# How to Use Probability Calculations

In many of my articles I include a probability calculation in order to give readers some idea of what kind of trade they are looking at. A trade with a high probability of success is a very different animal than a low probability long shot.

First let me explain that the probability calculation is based on the same type of mathematics that is used in the Black Scholes options model. It only assumes a log normal probability distribution similar to the famous bell shaped curve. There is no assumption that my opinion is right or wrong. The only assumption is that the future volatility of the stock will be similar to its recent volatility. If my directional opinion does pan out, so much the better but it is not factored into the calculation. So the probability calculation is unbiased by my directional view.

Another way to look at this is that the stock can go up or down with about 50-50 odds. But the options plays can be either high probability bets for out of the money options sales or low probability bets for out of the money option buys. Options offer us the opportunity and flexibility to shape our payoff distribution to our own preferences.

Another interesting aspect of the probability calculation is that it is based only on volatility. This is also true for the option models such as Black Scholes. They depend only on the estimated volatility of the stock and not on future expectations for the stock. This is the reason that a bull and a bear can trade options on the same stock and agree on a fair price for the option. It does not matter what their respective directional opinions are, only that they agree on an outlook for volatility.

Having said that it does not matter what your outlook is for the stock in order to price an option let me be clear in saying that it does matter in order to make money. The option price does not factor in directional bias but your P&L does!

The bottom line for me on these probability calculations is that it allows us to estimate the chance of a given trade paying off in a naïve unbiased way. If my directional opinion adds to the profit then it will only make a trade that much better. I think of these calculations as effectively simulating a random walk with no directional bias. Essentially they are assuming the stock will randomly fluctuate with no particular direction.

Another way to visualize the probability number is to think of it as the area under the bell shaped curve. For example if a stock is trading at $50 then the 45 strike price put will only be in the money if the stock drops to $45 or lower. There is relatively little area under the bell shaped curve below 45 so there is a smaller probability of that event happening. Roughly half of the area is below 50 and half above 50. This reflects the fact that the stock starts losing on any drop and gains on any rise above 50. On the other hand the put will only lose if it gets below 45 less any premium received, which is a much less likely event.

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Phil is a professional options trader and contributes regular commentary to the Daily Speculations web site. Prior to trading professionally, Phil was a software developer for Dollar/Soft, a financial software company specializing in options software for equities, indexes and futures. He also wrote the book, Optimal Portfolio Modeling, which was published by Wiley Trading in February 2008.