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February 15, 2011 - by Christopher Smith
  

Understanding Black Swan Market Events

The "Black Swan" in the context of options trading is an unexpected dramatic price move that can devastate monthly income option trades. Retail traders need to understand why the option pricing formulas fail to preduce these price moves and reconsider the probabilities they may have assumed would give them an "edge" in the market.
  
Many retail options traders just sort of trust that the tools and analytical studies they use are "right" and that we can rely upon them when planning our trades. After all, the tools are based upon a Nobel award winning mathematical formula, i.e., the Black-Scholes formula, and are offered to us by reputable analytical and financial firms.

The Black-Scholes options pricing formula and most of the modern option pricing formulas assume a normal price distribution. A normal distribution produces a "bell curve," whereby half of all potential pricing outcomes fall above the current market price and half willl fall below the current market price. Also, roughly 68% of all pricing outcomes will occur within one standard deviation of the current market price.Assuming a normal distribution allows us to project probabilities for potential market movement.

A norrmal distribution of pricing outcomes is an assumption. The reality is that a normal price distribution - or bell curve - does not fit true market conditions. The distribution of market prices is skewed, with more pricing outcomes falling to one side or another of the current market price. There is also a propensity for market price moves to exceed three standard deviations more often than a normal distribution would predict.

So, why don't we modify the option pricing model to account for the skew and kurtosis of the market? Some of the models have done this to a degree; e.g., the trinomial model can price the volatility smile. The problem is that the degree of skew or kurtosis in the market is not static. We already need to predict IV and adding predictions about the future skew and kurtosis that the market will adhere to from now until the next expiration would add further uncertainty to the resulting calculations. Whatever guess we make about the future price outcomes of the market would be wrong, so what can we hope to accomplish?

The normal distribution is the assumption upon which the pricing formulas are built and that assumption is false. It doesn't mean that the formula is without merit. The reality is that the Black-Scholes based models do a very good job modeling option prices within a standard deviation or two. It's the outliers that present the difficulty for the formulas. The formula remains a valuable tool, but you need to understand its short comings.

Analytic studies such as "Probability of Touching" and "Probability of Expiring" are built upon the same faulty underlying assumption. More than one retail options trader has designed a credit spread trading system based, at least in part, upon one or both of these metrics. The results are often encouraging with profits routinely rolling in, month-after-month. Then the unexecpted happens and painful losses are dealt. All of the probabilities, the analytics and metrics may convince an uninformed trader for the time being that the strategy has long-term viability but in fact it is often a "house built upon a foundation of sand" because the underlying assumption of a normal distribution is an incorrect assumption.

So, it is worth asking and directly answering a few questions. Do the option pricing formulas have value? Yes, they do. Do these analytic platforms have value and a place in our trading? Yes, they do. Should we pay attention to things like standard deviation? Yes, we should. However, it is critically important that we recognize these analytic tools for what they are, understand where they come up short, and realize that the probabilities we are being given do not disclose the true extent of the risk being taken. Caveat emptor.

It is not possible for us to predict when a "Black Swan" event will occur. By their very nature these events are not predictable, except by a very small number of people. In the Trading Room we discuss trading methods to incorporate protection into an options portfolio to help reduce the risk of loss. These methods are not always readily apparent because they do not adhere the underlying normal distribution assumption through which most analytic platforms view the market.

Taleb - The Black Swan: The Impact Of The Highly Improbable

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