geometric_brownian_motion.py

def geometric_brownian_motion(G0, mu, sigma, N, T):
    """Simulates a Geometric Brownian Motion.
    
    :param float G0: initial value
    :param float mu: drift coefficient
    :param float sigma: diffusion coefficient
    :param int N: number of discrete steps
    :param int T: number of continuous time steps
    :return list: the geometric Brownian Motion
    """
    # the normalizing constant
    dt = 1. * T/N
    # standard brownian motion
    W, _ = brownian_motion(N, T ,1.0)
    # generate the time steps
    time_steps = np.linspace(0.0, N*dt, N+1)
    
    # calculate the geometric brownian motion
    G = G0 * np.exp(mu * time_steps + sigma * W)
    # replace the initial value
    G[0] = G0
    
    return G