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What is Options Trading? Probability and Implied Volatility

In our quest to understand trading options for income, the topic of this article covers the importance of probability when making trade decisions and the role implied volatility plays.

Probability Model Inputs

To start with, option prices reflect expectations of the underlying asset (stock, future, ETF, etc.). If the expectation is that the underlying price movement is becoming more volatile, then option prices will increase. This has been defined mathematically with the Black-Scholes option pricing model, which includes implied volatility as one of a handful of inputs. See charts above.

The Black-Scholes model relies on the following: first, that markets are efficient; and second, that markets are random (i.e., unpredictable). In today's electronic age (for both information and the stock exchanges), where information is broadly disseminated nearly instantaneously and just as quickly reflected in the markets, it is fair to say that the efficiency of markets has never been higher. With regard to random market movement, numerous research studies over the decades (and research performed at have shown that the daily percent change in the S&P 500 (an index of 500 large cap stocks) does resemble a geometric Brownian motion; in other words, predominantly random with upward drift (prices increasing over time). When the daily percent change in the S&P 500 is charted, it closely resembles a normal distribution (i.e., bell-shaped). See charts above.

If the price movement of an underlying is random (unpredictable), then how can we expect to be successful trading options? The answer is: by considering the probability of price movement (its range) within a specified period of time; generally the DTE (days till expiration) of the option. It is important to understand that this approach is not directional, since we are dealing with a range (plus/minus) around the current price of the underlying. In addition, it does not preclude having a directional opinion when considering placing a trade.

Probabilities are expressed as a percentage of confidence, which are aligned with levels of standard deviation. For example, at 1 SD (standard deviation) we have a confidence level of approximately 68% that the price will fall within that range by the end of a defined period of time (say within the next 15-days). At 2 SDs, our confidence level increases to approximately 95%. See charts above.

How does IV (implied volatility) play a role? When determining probabilities, IV determines the width of the bell-shaped curve, which we call the expected move (at one standard deviation). IV is derived from the options pricing model (ex., Black-Scholes). Given the current price of an option, and assuming that option pricing for the underlying is efficient (sufficient option volume and open interest), then IV for an option chain (all options available for a given period: Weekly, Monthly, or Quarterly) can be calculated. (Most options platforms will provide the IV for an option chain; for the S&P 500, the VIX is often applied). See charts above.

Once we have IV, we can determine EM (expected move) using the equation:

EM = Price x IV x SqRt(DTE / 365); Price= price of the underlying; SqRt = square root

So, how can we apply probabilities, in conjunction with IV, to improve option trading outcomes? Whether we have a directional opinion or not, we can apply option strategies that take advantage of probabilities; that is, we can select a POP (probability of profit) that reflects our tolerance for risk.

For example, let's consider trading options in XYZ. The price of XYZ is $1,841. Using the current Weekly option chain for XYZ with 7 DTE, IV for the option chain is 10.8% (provided by the platform). Plugging those figures into our equation (above), EM = 27.5 (plus/minus). Looking at the strikes available in the options chain, and rounding EM to 30, at 1 SD we can expect the price of XYZ to fall between the strikes 1810 and 1870 with a POP of approximately 68%.

If we have no directional opinion and we are comfortable with a level of risk of 32% (100% - 68%), then we could apply an Iron Condor option strategy (or Strangle). The level of profit will be based on the level of capital we wish to risk: the higher the capital at risk, the greater the profit. To be clear, the POP is not affected by the capital at risk; however, the risk of ruin is impacted along with ROC (return on capital), and applying proper money management guidelines is essential to overcoming losses as they occur.

Let's assume we have a bullish expectation, a positive directional bias. We would apply another option strategy (Put credit spread, or a short Put) at the strike price of 1810 (1 SD level). Now our POP increases to approximately 84% reflecting unlimited upside movement (i.e., we are no longer restrained by the 1870 upside limit). With an increase in POP, our maximum profit is reduced reflecting a reduction in risk, now only 16% (100% - 84%). See charts above.

Does the probability approach work? Yes. In the example above, XYZ (actually the SPX) ended at 1831 at expiration. But more to the point, testing and experience has shown that the actual POP either equals or exceeds expected POP as trading volume (number of annual trades) increases. If you have just one trade per week, that's 52 trades per year, which is far better the one trade per month.

In conclusion, using probabilities not only provides a quantitative risk level (100% - POP), but also enables us to locate the proper strikes using EM (expected move). An important input to this process is IV (the implied volatility of the option chain).

If you would like to learn more about options, and how to generate consistent weekly income trading options, go to Options Annex.

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