def get_paths(p0: float, sigma0: float, t: float, theta: float, w: float,
k: float, no_paths: int, no_time_steps: int, seed: int):
paths = np.empty(shape=(no_paths, no_time_steps))
v_t = np.empty(shape=(no_paths, no_time_steps))
paths[:, 0] = p0
v_t[:, 0] = sigma0 * sigma0
t_i_s = np.linspace(0.0, t, no_time_steps)
np.random.rand(seed)
nu = np.sqrt(2.0 * k * theta)
for i in range(0, no_paths):
u_s = np.random.rand(no_time_steps)
u_sigma = np.random.rand(no_time_steps)
for j in range(1, no_time_steps):
delta_time = (t_i_s[j] - t_i_s[j - 1])
z_sigma_i = ndtri(u_sigma[j])
z_s_i = ndtri(u_s[j])
exp_t = np.exp(-theta * delta_time)
v_t[i, j] = v_t[i, j - 1] * exp_t + w * (1.0 - exp_t) + \
nu * np.sqrt(0.5 * ((1.0 - exp_t * exp_t) / theta)) * v_t[i, j - 1] * z_sigma_i
paths[i, j] = paths[i, j - 1] + np.sqrt(
v_t[i, j - 1]) * np.sqrt(delta_time) * z_s_i
return paths, v_t, t_i_s
def norm_inv(mu, sigma, z):
size_z = len(z)
normal_narray = np.empty(size_z)
for i in range(0, size_z):
normal_narray[i] = ndtri(z[i])
return normal_narray
def get_variance(k: float, theta: float, epsilon: float,
phi_switch_level: float, t_i_1: float, t_i: float,
v_t_i_1: ndarray, u_i: ndarray, no_paths: int):
# no_paths = len(v_t_i_1)
paths = np.zeros(no_paths)
for i in range(0, no_paths):
s_2_i = HestonTools.v_t_conditional_variance(k, theta, epsilon,
v_t_i_1[i], t_i_1, t_i)
m_i = HestonTools.v_t_conditional_mean(k, theta, v_t_i_1[i], t_i_1,
t_i)
phi = s_2_i / (m_i * m_i)
if phi < phi_switch_level:
parameters = HestonTools.matching_qe_moments_qg(m_i, s_2_i)
z_i = ndtri(u_i[i])
paths[i] = parameters[1] * np.power(parameters[0] + z_i, 2.0)
else:
parameters = HestonTools.matching_qe_moments_exp(m_i, s_2_i)
paths[i] = HestonTools.inv_exp_heston(parameters[0], parameters[1],
u_i[i])
return paths
def test_ndtri():
assert_almost_equal(ndtri(0.6), 0.253347103136)