Python Volatility-Based Catapult Indicator

As a catapult, this technical indicator uses three systems: Volatility (the fulcrum), Momentum (the propeller), and a Directional Filter (Acting as the support). The goal is to get a signal that predicts volatility acceleration and direction based on historical patterns. We want to know when the market will move. and where. This indicator outperforms standard indicators.

Knowledge must be accessible to everyone. This is why my new publications Contrarian Trading Strategies in Python and Trend Following Strategies in Python now include free PDF copies of my first three books (Therefore, purchasing one of the new books gets you 4 books in total). GitHub-hosted advanced indications and techniques are in the two new books above.

The Foundation: Volatility

The Catapult predicts significant changes with the 21-period Relative Volatility Index.

The Average True Range, Mean Absolute Deviation, and Standard Deviation all assess volatility. Standard Deviation will construct the Relative Volatility Index.

Standard Deviation is the most basic volatility. It underpins descriptive statistics and technical indicators like Bollinger Bands. Before calculating Standard Deviation, let's define Variance.

Variance is the squared deviations from the mean (a dispersion measure). We take the square deviations to compel the distance from the mean to be non-negative, then we take the square root to make the measure have the same units as the mean, comparing apples to apples (mean to standard deviation standard deviation). Variance formula:

As stated, standard deviation is:

# The function to add a number of columns inside an array
def adder(Data, times):
    
    for i in range(1, times + 1):
    
        new_col = np.zeros((len(Data), 1), dtype = float)
        Data = np.append(Data, new_col, axis = 1)
        
    return Data

# The function to delete a number of columns starting from an index
def deleter(Data, index, times):
    
    for i in range(1, times + 1):
    
        Data = np.delete(Data, index, axis = 1)
        
    return Data
    
# The function to delete a number of rows from the beginning
def jump(Data, jump):
    
    Data = Data[jump:, ]
    
    return Data

# Example of adding 3 empty columns to an array
my_ohlc_array = adder(my_ohlc_array, 3)

# Example of deleting the 2 columns after the column indexed at 3
my_ohlc_array = deleter(my_ohlc_array, 3, 2)

# Example of deleting the first 20 rows
my_ohlc_array = jump(my_ohlc_array, 20)

# Remember, OHLC is an abbreviation of Open, High, Low, and Close and it refers to the standard historical data file

def volatility(Data, lookback, what, where):
    
  for i in range(len(Data)):

     try:

        Data[i, where] = (Data[i - lookback + 1:i + 1, what].std())
     except IndexError:
        pass
        
  return Data

The RSI is the most popular momentum indicator, and for good reason—it excels in range markets. Its 0–100 range simplifies interpretation. Fame boosts its potential.

The more traders and portfolio managers look at the RSI, the more people will react to its signals, pushing market prices. Technical Analysis is self-fulfilling, therefore this theory is obvious yet unproven.

RSI is determined simply. Start with one-period pricing discrepancies. We must remove each closing price from the previous one. We then divide the smoothed average of positive differences by the smoothed average of negative differences. The RSI algorithm converts the Relative Strength from the last calculation into a value between 0 and 100.

def ma(Data, lookback, close, where): 
    
    Data = adder(Data, 1)
    
    for i in range(len(Data)):
           
            try:
                Data[i, where] = (Data[i - lookback + 1:i + 1, close].mean())
            
            except IndexError:
                pass
            
    # Cleaning
    Data = jump(Data, lookback)
    
    return Data
def ema(Data, alpha, lookback, what, where):
    
    alpha = alpha / (lookback + 1.0)
    beta  = 1 - alpha
    
    # First value is a simple SMA
    Data = ma(Data, lookback, what, where)
    
    # Calculating first EMA
    Data[lookback + 1, where] = (Data[lookback + 1, what] * alpha) + (Data[lookback, where] * beta)    
 
    # Calculating the rest of EMA
    for i in range(lookback + 2, len(Data)):
            try:
                Data[i, where] = (Data[i, what] * alpha) + (Data[i - 1, where] * beta)
        
            except IndexError:
                pass
            
    return Datadef rsi(Data, lookback, close, where, width = 1, genre = 'Smoothed'):
    
    # Adding a few columns
    Data = adder(Data, 7)
    
    # Calculating Differences
    for i in range(len(Data)):
        
        Data[i, where] = Data[i, close] - Data[i - width, close]
     
    # Calculating the Up and Down absolute values
    for i in range(len(Data)):
        
        if Data[i, where] > 0:
            
            Data[i, where + 1] = Data[i, where]
            
        elif Data[i, where] < 0:
            
            Data[i, where + 2] = abs(Data[i, where])
            
    # Calculating the Smoothed Moving Average on Up and Down
    absolute values        
                             
    lookback = (lookback * 2) - 1 # From exponential to smoothed
    Data = ema(Data, 2, lookback, where + 1, where + 3)
    Data = ema(Data, 2, lookback, where + 2, where + 4)
    
    # Calculating the Relative Strength
    Data[:, where + 5] = Data[:, where + 3] / Data[:, where + 4]
    
    # Calculate the Relative Strength Index
    Data[:, where + 6] = (100 - (100 / (1 + Data[:, where + 5])))  
    
    # Cleaning
    Data = deleter(Data, where, 6)
    Data = jump(Data, lookback)

    return Data

def relative_volatility_index(Data, lookback, close, where):

    # Calculating Volatility
    Data = volatility(Data, lookback, close, where)
    
    # Calculating the RSI on Volatility
    Data = rsi(Data, lookback, where, where + 1) 
    
    # Cleaning
    Data = deleter(Data, where, 1)
    
    return Data

The Arm Section: Speed

The Catapult predicts momentum direction using the 14-period Relative Strength Index.

As a reminder, the RSI ranges from 0 to 100. Two levels give contrarian signals:

• A positive response is anticipated when the market is deemed to have gone too far down at the oversold level 30, which is 30.

• When the market is deemed to have gone up too much, at overbought level 70, a bearish reaction is to be expected.

Comparing the RSI to 50 is another intriguing use. RSI above 50 indicates bullish momentum, while below 50 indicates negative momentum.

The direction-finding filter in the frame

The Catapult's directional filter uses the 200-period simple moving average to keep us trending. This keeps us sane and increases our odds.

Moving averages confirm and ride trends. Its simplicity and track record of delivering value to analysis make them the most popular technical indicator. They help us locate support and resistance, stops and targets, and the trend. Its versatility makes them essential trading tools.

This is the plain mean, employed in statistics and everywhere else in life. Simply divide the number of observations by their total values. Mathematically, it's:

We defined the moving average function above. Create the Catapult indication now.

Indicator of the Catapult

The indicator is a healthy mix of the three indicators:

• The first trigger will be provided by the 21-period Relative Volatility Index, which indicates that there will now be above average volatility and, as a result, it is possible for a directional shift.

• If the reading is above 50, the move is likely bullish, and if it is below 50, the move is likely bearish, according to the 14-period Relative Strength Index, which indicates the likelihood of the direction of the move.

• The likelihood of the move's direction will be strengthened by the 200-period simple moving average. When the market is above the 200-period moving average, we can infer that bullish pressure is there and that the upward trend will likely continue. Similar to this, if the market falls below the 200-period moving average, we recognize that there is negative pressure and that the downside is quite likely to continue.

lookback_rvi = 21
lookback_rsi = 14
lookback_ma  = 200
my_data = ma(my_data, lookback_ma, 3, 4)
my_data = rsi(my_data, lookback_rsi, 3, 5)
my_data = relative_volatility_index(my_data, lookback_rvi, 3, 6)

Two-handled overlay indicator Catapult. The first exhibits blue and green arrows for a buy signal, and the second shows blue and red for a sell signal.

The chart below shows recent EURUSD hourly values.

def signal(Data, rvi_col, signal):
    
    Data = adder(Data, 10)
        
    for i in range(len(Data)):
            
        if Data[i,     rvi_col] < 30 and \
           Data[i - 1, rvi_col] > 30 and \
           Data[i - 2, rvi_col] > 30 and \
           Data[i - 3, rvi_col] > 30 and \
           Data[i - 4, rvi_col] > 30 and \
           Data[i - 5, rvi_col] > 30:
               
               Data[i, signal] = 1
                           
    return Data

Signals are straightforward. The indicator can be utilized with other methods.

my_data = signal(my_data, 6, 7)

Lumiwealth shows how to develop all kinds of algorithms. I recommend their hands-on courses in algorithmic trading, blockchain, and machine learning.

Summary

To conclude, my goal is to contribute to objective technical analysis, which promotes more transparent methods and strategies that must be back-tested before implementation. Technical analysis will lose its reputation as subjective and unscientific.

After you find a trading method or approach, follow these steps:

• Put emotions aside and adopt an analytical perspective.

• Test it in the past in conditions and simulations taken from real life.

• Try improving it and performing a forward test if you notice any possibility.

• Transaction charges and any slippage simulation should always be included in your tests.

• Risk management and position sizing should always be included in your tests.

After checking the aforementioned, monitor the plan because market dynamics may change and render it unprofitable.

DATA MINING WITH SUPERALGORES

Old pots produce the best soup.

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:

With

Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:

With

and

L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close
}

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)
}

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

variable.allClose.push(candle.close)
if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
}
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1
}

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

variable.allE.push(variable.E)
if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    }
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    }
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
}
variable.allZ.push(variable.Z)
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    }
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    }
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
}
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA

Conclusion

We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.

Would you abandon your bank for Apple?

Banks are struggling.

• not as a result of inflation

• not due to the economic downturn.

• not due to the conflict in Ukraine.

But because they’re underestimating Apple.

Slowly but surely, Apple is looking more like a bank.

An easy new savings account like Apple

Apple has a new savings account.

Apple says Apple Card users may set up and manage savings straight in Wallet.

• No more charges

• Colorfully high yields

• With no minimum balance

• No minimal down payments

Most consumer-facing banks will have to match Apple's offer or suffer disruption.

Users may set it up from their iPhones without traveling to a bank or filling out paperwork.

It’s built into the iPhone in your pocket.

So now more waiting for slow approval processes.

Once the savings account is set up, Apple will automatically transfer all future Daily Cash into it. Users may also add these cash to an Apple Cash card in their Apple Wallet app and adjust where Daily Cash is paid at any time.

Apple Pay and Apple Wallet VP Jennifer Bailey:

Savings enables Apple Card users to grow their Daily Cash rewards over time, while also saving for the future.

Bailey says Savings adds value to Apple Card's Daily Cash benefit and offers another easy-to-use tool to help people lead healthier financial lives.

Transfer money from a linked bank account or Apple Cash to a Savings account. Users can withdraw monies to a connected bank account or Apple Cash card without costs.

Once set up, Apple Card customers can track their earnings via Wallet's Savings dashboard. This dashboard shows their account balance and interest.

This product targets younger people as the easiest way to start a savings account on the iPhone.

Why would a Gen Z account holder travel to the bank if their iPhone could be their bank?

Using this concept, Apple will transform the way we think about banking by 2030.

Two other nightmares keep bankers awake at night

Apple revealed two new features in early 2022 that banks and payment gateways hated.

• Tap to Pay with Apple

• Late Apple Pay

They startled the industry.

Tap To Pay converts iPhones into mobile POS card readers. Apple Pay Later is pushing the BNPL business in a consumer-friendly direction, hopefully ending dodgy lending practices.

Tap to Pay with Apple

iPhone POS

Millions of US merchants, from tiny shops to huge establishments, will be able to accept Apple Pay, contactless credit and debit cards, and other digital wallets with a tap.

No hardware or payment terminal is needed.

Revolutionary!

Stripe has previously launched this feature.

Tap to Pay on iPhone will provide companies with a secure, private, and quick option to take contactless payments and unleash new checkout experiences, said Bailey.

Apple's solution is ingenious. Brilliant!

Bailey says that payment platforms, app developers, and payment networks are making it easier than ever for businesses of all sizes to accept contactless payments and thrive.

I admire that Apple is offering this up to third-party services instead of closing off other functionalities.

Slow POS terminals, farewell.

Late Apple Pay

Pay Apple later.

Apple Pay Later enables US consumers split Apple Pay purchases into four equal payments over six weeks with no interest or fees.

The Apple ecosystem integration makes this BNPL scheme unique. Nonstick. No dumb forms.

Frictionless.

Just double-tap the button.

Apple Pay Later was designed with users' financial well-being in mind. Apple makes it easy to use, track, and pay back Apple Pay Later from Wallet.

Apple Pay Later can be signed up in Wallet or when using Apple Pay. Apple Pay Later can be used online or in an app that takes Apple Pay and leverages the Mastercard network.

Apple Pay Order Tracking helps consumers access detailed receipts and order tracking in Wallet for Apple Pay purchases at participating stores.

Bad BNPL suppliers, goodbye.

Most bankers will be caught in Apple's eye playing mini golf in high-rise offices.

The big problem:

• Banks still think about features and big numbers just like other smartphone makers did not too long ago.

• Apple thinks about effortlessness, seamlessness, and frictionlessness that just work through integrated hardware and software.

Let me know what you think Apple’s next power moves in the banking industry could be.