Pattern Recognition and future (unexpected) Jumps

Shelton [1997] describes trading from an interesting perspective: Game Theory where each market investor is calibrating his/her trades according to the different expected level of volatility.
 
Lesson 101 in trading, states to set stop-losses to trading positions. This is particularly true for directional positions on cash or futures, where the downside risk can potentially be unlimited.
Calibrating a stop-loss implies to forecast future volatility, and therefore estimate future adverse movements.
This can be done through an ARMA on Integrated Volatility, or EWMA on Daily close-to-close returns volatility for instance.
 
This is the linear component of the future volatility assessment. Non-parametric, quite precise, good job!
 
Then, the question arises: can we do better by integrating a non-linear component?
Let’s take a (locally) trending market. Prices will oscillate within a 2 standard deviation from the trend.
 
Pattern recognition implies to search for any geometrical pattern drawn from extrema of these fluctuations range.
One can think about this problem as looking for patterns in a cloud wandering above our heads. No doubt that thanks to human imagination, we will collect a very large variety of answers. In financial charts, this is basically the same result. The complexity in prices is so large that we will get very diverse answers. Coordination among market participants usually can’t emerge from the ups and downs of the market price (its volatility), because it’s completely random. 
 
The easiest way to start thinking consensus building is from local extrema of a range. From 2 local tops with some distance, one can easily draw a trendline (upward or downward), and try to infer from the subsequent price (re-)actions, if this trendline attracts some attention. 
Imagine the case of bullish market configuration, with 3 aligned points (Graph 1) : S1 and S2 are support points to draw a line a “V” acts as a validation point of this pattern. 
In this case, after “V” being confirmed, it is common-knowledge among market participants that the market is coordinating along this trendline, and that therefore one shall expect some significant buying orders, just before the price hit this trendline.
 
Well, if this is common-knowledge this feature in the volatility estimate, why not integrate this point in the trade calibration, as a non-linear component. 
Funny to see that trendlines are used to determine non-parametric & non-linear component of this volatility forecast! 🙂
 
Non-Cooperative, Simultaneous Game between a trader and the market
 
Let’s describe this game where the market is acting like “Nature” in standard Game Theory, namely a random acting player.
Ex-ante Payoff Calibration (=Sharpe Ratio)
 Price Action  Large Risk Small Risk 
 No Downside w
Small Downside  w -x
 Large Downside -y -x

 

Ex-post Payoff (=Sharpe Ratio)
 Price Action  Large Risk  Small Risk
 No Downside w w
 Small Downside w
-x
 Large Downside -y -x

Non-Cooperative, Simultaneous Game between a trader and the market when consensus has emerged

In this special case, the trade calibration is altered by the consensus being detected. If the trader’s opinion is based solely on fundamentals, he/she will post a stop-loss at a a certain price level with a uniform probability. If the trader’s conviction is more price action-dependent, then he will be tempted to post his/her stop-loss immediately below the upward resistance trendline.
Why ? Because he expects the trends to go on, and in case of adverse price movement, he is convinced that some buying limit orders will be posted just before this trendline.

If many traders post stop-losses below this trendline, in line with their own detection of a growing consensus building, one can expect a cascade of stop-losses if, inadvertently, the market price breaks the trendline and hit the stop-losses.

>> In this case, this will lead to a very particular price dynamics: an intraday “jump”, generated by this cascade of stop-losses. Jump in this situation is the signature of a past consensus, and contemporaneous unwinding of positions.
Traders will then experience some slippage on their stop-losses, because of the local market illiquidity. Intraday Jumps in this case are said to be “UNEXPECTED”.

 

R.B. Shelton [1997], Gaming the market – Applying game theory to create winning trading strategies, Wiley Trading