I love Las Vegas. Sure, I enjoy the lush hotels, the waterfall pools, the Cirque du Soleil acrobatics, and the all-you-can-eat buffets, but that is not what I mean. I mean I love the casino industry. It is the only industry I know of that has a business model based on mathematical certainty (life insurance is a close second). Casinos know that they will make a profit from their gaming operations (they don't like to use the word gambling) because the odds are always in their favor.

Take American roulette, for example. A bettor has 38 numbers to choose from: 0, 00, and 1 through 36. The odds of the ivory ball falling on the number chosen are 37 to 1, or, put another way, a 1-in-38 chance. Based on the odds, a gambler who bets $1 on a number should receive $38 back if her number comes up on the wheel. Does a bettor at a casino actually receive $38 for a winning number? Noooooooo. She gets only $36. This $2 deficit is what is known as the "house edge" and amounts to 5.26% of every dollar bet. In other words, over the long term, a casino knows, with mathematical certainty, that it will collect a profit of $0.0526 per dollar wagered. In fact, the decks are so stacked against gamblers that if they actually start winning, casinos will accuse them of cheating.

What does this casino talk have to do with stocks? Nothing, but it actually does have quite a bit to do with stock options. Before I explain the connection between casinos and stock options, a quick refresher course in options is called for. As the Fool has discussed in the past, options are contracts composed of either puts or calls. Puts give the buyer the right, but not the obligation, to sell a stock at a certain price. Calls give the buyer the right, but not the obligation, to buy a stock at a certain price. Options can also be sold. (And unlike stocks, which are physical pieces of paper, options are derivative contracts that can be created at will. The Securities and Exchange Commission, which enacted Regulation SHO to prevent naked short selling of stocks, has no such prohibition regarding naked short selling of options.) Sellers of options, unlike buyers, have no rights, only obligations, but get paid up front for assuming these obligations. Sellers of call options have the obligation to sell stock to the call owner at a certain price if the owner elects to exercise her call. Similarly, sellers of puts have the obligation to buy stock from a put owner at a certain price if the put owner so elects.

Back to the wheel
Now back to the connection between casinos and stock options. Just as the payout in roulette is based on the probability of the ball falling on a particular number on the wheel, so too is the price of a stock option based on the probability of the stock landing on a particular price on the date of the option's expiration. Let's say you are bearish to neutral on a stock and want to generate some income from this view. You could, for example, sell a December call spread on the stock. It's best to choose a heavily traded stock with a liquid options market. Some highly liquid possibilities include Motley Fool Inside Value picks Microsoft (Nasdaq: MSFT) and Intel (Nasdaq: INTC), Valero Energy (NYSE: VLO), General Motors (NYSE: GM), Altria (NYSE: MO), and Stock Advisor pick eBay(Nasdaq: EBAY).

Let's choose, for argument's sake, a December $32.50/$35 call credit spread on eBay. A credit spread is the simultaneous sale and purchase of two options -- one sale and one purchase -- with different strike prices but with the same expiration date. I like to trade spreads because they limit my risk. Let's assume that you sell the $32.50 call and buy the $35 call. The $32.50 call is priced at $1.40 and the $35 call is priced at $0.55. Your "net credit" (i.e., the amount of cash you will receive after you deduct the cost of the purchased option from the income generated by the sold option) will be $0.85 per contract ($1.40 minus $0.55) or $85 ($0.85 times 100 shares per contract). When the options expire, the price at which a seller of this call spread breaks even is $33.35 ($32.50 plus $0.85), meaning that you make at least a penny of profit on the option spread if eBay closes below $33.35 and you lose at least a penny if the stock closes above $33.35 on the date that December options expire (Dec. 15 for individual stocks).

Is a net credit of $0.85 a fair price to receive for selling the call spread? The short answer is yes. Unlike a casino, the options market doesn't rip you off, pricing at or very near "fair value," as I'll describe below.

As an aside, I wouldn't recommend placing any credence in those options newsletters that claim to have found "undervalued" options to buy or "overvalued" options to sell. If such valuation discrepancies actually existed, the institutional market makers in the options pits with their multimillion-dollar computer models would have exploited them in milliseconds, long before a retail investor ever even saw any such discrepancies. That said, let me hedge this statement by referencing a 2004 Ibbotson Associates study of index option prices, which found that "option writing can be very profitable." According to this study, certain index options (such as the S&P 500) have historically been overpriced. Thus, if I was forced to choose between options being slightly overvalued or slightly undervalued, I'd have to choose overvalued. Which, of course, favors selling (i.e., writing) options.

Because the actual math to prove an option's fair value is mind-numbingly complex (can anyone say "binomial tree distribution"?), we need to use a computer and options valuation software to determine the probability that eBay closes below $33.35 on the December options expiration date. And keep in mind that in options market pricing and valuation, even the best options valuation models are based on estimates of future stock volatility (unlike dice in a craps game, which have definite probabilities) and, in turn, "fair value," and these estimates could turn out to be wrong. Nevertheless, professional traders risk millions of dollars a day based on these models, so they must be pretty accurate over the long term.

Rule of thumb
Based on the options valuation software that I use, the probability of eBay closing below $33.35 when December options expire is about 65.6%. A simple rule of thumb can be used to verify that an $0.85 net credit is a fair price for a 65.6% probability of success. For the price of $0.85 to be fair, the credit received divided by the difference in strike prices should equal the probability that the stock closes above $33.35 ($0.85 divided by $2.50, or 34%), so the fair value probability that eBay closes below $33.35 at December options expiration is 66% (100% minus 34%).

If you look at this rule-of-thumb concept from a simple risk/reward perspective, it makes intuitive sense. Buyers and sellers will only enter into a transaction if they both think they are getting a fair deal. If a seller of the eBay spread receives $0.85 but is risking $1.65, she will demand that the probability of profit be at least 66%, because the expectation is that the trade will be profitable or will break even. The back-of-the-envelope formula for the probabilities would look something like this: (66% x $0.85) minus (34% x $1.65) is greater than or equal to 0. Similarly, on the other side of the transaction, the counterparty to my spread will accept a probability of profit of only 34% because her potential reward is greater than her potential loss. Again, the reason this simple rule of thumb works is because the options marketplace is very efficient. In conclusion, because the rule-of-thumb number of 66% is close to the probability calculated by our options valuation software, we have verified that an $0.85 net credit is a fair price for the eBay credit spread.

I should emphasize that you should never rely on rule-of-thumb calculations when risking actual capital in the options market. Always rely on probabilities calculated by reliable options analysis software. After all, a rule of thumb is referred to as a rule of thumb because it's generally reliable, though not always. However, if the rule-of-thumb probability isn't close to the software-generated probability, something weird is going on and I would likely pass on that particular spread.

So there you have the fundamentals of an option spread, the transactions, and the associated probabilities. In Part 2 of this options series, I will explain how our hypothetical eBay credit spread can make you money. Stay tuned.

For other options-related Foolishness:

This article was originally published on Oct. 13, 2005. It has been updated.

Fool contributor Jim Fink spent many years losing gobs of money buying options and watching his money disappear with time decay. Now he makes a little money selling options and having time decay work in his favor. May the odds be with you. He has no financial interest in any of the companies mentioned. The Motley Fool has an ironclad disclosure policy.