How Market Makers Determine the Options Theoretical Price

Imagine you seat in front of your laptop, one simple click and an order to buy or sell shares of stock, options or any other financial instrument is submitted. It looks pretty easy, isn’t it?

It does, but the reality is completely different. In order to trade safely, you must be aware of the several factors impacting on security prices and one of these are the overall dynamics behind stock options orders with the key role played by market makers.

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Market Makers and the Theoretical Option Price

Any time you trade, there is always somebody else on the other side that is willing to trade with you at the agreed price. Market makers are the entity you deal with and, in order to get your orders filled, you must meet their market conditions trying to obtain the best possible price. As a result, the premium paid by you to buy stock options is directly related to a series of risks that market makers face.

Market makers determine the option theoretical price by organizing a package of asset into a risk-free position and then finding the current value of that package based on the current interest rate.

At a first look, beginners may find this process hard to understand. An example may help. Imagine you want to know how much is worth buying a one-year $50 call option. By accepting to sell this one-year $50 call option the market maker faces unlimited upside risk. That occurs because you have potential unlimited gains at its risk. In order to shield itself against that risk, the market maker may decide to buy 100 shares of the underlying stock, which we will assume is also traded for $50.

At this point, the market maker faces a new risk because is long $5.000 stock and short $50 call sold to you. In fact, owning the shares the market maker is now facing the risk that the stock price may drop. To hedge that risk it can purchase a $50 put.

Doing the assumption that it costs $2 for buying that put or $200 total, in order to protect itself against the market risk, the market maker has to own a package of three assets called “conversion protection package”:

• Long Call;

• Short $50 Call;

• Long $50 Put.

The “conversion protection package” has the unique property to guarantee the sale of stocks at a particular price. In this way the market maker is absolutely protected against any risk whatever happens to the underlying stock. This package assures that the market maker has the guaranty to sell its 100 shares in a year for $50 per share.

There different scenarios are possible:

1. The stock price is worth $50 at the end of the year. Put and call options expire worthless and the market maker can sell the shares in the open market for $50 each.

2. The stock price is above $50 at the end of the year. The long put expires worthless, while the $50 call gets assigned and the market maker has to deliver the shares at the $50 strike price. Again the market maker receives $50 per share.

3. The stock price is below $50 at the end of the year. The short call expires worthless and the market maker exercises the long $50 put and sells the shares at the $50 strike price. Once again the market maker gets $50 per share.

The Mathematical Implications Behind your Orders

Now that you have a main idea of how market makers act, let's try to investigate deeper the mathematical implications behind options orders filled by market makers.

The price of a one-year $50 call option will be equal to the price the market maker has to pay to be guaranteed to receive $5,000 in one year. Given the assumption that the risk-free interest rate is 5%, the “conversion protection package” must be worth $4,762 today.

This is the amount of money required today in order to have exactly $5,000 in one year if the interest rate was 5% ($4,762 * 1.05 = $5,000). In financial terms we would say that the future value of that package $5,000 is worth only $4,762 today.

The total expenditure undergone by the market maker is of $5,200 on a package theoretically worth $4.762 today ($5,000 to buy 100 shares and $200 to buy a long put). The market maker has overpaid a difference of $438 ($5,200 - $4,762) for that package and. This represents exactly the amount of money you will be required to pay if you want to purchase the one-year $50 call option (in order for the market maker to make its trade risk-free). Each call is worth $4.38 per contract and, as each contract is made up of 100 shares, the total price will be $438.

Nowadays, many brokerage firms help you calculating the option theoretical price for the options chain. The option theoretical price can be checked too on the Chicago Board Options Exchange (CBOE) at www.cboe.com. Once on the website, click on the “Education” tab, "Tools" and then "Options Calculator”.

To check how much the call option of the previous example is worth enters the following data on the calculator: stock price $50, strike price $50 and days to expiration 360. You can also do the following assumptions: 15.67% implied volatility (this is the only value that makes the put value worth exactly $2 that is the assumption we have made before), 5% Interest Rate and 0 dividends paid through the life of the option. Click on “calculate” and check how much the call option is worth.

Happy Trading!