In the first article we discussed how options offer high probability strategies so that non-professional retail traders, like Karen the Super Trader, can make consistent income. In the second article we discussed why trading the SPX, as Karen does, is the optimum approach when trading high probability strategies. In this articles we will discuss the Probability Model, and how it is used to locate your short strikes.

Often referred to as probability traders, the use of the Probability Model to determine trade risk and probability of profit (POP) provides an objective approach (as opposed to discretionary traders and the reliance on subjective expectations or probabilities). In conjunction with high probability option strategies, the use of the Probability Model provides a distinctive edge.

So what is the Probability Model? It is the log-normal distribution of random outcomes (or asset prices); often referred to as a "bell curve" patterned after the geometric Brownian Motion (as applied in the Black-Scholes model). In other words, we are statistically determining the probability that the price of an asset (or index) will fall within a range over a specified period of time and current level of volatility.

This, of course, relies on the notion that the daily percent change in price of an asset (or index) is predominantly random. Much research has been done in this area, and it has been shown that the price action of indices (like the S&P500) are predominantly random (at OptionsAnnex.com we performed the same research for a 5-year period on the SPX, and found the skew to be extremely small reflecting a near normal distribution).

There are three key inputs to the Probability Model that probability traders focus on: price of the asset or index; implied volatility (which is derived from option prices of the asset or index); and days to expiration of the option (DTE). It then becomes a simple matter to determine the range of prices and the POP based on the expected move for a given level of risk. Risk is measured by standard deviation (SD), with 1 SD representing a 68.2% probability the price will fall within that range at expiration; 1.5 SD representing 90%; and 2 SD representing 95.4% for strangles and iron condors (ICs). The Expected Move for 1 SD is: Price x IV x sqrt(DTE/365). See image above.

Note: the POP for one side (Put or Call only; not both) would be: 1 SD = 84.1%; 1.5 SD = 95%; 2 SD = 97.7%.

For example, if an index has a price of \$1,800, DTE of 7 days for the option, and IV of 17.2%, then the expected move (EM) for 1 SD is 42.9. Therefore, the Put short strike at 1 SD would be 1755 (EM rounded to 45); the short Call strike would be 1845.

How reliable is the Probability Model? For the SPX, it is quite reliable. Keep in mind, that the shorter the DTE the more reliable the outcome, since IV is not fixed and will change over time as markets are impacted by future events.

In conclusion, using the Probability Model provides an objective approach to locating the short strikes for a high probability option strategy.

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