# 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
import pandas as pd
from tensortrade.stochastic.processes.brownian_motion import brownian_motion_log_returns
from tensortrade.stochastic.utils import ModelParameters, generate
[docs]def cox_ingersoll_ross_levels(params: 'ModelParameters') -> 'np.array':
"""
Constructs the rate levels of a mean-reverting Cox-Ingersoll-Ross process.
Used to model interest rates as well as stochastic volatility in the Heston
model. We pass a correlated Brownian motion process into the method from
which the interest rate levels are constructed because the returns between
the underlying and the stochastic volatility should be correlated. The other
correlated process is used in the Heston model.
Parameters
----------
params : `ModelParameters`
The parameters for the stochastic model.
Returns
-------
`np.array`
The interest rate levels for the CIR process.
"""
brownian_motion = brownian_motion_log_returns(params)
# Setup the parameters for interest rates
a, mu, zero = params.cir_a, params.cir_mu, params.all_r0
# Assumes output is in levels
levels = [zero]
for i in range(1, params.all_time):
drift = a * (mu - levels[i - 1]) * params.all_delta
# The main difference between this and the Ornstein Uhlenbeck model is that we multiply the 'random'
# component by the square-root of the previous level i.e. the process has level dependent interest rates.
randomness = np.sqrt(levels[i - 1]) * brownian_motion[i - 1]
levels.append(levels[i - 1] + drift + randomness)
return np.array(levels)
[docs]def cox(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 the CIR 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/Cox%E2%80%93Ingersoll%E2%80%93Ross_model
"""
data_frame = generate(
price_fn=cox_ingersoll_ross_levels,
base_price=base_price,
base_volume=base_volume,
start_date=start_date,
start_date_format=start_date_format,
times_to_generate=times_to_generate,
time_frame=time_frame,
params=params
)
return data_frame