# Copyright 2020 The TensorTrade Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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import numpy as np
import pandas as pd
from stochastic.processes.noise import GaussianNoise
from tensortrade.stochastic.processes.brownian_motion import brownian_motion_log_returns
from tensortrade.stochastic.utils.helpers import get_delta, scale_times_to_generate, convert_to_prices
from tensortrade.stochastic.utils.parameters import ModelParameters, default
[docs]def geometric_brownian_motion_log_returns(params: 'ModelParameters') -> 'np.array':
"""Constructs a sequence of log returns.
When log returns are exponentiated, it produces a random Geometric
Brownian Motion (GBM). The GBM is the stochastic process underlying
the Black-Scholes options pricing formula.
Parameters
----------
params : `ModelParameters`
The parameters for the stochastic model.
Returns
-------
`np.array`
The log returns of a geometric brownian motion process
"""
wiener_process = np.array(brownian_motion_log_returns(params))
sigma_pow_mu_delta = (params.gbm_mu - 0.5 * pow(params.all_sigma, 2)) * params.all_delta
return wiener_process + sigma_pow_mu_delta
[docs]def geometric_brownian_motion_levels(params: 'ModelParameters'):
"""Constructs a sequence of price levels for an asset which evolves
according to a geometric brownian motion process.
Parameters
----------
params : ModelParameters
The parameters for the stochastic model.
Returns
-------
`np.array`
The price levels for the asset
"""
return convert_to_prices(params, geometric_brownian_motion_log_returns(params))
[docs]def gbm(base_price: int = 1,
base_volume: int = 1,
start_date: str = '2010-01-01',
start_date_format: str = '%Y-%m-%d',
times_to_generate: int = 1000,
time_frame: str = '1h',
params: 'ModelParameters' = None) -> 'pd.DataFrame':
"""Generates price data from a GBM process.
Parameters
----------
base_price : int, default 1
The base price to use for price generation.
base_volume : int, default 1
The base volume to use for volume generation.
start_date : str, default '2010-01-01'
The start date of the generated data
start_date_format : str, default '%Y-%m-%d'
The format for the start date of the generated data.
times_to_generate : int, default 1000
The number of bars to make.
time_frame : str, default '1h'
The time frame.
params : `ModelParameters`, optional
The model parameters.
Returns
-------
`pd.DataFrame`
The generated data frame containing the OHLCV bars.
References
----------
[1] https://en.wikipedia.org/wiki/Geometric_Brownian_motion
"""
delta = get_delta(time_frame)
times_to_generate = scale_times_to_generate(times_to_generate, time_frame)
params = params or default(base_price, times_to_generate, delta)
prices = geometric_brownian_motion_levels(params)
volume_gen = GaussianNoise(t=times_to_generate)
volumes = volume_gen.sample(times_to_generate) + base_volume
start_date = pd.to_datetime(start_date, format=start_date_format)
price_frame = pd.DataFrame([], columns=['date', 'price'], dtype=float)
volume_frame = pd.DataFrame([], columns=['date', 'volume'], dtype=float)
price_frame['date'] = pd.date_range(start=start_date, periods=times_to_generate, freq="1min")
price_frame['price'] = abs(prices)
volume_frame['date'] = price_frame['date'].copy()
volume_frame['volume'] = abs(volumes)
price_frame.set_index('date')
price_frame.index = pd.to_datetime(price_frame.index, unit='m', origin=start_date)
volume_frame.set_index('date')
volume_frame.index = pd.to_datetime(volume_frame.index, unit='m', origin=start_date)
data_frame = price_frame['price'].resample(time_frame).ohlc()
data_frame['volume'] = volume_frame['volume'].resample(time_frame).sum()
return data_frame