Probabilities are fundamental to my system because they are a major element of the expectancy calculation.
Recall the expectancy calculation: Expectancy = (The probability you will win * the amount you will win) - ( The probability you will lose * the amount you will lose)
My system allows for the sale of both calls and puts in the most volatile index Exchance Traded Funds (ETFs). The stock market action since January 1, 2008 has created a huge demand for index ETF puts as “insurance” against long stock portfolios. This demand has driven the price of these puts to historically high levels. So, I am selling these puts. Success for my system is to collect all the premium planned for the puts I sell. To achieve this, the underlying instrument (the actual ETF) must not close below the stike price of the puts I sell on the option expiration day.
So, we need to estimate the probability that the underlying instrument will be below our strike price at the expiration.
For those of you wanting a quick and easy way, with mediocre accuracy, you can just use the option Delta. Delta is one of the option greeks. It is a value which is typically used as the expected rate of change in the price of the option relative to the price change of the underlying instrument. (if you are new to options you can pick up a book on option basics or research the greeks on wikipedia.org) But, many consider the Delta calculation as an approximation of the probability of the underlying reaching the associated stike at expiration. I do not use delta, because I find it is frequently 1-5% different than my calculation. But, you can obtain delta easily, so that makes it attractive and it may be “good enough” for some traders. All trading websites that support options and most free option informationsl websites offer the greek calculations for free. I trade with Fidelity and they give me the greek values in real-time for free.
Right now, the delta of my (short) April IWM calls at 57 is .06. You could translate this directly into a 6% probability that the IWM will reach 57 by 4/19/08. My probability calculation (described below) shows a 3.15% probability that IWM will reach 57 by 4/19/08.
For those wanting the most accurate estimate, you can find the formula I use for this calculation in Lawrence G. McMillan’s book “Options as a Strategic Investment”. Be sure to use at least the 3rd edition. McMillan explains the method and the model. He also describes how the probability calculation is different than Delta. He lays out the details for the calculation which you could plug into a program or spreadsheet if you have the time. I found it tedious, and I have a minor in mathematics. I worked out the math in my spreadsheet and I use that spreadsheet to this day for trade decisions. This spreadsheet covers probabilities but also expectancy and return on capital calculations.
