So how do market participants take advantage of beneficial price movements or removing the downside associated adverse price movements? Well, to do so they need to buy themselves some insurance. When we talk about insurance against adverse price movements, we're talking about options markets. So recall our discussion in the previous section with respect to the payoff to forwards and futures positions. By locking in a buying price of $8 a bushel, Judy was saving a dollar for each dollar above $8 at the price reached on March 31. But she also suffered a dollar loss for every dollar that the price of corn finished below $8 on March 31. So if the price of corn finished at $12, Judy enjoyed a gain of $4 on her contract. She's locked in a purchase price of $8. If the price finished at $6 though then Judy incurred an opportunity cost of $2 as she forgone the opportunity to buy at $6 and she must abide by her agreement to pay $8. Now, note that Frank's payoffs from the forward contract are the complete opposite to Judy’s, which makes sense as he sits other side of the forward contract to her and it's a zero sum game. Options, unlike forward contracts give the holder the right but not the obligation to buy or sell an asset at a predetermined exercise price, sometime in the future. There are two categories of options. Call options give you the right to buy the asset, that is to call the asset to you. Put options give you the right to sell the asset, that is to put the asset into somebody else's hands. Now, just like futures contracts, we can buy options or we can sell options. So we can buy the right to buy or we can buy the right to sell and we can sell the right to buy and we can sell the right to sell. All right. After many years of saying that sentence, I know exactly what face many of you are pulling at this very moment. Fortunately, there's a convention that has developed that we've already touched upon in terms of describing bought or sold positions. When you buy an option, you're taking a long position and when you sell an option, you're taking a short position. So if you buy a call, you have a long call. If you buy a put, you have a long put. Selling a call gives you a short call and selling a put, a short put. That's better, right? So back to our problem at hand. A forward futures contract removes both the downside associated with adverse price movements but at the cost of the upside associated with beneficial price movements. Options are able to keep the upside intact while removing the downside risk. To illustrate this, let's head back to Judy from Kellogs and Frank from Nebraska. Judy has reconsidered her position and now wants to put a cap on the price she pays for corn at $9 a bushel. So she buys a call option, that is she goes long in a call with an exercise price of $9. Frank, on the other hand wants to put floor on the price he will receive for corn. So he buys a put option, going long in a put with an exercise price of $5. Let's have a look at the payoff on 31st of March from a long call with an exercise price of $9. If the price of corn on the expiry date of the option was $3, Judy would allow her option to expire and simply go out and purchase corn at $3 per bushel. If on the other hand, the price of corn had risen to $12 per bushel, then Judy would exercise her right to purchase for $9 per bushel, implying a payoff from the call option of $3 per bushel. What about Frank? If the price of corn falls to $3 per bushel, he will exercise his right to sell corn for $5 per bushel, which implies a payoff from the long put of $2. If the price had risen to $12 per bushel, then Frank would have allowed his right to sell at $5 to lapse. And instead sold his corn on market at $12 per bushel. So the net effect from both of these examples is that options provide the option holder with the ability to take advantage of beneficial price changes while removing the risk associated with adverse price changes beyond a desired level. Now, let's pause for a moment while we define a very important concept in options analysis. The intrinsic value of an option is the payoff from the option, if the option were to expire immediately. So for a call option it is the maximum of the price now, less the exercise price or 0. For a put option, it is the maximum of the exercise price less the current price of the asset or 0. An important point to make here is that options cannot have negative intrinsic values because the option buyer, the long position can always allow the option to lapse. So for different current values of the asset, we have different intrinsic values. To illustrate, let's say the current price of corn is $4 per bushel. Well the call option that Judy holds gives her the right to buy corn at $9. So if that were to expire immediately, she would not exercise the option, hence the option has zero intrinsic value. Conversely, Frank's put option with an exercise price of $5 gives him the right to sell for $5, which he would elect to do if the option were to expire when the current price of corn is $4 per bushel. This would provide a payoff immediately of $1, which is the intrinsic value of his option. Now, instead let's assume a current price of $12. If Judy's right to buy at $9 were to expire today, she would most definitely exercise her right to buy for $9 and she would enjoy a payoff of $3 from the option. Frank, on the other hand would not exercise his right to sell for 5, when he could sell his corn on market for $12 per bushel and so his option has no intrinsic value. Another term that is related to an option's intrinsic value is the option's moneyness. To illustrate, let's consider Judy's call option with an exercise price of $9. If the current value of corn was also $9, that is if the value of the underlying asset matches the exercise price of the option, then the option is said to be at the money. If the current value of the asset exceeds the exercise price on a call option say if corn was $10 per bushel, then the option to buy at $9 is said to be in the money. If the current price of the asset was far in excess of the exercise price in the call option, the new option is said to be deep in the money. As when in the example the current value of the asset was $15 and the call option had an exercise price of only $9. On the other hand, if the value of the asset was below the exercise price of the call, the option is said to be out of the money. And if it is far below the exercise price then it is said to be deep-out-of-the-money. So you can see the concept of moneyness is inextricably linked to the intrinsic value of an option. Now, let's mix things up a bit and consider short positions in options. On this diagram, we can see that the payoff to a long call is the exact opposite to the payoff to a short call. So the opposite to buying a call option is not buying a put option. The opposite to buying a call option is selling a call option. Similarly, we can show that the opposite to buying a put option is selling a put option. Looking at this diagram, you have to wonder why anyone would actually ever sell an option? Well, the answer to this question begins with the point that the diagrams that we've been using have been payoff diagrams. Payoff diagrams that reflect the terminal payoff of the options at expiry. They don't include the price paid for the option initially. This price is what we call the options premium. If the option remains unexercised at expiring, the option seller gets to keep the premium without paying anything out at all. If we include the premiums paid for options in our diagrams, then we end up with profit diagrams instead of payoff diagrams. For example, here is a profit diagram for Judy's call option with an exercise price of $9. We can see that she has paid 0.50 cents for her option. That implies that she needs a payoff option of at least 0.50 cents to break even. And as we know, this will occur if the price of corn at expiry of the contract is equal to $9.50. If the option is not exercised then Judy is 0.50 cents out of pocket. This diagram shows the profits that would accrue to the trader that sold Judy the option. As you can see, they are the mirror image of Judy's own profits which is indicative of this whole transaction being a zero sum game. Where each cent gained by one party necessarily implies that the other party has lost a cent on the same transaction. So let's assume that Frank paid $0.30 for his option. Well, we can readily see that he needs the price of corn to fall to below $4.70 before he starts making money from his option position. Conversely, the trader that sold Frank the put option, will make a profit on the transaction provided that the price of corn exceeds $4.70 at the expiry of the option contract. One other important feature of options relates to the point of time at which the option is able to be exercised. So called European style options can only be exercised at maturity of the option contract. In contrast, American style options can be exercised at any time up to and including the maturity date. As a matter of logic therefore, the value of an American style option will always be worth at least as much as its European equivalent. As a final point on this, both American Style and European style options are traded in both America and Europe. So don't be misled by the simple naming convention. In summary, options, unlike forwards and futures enable those wanting to hedge price risk to keep their upside intact while removing downside risk to a desired level. There is a cost associated with removing that risk and this is referred to as the option premium. In this session, we have distinguished between call and put options, long and short positions, payoffs and intrinsic values, payoffs and profits. One area that we haven't touched upon relates to the factors that drive the value of options and this will be the subject of our next session together.
