Stochastic Oscillator

Introduction#

The Stochastic Oscillator is a momentum indicator used in technical analysis that compares a particular closing price of a security to a range of its prices over a specified period. It helps traders identify overbought and oversold conditions in a market, assisting in potential buy and sell decisions.

Calculation of the Stochastic Oscillator#

The Stochastic Oscillator consists of two lines:

1. %K Line: This is the main line that represents the current closing price relative to the price range over a given period.
2. %D Line: This is a smoothed moving average of the %K line (usually a 3-period simple moving average) that helps reduce noise.

Formulas#

1. %K Formula:

• C = Current Closing Price
• L_n = Lowest Price over the last n periods
• H_n = Highest Price over the last n periods

2. %D Formula:

(where SMA stands for Simple Moving Average)

Example Calculation#

Let’s assume we have a security with the following closing prices over the last 5 days:

Assuming we want to calculate the Stochastic Oscillator with n = 5 days:

1. Calculate the Highest High (H) and the Lowest Low (L) over the last 5 days:

   • Highest High (H) = Max(22, 23, 24, 22, 25) = 25
   • Lowest Low (L) = Min(19, 19, 20, 19, 19) = 19

2. Current Closing Price (C) = $23 (Day 5).

3. Calculate %K:

4. To calculate %D, we would typically average the last three values of %K, but for simplicity in this example, we’ll just represent %D as using a 3-period simple moving average of the %K values over a chosen period (e.g., using values from previous calculations).

Python Code#

import pandas as pd

def calculate_stochastic(data, k_window=14, d_window=3):
    """Calculate the Stochastic Oscillator (%K and %D)."""
    # Calculate the lowest low and highest high over the specified %K window
    low_min = data['Low'].rolling(window=k_window).min()  # Lowest low over k_window
    high_max = data['High'].rolling(window=k_window).max()  # Highest high over k_window

    # Calculate %K
    data['%K'] = 100 * ((data['Close'] - low_min) / (high_max - low_min))

    # Calculate %D as a simple moving average of %K
    data['%D'] = data['%K'].rolling(window=d_window).mean()

    return data

Interpretation of the Stochastic Oscillator#

• Overbought Conditions: A value above 80 is typically considered overbought, suggesting that the asset might be due for a price correction.
• Oversold Conditions: A value below 20 is considered oversold, indicating that the asset might be undervalued and could see a price increase.
• Crossovers: When the %K line crosses above the %D line, it may signal a buying opportunity, while a crossover below may indicate a selling opportunity.

Analogies#

Think of the Stochastic Oscillator like a musical scale, where the notes represent price levels over time. Just as a scale can help you determine whether a song is in a high or low pitch, the Stochastic Oscillator indicates the momentum of a security’s price, helping traders identify whether the asset is poised for a price increase (in tune) or a decrease (out of tune).

Conclusion#

The Stochastic Oscillator is a valuable tool for traders looking to assess momentum and identify potential overbought or oversold conditions in the market. By comparing the closing price to historical price ranges, it provides insights that can aid in timing market entries and exits.

References#

• Wilder, J. W. (1978). New Concepts in Technical Trading Systems. Trend Research.
• Investopedia: Stochastic Oscillator
• TradingView: Stochastic Oscillator