# 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
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License
import numpy as np
from tensortrade.stochastic.utils import ModelParameters, convert_to_prices
[docs]def brownian_motion_log_returns(params: 'ModelParameters') -> 'np.array':
"""Constructs a Wiener process (Brownian Motion).
Parameters
----------
params : `ModelParameters`
The parameters for the stochastic model.
Returns
-------
`np.array`
Brownian motion log returns.
References
----------
[1] http://en.wikipedia.org/wiki/Wiener_process
"""
sqrt_delta_sigma = np.sqrt(params.all_delta) * params.all_sigma
return np.random.normal(loc=0, scale=sqrt_delta_sigma, size=params.all_time)
[docs]def brownian_motion_levels(params: 'ModelParameters') -> 'np.array':
"""Constructs a price sequence whose returns evolve according to brownian
motion.
Parameters
----------
params : `ModelParameters`
The parameters for the stochastic model.
Returns
-------
`np.array`
A price sequence which follows brownian motion.
"""
return convert_to_prices(params, brownian_motion_log_returns(params))