Basic Points

• A black swan in trading is a tail risk event that is unpredictable and rare enough that it is usually not priced in by the market.
• Tails can either happen in the form of a severe rally or crash.
• Generally, the boundary of a tail would be something that has at least a 99.7% (three standard deviation) chance of not happening. 
• Black swans can either refer to a market move itself, or a combination of market and exogenous risk factors such as sudden wars, currency defaults, or volcanos and major earthquakes. 

Intermediate: Systematic vs Unsystematic Black Swans

The exposure to independent events that can shock the entire market into 99.7%+ chance moves is called systematic tail risk because it affects all markets. However, black swans can also pertain to unsystematic risk, such as a severe news cycle for an individual stock; this happens often enough in biotechs. 

Advanced: Strategy

Earnings are frequently a point where black swan oriented moves are more likely. Option traders are aware of this however, and so are willing to pay extra for long gamma right before these events, even though they expect that excess IV (event vol) to crush by the next day unless something major happens. In a general way, tail protection is always in demand to anticipate the unanticipated with strategies like deep OTM long strangles. Whether speculating or hedging, many will accept a probable disadvantage for a shot at a stake in a potentially explosive move. 

Usually, the most important part of the design for a trading strategy is size. Traders often fall for the trap of becoming overconfident and use far more size than is responsible for them. Another mistake is having no hedges or risk management in place such as stop-limit orders during emergencies, in which case a 13% melt-up could be considered a black swan for those with naked short calls. Using stop-loss orders is more practical as undefined risk can lead to ruin. This must be understood in full before attempting any strategies with undefined risk, such as naked short calls, short strangles, short straddles, or frontspreads.