Hello. In the next seven modules, we'll be discussing options pricing via transform technique. But before even we discuss exactly what we mean by options pricing or what we mean by transform techniques, let's just see what options are. What is an option? The type of derivative security, but the minute I am writing here derivative, then you wonder why I'm calling it or what is called a derivative security. The reason is because, its price, the options price is linked to the price of something else, which that something else is actually what we call underlying assets. For example, if you have stock, and then you have the option on the stock, that underlying would be actually the value of the stock itself. Now, there are two main types. Actually there's a typo here. My apologies. The two main types of options, which are called calls and puts. Now, a call option the definition is, the buyer of the option has the right, the minute we're saying the right, that means no obligation, to buy the underlying, which in this case for example could be a stock from the seller of the option at maturity. This maturity is sometime in the future, pre-specified. Some people call it expiration, for certain price which is already fixed, and his again pre-specified which is called the strike price. Now, the seller that was a buyer, now the seller is obligated. She or he has to sell the underlying to the buyer upon buyer's call, because the buyer has the right. If the buyer is calling it, then definitely the seller should sell it at that specified price which is a strike price. For sure for this transaction, the buyer pays a fee which we call a premium, for this right. The premium is exactly what we trying to value. That's called the option price. Now, the put option on the other hand, the buyer has the right, again not the obligation, to sell the underlying, the stock at a specified price, which we call it the strike price at maturity or expiration, sometime in future to the seller. The very first question will come in mind is, who are the buyers or seller of option contracts? The two main types actually called Hedgers and Speculators. Then what I will be doing is, I'm coming up with two simple cases. One for a speculator, and one for hedger to see exactly how it works. For the quiz or homework, I definitely make sure that I come up with some more for you to practice. For the, in case of a speculator, let's assume, for example, that you are speculating the Apple stock. I mean, you can imagine any stock, is going to go higher over time. Then I'm seeing over time, by overtime, you may assume three months, six months, nine months or a year from now. You need to have in mind, because your option has a maturity or expiration, if you think that you're going to go up within a year or something like that, you think about the option which expires in a year. Now the question is, if you think the apples are going to go up, what would you do? Would you buy the stock itself or would you buy a call option on this stock? I'm saying, you would buy a call option, and I'm going to explain to you why. Actually, I have a very, very simple example, you'll see why one would buy a call option as opposed to the stock itself. Now, but the next question would be, what would be the benefit of buying the option as opposed to buying the stock itself? The benefit of buying the call option, I intentionally write it the way that I'm seeing here buying one call option versus purchasing a 100 shares of Apple is, because each call option is writing on a 100 shares of its underlying. Then in that regard, I'm just saying one call option versus purchasing a 100 shares of Apple is that, the maximum loss is lower in the former. Now, let me go with this scenario for you to see how it happens. Then as you see, I'm coming up with two tables. The table above is the case that the speculator, let's say, you decide to buy a 100 Apple shares. Then a speculative bought a 100 Apple stocks at 190. Then today's price is a 190. Now, what could happen in the future? I'm looking at five different scenarios. The first scenario is the stock goes to 140. That means, as opposed to is going up, it goes down and it goes down drastically. That means you were wrong in your speculation and you went to the best-case scenario. I am assuming that, it would actually go to 240 and scenarios in-between then, either 140, 170, 190, 210 and 240. Then I'm looking at your profit and loss, the so-called P and L. Now, let's see what happens, if you bought it today at 190, and it went down to 140, peristaltic you lost $50 and knowing that you bought a 100 of them, then definitely that would become your loss. You can do this for the case of 170. In the worst case scenario, you lost 5,000, the best case scenario you gain 5,000. That's the scenarios you will be having. That's in a case that you are not utilizing a call option. Now, let's look at the next scenario. This scenario, the speculator bought a three months maturity call option. That means, he's going out there buying a call option, three months maturity in three months is going to expire at the strike 200. That means, the seller of it you bought it but the seller agreeing to sell the Apple in stock at 200 no matter what happens in three months, no matter what. But then, the buyer has the right to exercise or not and you would see how that would work. Let's say, you agreed to pay five dollars. That means, because it's written on 100 stocks you already paid $500 today, which I am writing it as minus 500, because it's out of your pocket. That's expense to you. Let's see now what happens to P&L, let's go to see what happens here. Today's price is one 190, exactly as above, future price as exactly what I'm having is 140. Let's look at the payoff. Now the payoff means, what would happen in the future. If the stock goes lower, what happens is, you're not going to go and exercise it, because you have the right, not an obligation. If it goes low, you not going to exercise. You definitely let it expire and you don't get anything, zero as far as your payoff. 170, again you decide not to exercise. 190, again you would an exercise zero. Now, if he goes to 210, now he goes higher, definitely can exercise. Then you exercising is important for you to recognize, is not the difference between 210 and 190 that you would gain. It would be the difference between 210 and the strike price of 200, because that's what he's agreeing to sell it to you. Then it becomes 210 minus 200. Then you gain $10 per stock. You multiply this by 100, that becomes $1,000. That becomes your payoff. 240 again becomes 240 minus 200 just take 40 multiplied by a 100, that becomes $4,000. That's the payoff. But the P&L for you would be whatever payoff is, minus what you pay day one. That's fee premium that you paid. Then for here is minus 500, because there wasn't any pay of minus 500, minus 500. Here you the payoff was $1,000, but you paid already 500 in the beginning becomes 500 and 4,000 becomes 3,500. Now, this would be the P&L scenarios for the case that you bought a call option. This is the P&L scenarios in case you didn't buy it. If you look at it here, you will see that when it comes to your risk, your downside risk. The worst case scenario for you is minus $500, minus 500. If you look at this case, you see actually you don't have protection on your downside loss. Then, I summarize this one here by saying that as far as the observations from the table I had from you is very easy to see. What's the trade-off? The trade-off is by buying the option. The speculator who was you, kept her downside risk by both lowering her upside gain. It's true that you're not gaining as much because of this strike and because of the fee which you already, you've been designing it. But at least, you completely protecting yourself from huge losses. That was a very simple example, but it gives you insight exactly at that works. It's very important to know that. That's why I'm asking this, do a speculators have to hold on on the contract, that option contract until maturity? The answer is no. You bought the option at $5. I mean, before maturity which was three months, a week later if the apple stock goes higher from say 190, goes to 200. You could sell this up to at seven dollars, because the price of the option would go higher too, because the order the slug one higher, then what you can do is, you can simply decide to exercise a week later. That means, you make seven minus five multiplied by 100. You take 200 and you say I'm out. That's what could also happen. Then it doesn't mean that you have to hold it until maturity. The scenario that I had here for you is in a case that, you bought the option you hold it until maturity. But, if you at some point, if you see that the value of the call price in the market goes higher. That means as opposed to people getting charged five dollars, which you paid. It goes to seven and you decide to go out there and sell it. Actually, most options traders, at some point they do it. They never hold it until maturity. This is actually what the speculators in most cases might do.