And the put option allows you to sell. For calculations we can use an online option pricing calculator. If the price of Apple is 160 and the strike price of the option is 150 at the expiry date. So we put here one and let's ignore all the other parameters for now.

We put calculate. So what this diagram says is that since we buy this call option for $10, if the price is 150, then we lose these $10. If it's 160, then we make zero. If it's 170, then we make $10 profit. Then on 180 we make $20 profit and so on. Okay, so this is where options get really interesting because they have this extra dimension which is how many days ahead the expiry date is. So exactly the same option. If we say that it expires in 30 days, how does the price change? So we can see here that it became more expensive. So instead of $10, now it's worth $14. If we change again the expiry date to 131 days, which is actually how many days remain until that day from today then it becomes even more expensive. So $22 and that is assuming that the underlying price is 160.

With today's price of 138, the price is $10. Now where do all those numbers come from? They come from the Black-Scholes formula that we can see here. Quite complicated, but the important thing is the variables it has and they also map to what a calculator has. So you can see here interest rate goes into play, especially if the option is far in the future. This helps project net present value. Dividend yield is somewhat important because by buying the option and not the underlying, we don't take any dividend profit. So this has to be taken into account. But the most important variable here is volatility really. So where can we find those numbers for a stock? If we Google the stock and volatility, they're well known for every stock. So dividend yield, that's exactly what I've put there. And then you have the historical volatility and the implied volatility.

So you plug those numbers in there and then you get this pricing. Let's see how these maps to Robin Hood. So 150 call is priced at 8.20 and the theoretical value is $10.50. That means that the market disagrees highly likely about the volatility since the other numbers are kind of fixed. So if I try to find here what value volatility gives me this price, we see that 36 seems to be closer to the price we're looking for. This is called implied volatility. So it's the volatility of the market prices in contrast to what you see in current data. Might be also that the market disagrees on the value we have on the interest rates and this influences the price a little bit also. But there is something missing in this equation. There is no way to express your position. For example, if you see a trend going up or down or if you know about market conditions or other significant events for the company, you cannot really put them in that equation. Most often

this is the most important source of disagreement between the implied volatility and the volatility you see on the data of the underlying asset. You can see that options close to the current price are pretty expensive and this percentage here is how much it changed during the last trading day. So you can see that the changes are pretty small, but if you go far away up you can find some options that are really, at least they look cheap, right? So here is one that is 8 cents. In order to break even with this one you would have to go very up. So the price of apple should be 240 and then you can see even with $800 of downside, the maximum profit is like insane. But this is not the question we are really asking here. We know that the price of the call option is now 8 cents. If we wanted to double our money, the question is what should the price of the underlying asset be? So after we fit the implicit volatility to 36, let's see what price will make this to go to 16 cents.

So we can see that if in a few days the price of Apple becomes $145. Actually this option will have double this price. This means that those $800 would become one half thousand. So if you have specific events like you expect for example Apple to release great products or you think it'll fail miserably for some reasons, maybe it's preferable to use an option instead of buying or shorting stocks with leverage. And I'm going to give some more kind of intuition and leave it there. So if the current price is 138, then if we assume that the future price at the expiry date follows a gaussian distribution, if we were just one day before expiry, then given some volatility, the probability that the price is going to be 150. So a huge jump in the price from 138 to 150 is highly unlikely.

On the other hand, if the volatility is even larger than this, sigma becomes larger and the probability you will have a price above 150 becomes more likely. Now if we have an option far away in the future and we are pricing months in advance, the probability that the price will be above 150 becomes even larger. Options can also be thought as insurance contracts because they allow you to assume a certain price level at a given date. They can be combined with other instruments and they can give very interesting profit and loss curve. You can actually do pretty much everything you want. For example, straddle is when you buy a call and a put at the same price. And you can see what happens here. Actually, you start making profit no matter if the price of the stock goes up or down as long as the price doesn't remain in a narrow area. This allows you to effectively trade volatility. So when you hear that this year, the prices are very volatile. Some people make money by using options just by that, no matter if the stocks go up or down. Pretty interesting stuff and pretty interesting that you can do those things yourself with Robin Hood. So that's all I have to say right now about options trading. I hope you find it useful and thanks for watching.


* "Options, Futures, and Other Derivatives" book:

* Pricing calculator:

* Volatilities for Apple:

* Duration calculator:

* The Black-Scholes Model Formula:

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