def test_FBM_fgn_adjust_rnd(n_good, hurst_good, length_good,
fbm_method_good, adjust_rnd_good):
f = FBM(n_good, hurst_good, length_good, fbm_method_good)
fgn_sample = f.fgn()
fgn_sample = f.fgn(adjust_rnd_good)
assert isinstance(fgn_sample, np.ndarray)
assert len(fgn_sample) == n_good
class FBM2D:
def __init__(self, H, N, L):
"""
init of FBM2D
parameters:
H : Hurst index with 0 < H < 1
N : number of observations along both dimensions, constructed field will contain (N x N) points
L : number of one dimensional fbm used in construction of 2D Fields
"""
if H <= 0 or H >= 1:
raise ValueError("Hurst parameter must be in interval (0, 1).")
self.H = H
self.N = N
self.L = L
self.fbb_gen = FBM(
n=int(1.5 * self.N), hurst=self.H,
length=1.5) #init generator for fractional Brownian motion
def fbs(self):
"""
returnes fractional Brownian surface (scalar fractional Brownian motion) in 2D
"""
#generate self.L bands with equidistant angles theta between band and x-axis
theta_i = np.linspace(0, np.pi, self.L + 1)[:-1] #angles
oneDfbm = np.zeros((self.L, int(1.5 * self.N) + 1))
for i in range(self.L):
fGn = self.fbb_gen.fgn()
oneDfbm[i, 1:] = np.sqrt(
np.sqrt(np.pi) * math.gamma(1 + self.H) /
math.gamma(1 / 2 + self.H)) * np.cumsum(fGn)
# perform turbing band algortihm in fortran
return f.turningband2d(oneDfbm, theta_i, self.N)
class FractionalBlackScholes(BlackScholes):
def __init__(self,
drift,
volatility,
hurst,
nb_paths,
nb_stocks,
nb_dates,
spot,
maturity,
dividend=0,
**keywords):
super(FractionalBlackScholes,
self).__init__(drift, volatility, nb_paths, nb_stocks, nb_dates,
spot, maturity, dividend, **keywords)
self.drift = drift
self.hurst = hurst
self.fBM = FBM(n=nb_dates,
hurst=self.hurst,
length=maturity,
method='hosking')
def generate_one_path(self):
"""Returns a nparray (nb_stocks * nb_dates) with prices."""
path = np.empty((self.nb_stocks, self.nb_dates + 1))
fracBM_noise = np.empty((self.nb_stocks, self.nb_dates))
path[:, 0] = self.spot
for stock in range(self.nb_stocks):
fracBM_noise[stock, :] = self.fBM.fgn()
for k in range(1, self.nb_dates + 1):
previous_spots = path[:, k - 1]
diffusion = self.diffusion_fct(previous_spots, (k) * self.dt)
path[:, k] = (previous_spots +
self.drift_fct(previous_spots,
(k) * self.dt) * self.dt +
np.multiply(diffusion, fracBM_noise[:, k - 1]))
print("path", path)
return path
from fbm import FBM import matplotlib.pyplot as plt f = FBM(n=100, hurst=0.9, length=1, method='daviesharte') # Generate a fBm realization fbm_sample = f.fbm() # Generate a fGn realization fgn_sample = f.fgn() # Get the times associated with the fBm t_values = f.times() plt.plot(t_values, fbm_sample) plt.show()
# flake8: noqa
from fbm import FBM
import matplotlib.pyplot as plt
import time
import math
import numpy as np
def h(s):
# return 0.499*math.sin(t) + 0.5
# return 0.6 * t + 0.3
return 0.5 * np.exp(-8.0 * s**2)
fbm_generator = FBM(2**8, 0.85)
t = fbm_generator.times()
fbm_realization = fbm_generator.fbm()
fgn_realization = fbm_generator.fgn()
h_t = np.array(h(fbm_realization))
plt.plot(t, fbm_realization)
plt.plot(t, h_t)
# plt.plot(t[0:-1], fgn_realization)
plt.show()
