Create Call Options

Q. I have heard that options are not physically issued by the company. If that’s true, can you tell me how a call option is created?


A. Options are simply agreements between investors to buy and sell shares of stock. They are not physically issued by a company like shares of stock so there is no “supply” of options in the traditional sense of the word. Instead, options must be created.

To understand how options are created, think about the process used by a manufacturer, say a homebuilder. Assume you wish to buy a house and are speaking with the manufacturer. The builder will take your order and find out exactly what you’re looking for. From there, he’ll use inputs such as wood, nails, concrete, etc. to “shape” the house into the design you need. Once he builds the home that you want, he will transfer it to you with a “bill of sale.”

(It is possible that the manufacturer has a pre-existing home in inventory that you find interesting. The important point to understand is that even pre-existing homes had to be built. They do not come into existence otherwise.)

In a similar way, option contracts must be built and then transferred to the buyer (or seller). Let’s take a closer look at how market makers construct options. We’ll start by assuming that ATZ stock is trading for $50 and you wish to buy one $50 call option. To make some of our upcoming calculations easier, we’re going to also assume that this call expires in exactly one year.

You place the following order:

Buy to open, one ATZ $50 call, at market.

Upon receiving the order, the market maker can either sell you a call option from inventory (if he has it) or must build it for you. Let’s assume this call must be built and sold to you.

When the market maker receives your order to buy a call option, he knows you’re looking for the right to buy 100 shares of ATZ stock. You do not want the shares today but would like the right to purchase them in the future.

If the market maker sells you that right (sells you the call) he is accepting the potential obligation to deliver 100 shares of ATZ to you in the future and there’s no telling how high that share price may be. He would be exposed to the risk of higher share prices. To eliminate this risk, the market maker will purchase 100 shares of ATZ for you today.

By purchasing the shares, however, he has introduced a new risk. He is now at risk if the price of ATZ falls. To protect himself, the market maker will find a client who is willing to accept the potential obligation to buy the shares from him for his $50 purchase price. Of course, once he finds such a client, the market maker has eliminated his downside risk since he can always elect to sell his shares to this investor or speculator. The market maker’s downside risk of holding the stock has now been transferred to the client. For accepting this risk, the market maker must pay him a fee for “insuring” his $50 purchase price.

Let’s assume that the client and market maker both agre
e that $2 per share is a fair price. By paying the client $200, the market maker has purchased right to sell his 100 shares of ATZ for $50 at any time during the next year. The client has the potential obligation to purchase the shares.

The arrangement between the market maker and the client is, in fact, a put option. By accepting the $200 cash, the client has effectively sold the market maker a one-year $50 put for $2. Just like call options, put options are not issued by companies; they are created when two investors are willing to make such an agreement – a contract.

Creating a Call Option
At this point, the market maker owns 100 shares of ATZ stock plus the right to sell those shares for $50. Now here’s the critical point to understand: By owning the shares plus the right to sell, he is effectively doing the same thing as someone holding cash plus the right to buy the shares. In other words, the market maker is effectively holding a call option.



How is it that the market maker’s position of stock plus a put option is identical to a call option? The answer is that either choice performs exactly the same way for all stock prices. The only difference is whether the shares are purchased today or in the future.

For instance, assume the market maker also owns a $50 call option purchased for $2 and let’s see how these two choices perform. Assume that ATZ rises to $60.

How does the stock plus put perform? With the stock at $60, the market maker will let the put option expire worthless and will make $10 on the stock. After subtracting the $2 paid for the put, he will net $8.

On the other hand, had he been holding cash with the right to buy the shares for $50, he would exercise that right, pay $50 for the stock, and immediately sell the shares for the current $60 market price thus making $10 on the deal. If he paid $2 for the right to buy the shares (rather than the right to sell them) he would also net $8 on the transaction.

By purchasing a put option, the market maker had to purchase the shares today. By using a call, he purchased the shares in the future. But aside from that difference, either method nets an $8 gain. No matter how high the share price may be, either choice performs the same.

Of course, there is an obvious difference in these two choices. With all else being equal, we’d rather pay for the shares in the future thus allowing our money to earn interest longer. The amount of interest that could be earned by not paying for the shares today is called the cost-of-carry (that's what it "costs" to "carry" the shares in your account). So on the surface, it seems that the call option is the better choice since it allows you to pay for the shares later. However, in the real world of trading, call option prices will be higher than the put prices by this cost-of-carry. But for now, we’re just trying to get the concepts across so just realize that, aside from the cost-of-carry, owning shares of stock with the right to sell them is identical to having enough cash to buy the shares plus the right to buy them.

We just found out that both choices perform the same if the stock price rises. What happens if the stock price falls below $50? For the stock plus put choice, the market maker will exercise the put and collect the $50 strike price. If he is holding cash plus the right to buy shares, he will forego his right to buy the shares and continue to hold the $50 cash. No matter how low the stock’s price may fall, either choice performs the same.

Now that you realize that the market maker’s position of stock plus put is identical to a call option, let’s revisit your original order. Remember that we assumed you placed an order to buy a one-year $50 call option. The market maker has purchased the shares and then purchased a put, which you now know is the same thing as a call option.

So when your order arrives to “buy calls to open” the market maker simply places an order to “sell calls to open” and that “stock + put” package is transferred to you as a call.

Notice that even though no call options were available or sitting in inventory the market maker “built” a call option for you by using inputs (stock plus put) and then transferred that package to you from the sale – exactly like the homebuilder.

A Graphical Look
We can look at your option order graphically by using profit and loss diagrams. (If you are not familiar with these diagrams, you may wish to review our free training video by clicking here.

When the market maker receives the order, he knows you want a profit and loss profile that looks like a call option, which is shown in Figure 1:

Figure 1: Profit and loss diagram for Long $50 call 



However, we assumed that the market maker has no call options to sell you. However, he can create this same profile by purchasing the inputs of stock and a $50 put, which we assumed was purchased for $2. Once he does, the market maker has created a profile shown in Figure 2:

 Figure 2: Profit and loss diagram for long stock + long $50 put

 
Notice that Figures 1 and 2 look identical, which is in keeping with what we said before; that is, both positions are identical. They behave exactly the same way for all stock prices. Because of this, we say that the long stock plus long put position is the “synthetic equivalent” to a long call. The market maker has therefore created and “shaped” a profile that suits your needs just like the homebuilder. But how does the market maker transfer this profile to you?

He simply places an order to “sell calls to open” and that profile is now yours. His order to “sell to open” transfers the risk profile to you much like the “bill of sale” for the homebuilder example we discussed at the beginning.

To reiterate the process: You placed an order for a call option and the market created a synthetic position that behaves just like a call and then sold that synthetic position to you. That’s how call options can be created. Our next question is how much should the market maker charge you for the $50 call?


The Magic of Conversions
To answer that question, let’s start by reviewing the market makers transactions so far:

Buys 100 shares for $50 = -$5,000
Buys one-year $50 put = -$200
Sells one-year $50 call = ?

When you placed your order to buy a $50 call, the market maker purchased 100 shares of stock for $50 and spent $5,000. He then purchased the $50 put and spent another $200 for a total of $5,200. He therefore has $5,200 tied up into a package that he will transfer to you by selling you a call. The question we’re trying to answer now is how much is the call worth? How much should he charge you?

It might appear to be a difficult question but, upon closer investigation, it’s quite easy. You see, the market maker's three-sided package has a magical quality. In the financial world, this package is called a “conversion” and is a guaranteed sale of stock in disguise. How is it guaranteed?

Let’s run through all stock price possibilities and show that the market maker always receives $50 at expiration. If the stock’s price is below $50 at expiration, the market maker will exercise the put and receive the $50 strike price. And if the stock’s price is above $50 at expiration, the long call holder will exercise the call thus forcing the market maker to sell his stock for the $50 strike price. Finally, if the stock’s price is exactly $50 at expiration, the put and call expire worthless and the market maker will sell his stock for the $50 market price. So no matter where the stock’s price may be at expiration, the market maker is guaranteed to sell his 100 shares of ATZ for $50 in one year.


Present Value
Because this is a guaranteed sale of stock, all we have to do is find the “present value,” which is a financial concept that allows us to value different cash flows at different times. If the market maker is guaranteed to receive $5,000 in one year ($50 strike * 100 shares), how much is that worth today? All we have to do is divide $5,000 by one plus the interest rate. If we assume the interest rate is 5% the market maker’s three-sided package is worth $5,000/1.05 = $4,761.90.

In other words, if the market maker were to deposit $4,761.90 in a risk-free CD at 5%, it would be worth $4,761.90 * 1.05 = $5,000 in one year. The two cash flows ($4,761.90 and $5,000) are identical – just lined up at different points in time. That is, you should be indifferent between accepting $4,761.90 today or $5,000 in one year if interest rates are five percent. Either choice is worth $5,000 in one year.

Now we’ve discovered that the three-sided package (conversion) is worth $5,000 in one year and therefore worth $4,761.90 today. However, the market maker has spent $5,200 for it. How can he reduce that cost to $4,761.90? Easy, he will sell the call for the difference of $438.10, or about $4.38. Once he sells you the call, his transactions are as follows:





The total dollars spent is $4,761.90, which is exactly what it should be considering the market maker has a guaranteed sale and will receive $5,000 in one year. After selling the shares in one year for $50, he will exactly earn the risk-free rate of interest, which is in accordance with the risk-free conversion.

In the real world of trading, you’d find that this call option will sell for a little higher than $4.38 in order to provide a profit for the market maker although competitive pressures will keep the call from being priced too much higher. But the theoretical value is $4.38 as shown from the Black-Scholes Model in Figure 3:
Figure 3: Black-Scholes Model



In Figure 3, we used volatility = 15.8% in order to make the value of the put exactly two dollars, which was an assumption in our example. Notice that the remaining inputs on the left side are identical to our example. We have a $50 stock and strike price, 360 days to expiration, and five percent interest rates. Under those assumptions, the theoretical value of the call is $4.38, which is exactly what we deduced the long way!

The market maker’s conversion leaves him in a risk-free position. His role in the financial markets is matching up clients who are willing to take the opposite sides of transactions, putting them together, and then leaving the risk between those clients.

In our example, the market maker had to find someone willing to sell stock in order for him to buy it. He also had to locate someone willing to sell a put. Once he did, he packaged those together as a long call and transferred it to you by selling calls. Your order was to buy calls. His order was to sell calls. His sell order transferred the synthetic package to you and the risk is now held among the three market participants who took the opposite sides of the conversion -- (1) you, (2) the short put, and (3) the investor who sold the stock.

We can use the reverse set of transactions – short stock, short put, long call – to create the opposite of a “conversion,” which is called a “reversal.” The point is that market makers can fill any order you can imagine by using combinations of options and stock.

At the beginning, we said that a homebuilder may either create a home for you or sell it from inventory. Market makers can do the same thing. If, at a later date, you decide to sell your call to close, the market maker may buy that same call to open. If you are closing and he is opening there is no effect on the “open interest” and the market maker has effectively swapped places with you. He now has a “pre-owned” call sitting in inventory.

So while options are not physically issued by a company they come into being simply by market participants – investors, speculators, and market makers – willing to enter into agreements to buy and sell shares of stock. Market makers simply match them together and create options. 
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