# Stochastic

Stochastic is an indicator that George Lane announced in the 1950s. The concept of the indicator is to measure how high the current stock price is out of the stock price range for the last N days. If you look at the formula, you will see how it works.

$Stochastic\ N=\frac{Current\ price - Lowest\ price\ of\ N\ days}{Highest\ price\ of\ N\ days - Lowest\ price\ of\ N\ days} \times 100$

Let's get Stochastic 3, a 3-day stochastic, with an 8-day stock price hereunder. When calculating the stochastic, not only the close price is used, but all prices including open, high, low is used.

Day Open High Low Close Highest Lowest Stochastic 3 K D
1 10 11 9 10 11 9 - - -
2 11 12 10 11 12 10 - - -
3 8 10 8 9 10 8 25.0 - -
4 10 13 10 12 13 10 80.0 - -
5 13 15 12 15 15 12 100.0 68.3 -
6 13 20 13 17 20 13 70.0 83.3 -
7 17 18 15 16 18 15 50.0 73.3 75.0
8 15 16 13 14 16 13 14.3 44.8 67.1

(Step 1) Since we have to calculate a 3-day stochastic, the first two days cannot be calculated due to data size. We are to start from day 3. The highest price for the day 1 to day 3 is 12, the lowest is 8, and the close price on the day 3 is 9, so Stochastic is $\frac{(9-8)}{(12-8)} \times 100 = 25$.
On day 5, the highest price of 15, the lowest price of 8, and the close price is 15, so stochastic is $\frac{(15-8)}{(15-8)} \times 100 = 100$.

(Step 2) The stochastic obtained in this way shows the level of the stock price that day, but it is inconvenient to use for trading because it is very jagged. So, we need to get the moving average of the stochastic values and smooth them. The moving average value obtained in this way is called Slow K, and Slow K is used as a trading index.

(Step 3) Lane made Slow D by smoothing Slow K one more time to make it more sophisticated. Slow D is the moving average of Slow K once more. And the difference between Slow K and Slow D is also used as a trading index.

A three-step criterion is required when calculating the stochastic. The period N to find the initial stochastic, the period required to calculate the moving average value with the stochastic, m, and the period required to calculate the moving average from Slow K to Slow D. t. This can be simply expressed as STO(N, m, t). The default setting by Lane is STO(14, 3, 3). Some trading system can be set for both N, m, and t, and some can be set only for N.

For informational purpose only.