Deep Learning for VWAP Execution

This repository presents Aplo's latest research on VWAP execution and contains the code discussed in the paper Deep Learning for VWAP Execution in Crypto Markets: Beyond the Volume Curve.

Model

The model is proposed as a keras3 package that works with any backend (tensorflow, jax, or torch), although we recommend using jax for optimal performance.

Installation

1. Download the repository
2. Run pip install . or poetry install (recommended) in the root folder of the repository

Alternatively, you can install the package from PyPi:

pip install dvwap

Usage

from dvwap import StaticVWAP, quadratic_vwap_loss, absolute_vwap_loss, volume_curve_loss

BATCH_SIZE = 128
N_MAX_EPOCHS = 1000

# Specify your model parameters
# lookback and n_ahead are integer values representing the window sizes
model = StaticVWAP(lookback=lookback, n_ahead=n_ahead, input_include_aheads=False)

# The StaticVWAP is a keras model, so it works similarly
# To minimize the VWAP loss effectively, use a loss function that accounts for it
# These losses are available in the dvwap package
model.compile(optimizer='adam', loss=quadratic_vwap_loss)

# Training
history = model.fit(X_train, y_train, batch_size=BATCH_SIZE, epochs=N_MAX_EPOCHS, 
                    validation_split=0.2, callbacks=callbacks(), shuffle=True, verbose=False)

# Prediction
preds = model.predict(X_test, verbose=False)

Model Parameters

• lookback and n_ahead are integer values representing the window sizes.
• input_include_aheads: You can have two formats of inputs for your model:
  1. If True, the feature inputs should be formatted to have a size of lookback + n_ahead on the sequence length.
  2. If False, pass inputs with only lookback on sequence length.

Note: Future values are not used by the static model, as it gives its prediction at t0 for the full period. The input_include_aheads option is provided for flexibility when comparing with dynamic models that require future inputs to progressively update their predictions.

Loss Functions

The StaticVWAP is a Keras model. To minimize the VWAP loss effectively, you should use a loss function that accounts for it. These loss functions are available in the dvwap package:

• quadratic_vwap_loss
• absolute_vwap_loss
• volume_curve_loss

Data Formatting

The model expects inputs as a dictionary:

{
    "prices": array shape (num_elem, seq_len, 1),
    "volumes": array shape (num_elem, seq_len, 1),
    "features": array shape (num_elem, seq_len, num_features)
}

Training targets should be an array of shape (num_elem, n_ahead, 2) with volumes in the first element of the last dimension, and price in the second.

To use the default data formatter from the paper:

import pandas as pd
from dvwap.data_formater import full_generate

volumes = pd.read_parquet('path_to_your_volume_data.parquet')
notionals = pd.read_parquet('path_to_your_notionals_data.parquet')

X_train, X_test, y_train, y_test = full_generate(volumes, notionals, target_asset, 
                                                 lookback=120, n_ahead=12, test_split=0.2, 
                                                 include_ahead_inputs=False, autoscale_target=True)

Other models

The package also contains the dynamic framework following the paper 'Improving VWAP strategies: A dynamic volume approach', Jedrzej Bialkowski (1) , Serge Darolles (2) , Gaëlle Le Fol (3). It is available importing DynamicVWAPStandardModel. For more details look in the example and results section, or in the code.

Results

Tables and graphs of results from the paper can be found in the example_and_results folder.

License

Shield:

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.