Standard deviation applied to the Bell Curve

Standard deviation now gives us a measure of what is normal or abnormal which can then be applied in various ways to give us a yardstick to judge whether a market or instrument is volatile, and if so the degree of this volatility.
Average True Range (ATR):Average true range (ATR) is a further attempt to define and display volatility in a more meaningful way. It is very different from the standard deviation model, as ATR considers historical price action as the key event in forecasting future volatility.

This was developed by J. Welles Wilder and started life as ‘True Range’ before a moving average was added tosmooth out the calculation, and provide a more useful measure of volatility.If we start with ‘true range’, this is calculated as follows, and is taken as the largest of three possible values. As you will see the approach considers not simply the current price bar, but also its relationship to the previous bar in terms of the spread of price action:

The distance from the current high to current low
The distance from the previous close to current high
The distance from the previous close to current low

This is shown in Fig 7.13 and it is important to note that in calculating the second and third of these numbers, an absolute value is used. In other words no negative numbers, as the interpretation and measurement of volatility is non directional.True range calculations:In order to make this measure of volatility more meaningful, Wilder then introduced the ‘average’ over a given number of bars to produce the Average True Range or ATR.

This is generally set at 14 periods as the ‘norm’ although values can be changed according to the timeframe under consideration.There are many other models that have been developed to try to capture and display this ethereal term we refer to as volatility. Standard deviation and the ATR are just two, and two of the most commonly used by traders, but I must stress there are others.

However, in my humble opinion it is these two models which have come closest, but as with every other measure these are premised on the belief markets follow mathematical principles, which clearly they do not. Therefore the best we can hope to come up with is a ‘best fit’ for measuring and interpreting volatility however we understand the term in the context of trading.

Every model is flawed in some way, and what we have to decide for ourselves, is which approach do we believe provides the closest approximation to market behavior. It is also important to understand that volatility, as a decision making tool, is not a standalone one. It is always used in conjunction with other tools, such as volume and a full array of analytical techniques.

For option traders what it is attempting to signal is those periods of high, medium or low volatility,which are so critical in predicting the future behavior of the binary option, and the reason is very simple. It is to do with what is known as Delta.Delta In the world of vanilla options, Delta refers to how much an option price changes with that of the underlying market.

Delta will vary over the life of the option, and will be influenced by the underlying market as well as the time to expiry for the option. Delta is expressed between -1 and +1 depending on whether we have a put or a call. In simple terms a Delta of + 0.5 indicates that for every \$1 rise in the underlying price, the option price will rise by 50 cents. For put options the Delta would be negative.However, the Delta in binary options is very different, and reflects the volatility associated with the binary instrument, and is what is referred to as exponential Delta.

The relationship here is a non linear one. Imagine for a moment the binary option is very close to expiry, perhaps only seconds away and at the strike price. In this case, a 1 tick move or a 1 point or pip move would see the probability of the option swing from 100 to 0 and perhaps back to 100 again, literally in milliseconds. In other words huge volatility swings for tiny movements in price which confirms two things for us.

First, the volatility profile associated with a binary option is very different to any other instrument, and second, it is crucial you have the best tools and techniques to signal and forecast changes in the underlying markets. A binary option with a probability of 90 or above may look attractive, but if it is close to the strike price and close to expiry, exponential Delta will move this dramatically and suddenly.

And if you have ever had the misfortune to suffer from clear air turbulence when flying, you will know the feeling. The plane literally appears to fall out of the sky. This is the effect exponential Delta has on binary options and on the probabilities being quoted, and it is why I have spent some time explaining the basics of this elusive measure we all call volatility.