[MUSIC] Let's now look at the second type of derivative contract, namely option contract. So an option contract can give you the right to buy a certain number of underlying assets at a pre-determined price, which is the strike price, and at a given date, which is the maturity date of the option contract. You can also have some contracts, some option contracts that give you the right to sell at a given strike price and at a given maturity date. In this case, we'll talk about a put option contract. If you can only use your right to buy or to sell at maturity, we'll talk of European options. And if we can exercise at any given point up to maturity and including the maturity date, we'll talk about an American option. This terminology, American option versus European option, has nothing to do with where these options are traded. For instance, in Switzerland you can trade European options as well as American options on the OTC markets, or Eurex allows you also to trade American and European options. So that leads me to the second point, namely, where do these contracts trade? They can trade on organized exchanges like the CBOE or Eurex, or they can be, like forwards, over-the-counter derivatives. And remember, the OTC market is the bulk of the market in derivatives and in options. And nothing is free, so in order for the buyer to get the right to buy in the case of a call, or to sell in the case of a put, he will have to pay a price which is the premium of the call or the premium of the put. It's also called the option price, the call price or the put price in the case of the put. And the size of a contract, this is another definition, defines how many units of a given stock, let's say 5,000, you can actually buy or sell if you got a call or a put. So now a little bit of key insight is, what is different between a forward and an option contract? An option contract, when I teach it to my classroom, I always say it provides you with a right to be flexible. So the owner has the right but not the obligation to exercise his right at maturity. Which means that in this case, the seller, he has the obligation in particular to deliver a specific quantity of the assets in the case of a call. Or to pay the price, the strike price, and get delivered a certain quantity of the underlying in the case where the put is exercised. So really, the rights are with the buyer and the obligations stand with the seller of the option. And then we have a terminology which says that option can trade in-the-money, at-the-money or out-of-the-money. So this is a little bit of a new vocabulary. So if I call S the stock price, let's say of stock XYZ, I call K the strike price of stock XYZ, and I can say that if the spot price today of XYZ is above the strike price, the call will trade in-the-money. If the two, the spot and the strike price, are equal, the call will trade at-the-money. And if the stock price is below the strike price, the call trades out-of-the-money. And it's going to be exactly the opposite for the put contract. Now, let's look at what is unique about the payoffs of calls and puts. And the unique feature is that in contrast to forwards, they provide these non-linear payoffs. So let me be more specific, supposed you enter a long position in a call on Apple stock on the 6th of April. The call matures on the 21st of October. It has a strike price of $115, while Apple stock price at initiation was $110. And you pay the premium to get this right to buy some Apple stock in October, you got the premium of $5.45 that you had to pay. And what you see is that of course if at maturity date, that means on the 21st of October, the strike price is below the spot price of Apple, which means the spot price is above $115. You will exercise and make a profit. Whereas, if the spot price of Apple is below the strike price of $115, you will not exercise. And what you will have lost is the call premium that you paid at initiation, which was the $5.45. So this is your maximal loss, and in principle, your profit can be unlimited if the call expires in-the-money. So let's look at the payoff of a short call. It's exactly the opposite. The seller of the call will make a profit equal to the premium if the option expires out-of-the-money. And on contrast, he will make a loss which is unlimited, which is equal to the call price minus the spot price of Apple plus the strike price if the price of Apple is very high at maturity. And potentially, it could be infinite if Apple makes very good deals. So his position is quite dangerous as the seller of such a call. Now, let's look what happens for puts. Now you can be long a put which means you buy a put and in this case we're talking about a put written on Microsoft Corporation. The put transaction is initiated to gain the 6th of April, it expires the 17th of June. The strike price is $52.50 when the spot price of Microsoft was $54.30. And for that right you paid the price of $1.60. So, what happens at maturity? You will only exercise if the put expires in-the-money, which means the price of Microsoft is below the strike price of $52.50. And your gain is limited because the spot price of a corporation can only go so low as zero. And in this case, your gain is the strike price minus the put price that you paid. And in the case where it expires out-of-the-money, you will have paid the premium which is a limited loss. Okay? And you see again that in this case the payoff pattern is nonlinear in contrast to what we have seen with a position in the forward contract. For instance, a short forward contract. So now let's look at the last possible case, which is the one of shorting a put on Microsoft, which has the same specificities as the one we've seen before. So we see that here the gain is limited. That means if the put expires out-of-the-money, you get the premium which is the put price. And if it expires in-the-money, you could make a limited loss, which amounts to the put premium minus the strike price if the stock price went to zero. Again, the key feature is that the payoff is nonlinear. And I always say the buyers of such instruments buy flexibility. The seller of such instruments sell flexibility to exercise the right by the buyer. So before concluding, we have shown the definitions of forwards and options contracts. We have looked at their payoffs, linear for forwards, nonlinear for option contracts. The last issue is what is the usage? What are the functions performed by these derivatives? So the first one which is really related to these set of lessons that you're going to follow is the fact that derivatives, whether they be forwards or option contracts, allow you to manage financial risks. The risks stemming from changes in the price of the stock, of the bond that you own, or of an index in case you own an index-replicating portfolio. So they're used for risk management purposes. There's some two other functions, however, that are less known by practitioners and even by students. And the first one is that you can use derivatives, like options and forwards, in an asset allocation strategy. So think about an international investor who has to buy stocks in Brazil, in China, in Switzerland, in the US. Well, if he invests in a lot of stocks, it's going to cost him a lot of money if he diversifies worldwide. What he could do is buy forward or futures contracts that are written on the Swiss market index, the Chinese market index, the Brazilian market index, and so forth. So this allows him to make a portfolio allocation strategy which is international and at a cheaper transaction cost. And the last feature or property of these contracts, whether they're forwards or options, is a function of what we call in finance, price discovery. Let me say what I mean with an example. If I give you today the forward price of the Euro with respect to the Dollar at one months, two months, three months, four months maturity, that tells you today what the market expect this exchange rate to be in one, two, three or four months. So, it's a price discovery function. And those of you who will maybe study more finance will learn that by looking at option prices, they can, from the option premium, extract a very valuable indicator which is the volatility that's expected by the market for the underlying stock return or the underlying bond return or the underlying Swiss market index for instance, with the examples we have considered. So thank you very much and enjoy all these classes on the risks of financial markets and how to hedge them and to manage them. [MUSIC]
