Another Pricing Method
I just got back from 2 trade shows, the Orlando Money Show and the NY Traders Expo and I'm angry. It seemed to me that the Orlando attendees were generally older folks looking to invest retirement money. The New York crowd had a greater mix in age and a higher number of people who wanted to learn to trade for a living. Both shows had over 10,000 attendees.
Unfortunately, at both shows there were many exhibitors (in order to protect the guilty, I will not name names) with advertising and sales pitches that were totally unreasonable. One options guy was selling a program that claimed a consistent 20% per month rate of return! Do the math and you'll see that if you start out with $20,000 and compound your earnings at 20% per month, after 5 years you will have over $1 Billion. That's not a typo; it's a B, not an M! Of course, if in some months you earn less than 20%, you might end up with only a few hundred million. The sad truth is that many people fall for this type of advertising and end up terribly disappointed. Our Online Trading Academy students and graduates know better! Whew, I feel better now!
**Options Alert** On February 18, 2008, the Options Clearing Corporation announced that beginning with the June 2008 expiration, options that are .01 in the money at expiration will be automatically exercised. This is a reduction in the threshold from the current level of .05. You can tell your broker not to automatically exercise an option, but the instruction must be for a specific option on a particular expiration date. In other words you can't just give a blanket instruction to not automatically exercise any options that are in the money. It's important that you check with your broker to find out the latest time these "contrary intentions" (their term, not mine) will be accepted, and if they will take a conditional contrary intention, i.e., "if my option is in the money by 3 cents or more do the exercise, otherwise let it expire worthless."
Why is this important? Failure to pay attention to this rule can, in rare situations, cause you to lose more than you paid for an option. You've probably had it drilled into your head that when you buy options, the most you can lose is what you paid. Suppose, some time ago, you bought 10 XYZ March 30 Calls for .20 (total cost of $200.) On Thursday, the day before expiration, the stock is trading at $26 and the Calls are 0 bid. You leave for your Caribbean vacation assuming that the Calls will expire worthless. Friday, while you're on the beach, news comes out and the stock gaps up and closes at $30.02. Since you didn't give your broker a contrary intention, the options are automatically exercised, and you've unknowingly bought 1000 shares of XYZ for $30.
It's possible that on Monday when you realize you own the stock, you could get lucky and the stock may continue to climb and you sell it out for a profit. More often though, it seems the stock will open lower and you'll get out with a loss. So if it opens at 30.65 for example and you sell it out at that price you will end up losing $350 on options that you only paid $200 for. Much worse situations can be envisioned.
Last week's article on probability generated some controversy. In particular, question number 2:
A man states that he has 2 children at least one of which is a boy. What is the probability that he has a girl? Answer 2/3 or 66-2/3%.
It was suggested, in rather strong terms, that the correct answer is 50%. Well, the math is on my side and I'm not sure how to make it clearer than my original explanation. If anyone is still bothered, I'm sure a brief review of any high school probability text would clear it up and offer some additional examples. The second issue had to do with my claim that there is no system that will allow you to win at roulette over the long run. One person claimed that he agreed with the math, but on the other hand had a system that worked. You can't have it both ways!
Moving on, in a prior article, I discussed the famous Black-Scholes pricing model. You plug some variables (do you remember what they are?, they're listed further down) into a formula and it gives you the value of the Puts, Calls, and the associated Greeks. Without getting too carried away with the math, I want to give you some insight into other types of pricing. Another popular model is called the Cox, Ross, Rubenstein Binomial Pricing Model. It is very useful and popular and will be the subject of a later article. This week, I want to describe another type of pricing that is sometimes referred to as the non-arbitrage method of options pricing. Basically, if we price an option and set up a hedged portfolio, such that a risk free arbitrage does not exist, then the option is priced properly. It can get a bit confusing, so we won't go into all the details, just enough to make sure you understand the basic concepts of this method of pricing.
Let's assume it's the day before expiration and that stock XYZ is exactly $100. Further assume that there is a 60% probability that the stock will go to $101, and a 40% probability that the stock will go to $99. We'll also assume that the interest rate is 0%. It's not conceptually harder to have a non-zero interest rate, it just complicates the computations. The question is, what is the fair price of the one day XYZ 100 strike Call? The situation can be illustrated as follows:
Think about what would be the fair value of the Call that I'm referring to as C. By fair value I mean the value that would be a fair price for both the buyer and seller. We saw last week that the expected value is equal to 60 cents, calculated as:
Expected Value = 1 X .60 + 0 X .40 = .60
Did you come up with 60 cents as the fair value of C? If you did you get an A for effort, because you calculated the expected value correctly, but let's see how we can calculate a fair value to price this option. First, we'll set up a "hedged portfolio." It will consist of one Call option contract representing 100 shares of stock, and short 50 shares of stock. Note that the Call option contract value is equal to 100 X C.
Remember that at expiration, the stock is either worth 101 or 99. With the stock at 101 the value of this portfolio is equal to:
Call option contract value – (50 X value of stock) = 100 – (50 X 101) = -4,950.
On the other hand, if the stock were to end at 99, the value of the portfolio would be:
0 – (50 X 99) = -4,950, the same as above.
So it doesn't matter to my portfolio if the stock goes up or down! When I hedged the Call option with the sale of stock, I eliminated all possible variation in the portfolio value.
Since the value of the portfolio at expiration is known to be fixed at -4,950 and since there is no interest assumed, we know that the value of the portfolio on the day before expiration is equal to the value at expiration. So, 100 X C – 50 X 100 = -4,950 or C = .50.
Did you notice anything interesting about the calculation of the Call value? How about the fact that nowhere in the calculation of the value of the Call (and by the way, this also applies to Puts) did we take into account the probability of the stock going up or down! This is also borne out by the fact that the Black-Scholes model does not have probability of stock increasing as one of its variables either. (The 6 variables are; stock price, exercise price, time to expiration, projected volatility, risk free rate of return, and the annual dividend rate.) This must seem very counter intuitive, if you're hearing it for the first time.
So if the probability of a stock increasing doesn't matter, what's the real key to pricing options? The answer is volatility, volatility, volatility. This is why you will hear options traders talk in terms of trading volatility. In most situations it's the most critical part of pricing and therefore trading options. I hope this article gives you some understanding as to how critical it is to understand volatility when trading options.
As always, if you have any questions about my articles, have suggestions for future topics, or want more information about our options mentoring program, feel free to email me at: SFreifeld@tradingacademy.com or call me at: (888) OTA-2580 ext. 2010.
11. Know Thy Options!
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Stan Freifeld comes to us from the Floor of the American Stock Exchange where he traded options for his own account from 1994-2001. He was a Market Maker for the options on several popular equities including Dupont, Schering Plough, Walgreen's, CBS, U.S. Surgical and Biovail.When he is not trading or thinking about trading, Stan relieves his stress by playing competitive squash, competing in local road rallies with his Ferrari Cabriolet and tutoring local high school students for the SAT's. The bottom line is that Stan, a long time MENSA member, is an engaging teacher with an extraordinary background in options trading and risk management. He is helpful and patient by nature and equally at ease with all levels of traders, from complete novices to advanced pros and academics. He'll be happy to teach you to trade!