BrownianMotion.py

import math
import numpy
import random
import decimal
import scipy.linalg
import numpy.random as nrand
import matplotlib.pyplot as plt

"""
Note that this Gist uses the Model Parameters class found here  - https://gist.github.com/StuartGordonReid/f01f479c783dd40cc21e
"""

def brownian_motion_log_returns(param):
    """
    This method returns a Wiener process. The Wiener process is also called Brownian motion. For more information
    about the Wiener process check out the Wikipedia page: http://en.wikipedia.org/wiki/Wiener_process
    :param param: the model parameters object
    :return: brownian motion log returns
    """
    sqrt_delta_sigma = math.sqrt(param.all_delta) * param.all_sigma
    return nrand.normal(loc=0, scale=sqrt_delta_sigma, size=param.all_time)


def brownian_motion_levels(param):
    """
    Returns a price sequence whose returns evolve according to a brownian motion
    :param param: model parameters object
    :return: returns a price sequence which follows a brownian motion
    """
    return convert_to_prices(param, brownian_motion_log_returns(param))