def test_gbm_log_euler_step_nd_output_changes_with_t(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]],
dtype=np.float32)
dt = 0.01
t_0 = 0.0
num_samples = 8
num_dims = drift.shape[0]
t_1 = t_0 + dt
log_states = tf.zeros([num_samples, num_dims])
next_log_states_0 = dynamics.gbm_log_euler_step_nd(
log_states, drift, vol_matrix, t_0, dt)
next_log_states_1 = dynamics.gbm_log_euler_step_nd(
log_states, drift, vol_matrix, t_1, dt)
with self.session() as session:
next_log_states_0_eval, next_log_states_1_eval = session.run(
(next_log_states_0, next_log_states_1))
self.assertEqual(next_log_states_0_eval.shape, (num_samples, num_dims))
self.assertEqual(next_log_states_1_eval.shape, (num_samples, num_dims))
# The step is a bijection w.r.t. dw_t, all terms should be different.
self.assertAllDistinct(next_log_states_0_eval, next_log_states_1_eval)
def test_gbm_log_euler_step_nd_is_deterministic(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]], dtype=np.float32)
dt = 0.01
t = 0.0
num_samples = 8
num_dims = drift.shape[0]
key = 128
log_states = tf.zeros([num_samples, num_dims])
eps_t = contrib_stateless.stateless_random_normal(
shape=[num_samples, num_dims], seed=[key, int(t / dt)])
next_log_states = dynamics.gbm_log_euler_step_nd(
log_states, drift, vol_matrix, t, dt, random_normal_op=lambda: eps_t)
next_log_states_bis = dynamics.gbm_log_euler_step_nd(
log_states, drift, vol_matrix, t, dt, key=key)
with self.session() as session:
next_log_states_eval, next_log_states_bis_eval = session.run(
(next_log_states, next_log_states_bis))
self.assertEqual(next_log_states_eval.shape, (num_samples, num_dims))
self.assertEqual(next_log_states_bis_eval.shape, (num_samples, num_dims))
self.assertAllClose(next_log_states_eval, next_log_states_bis_eval)
def test_gbm_log_euler_step_nd_expects_static_shape(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]], dtype=np.float32)
dt = 0.01
t = 0.0
num_dims = drift.shape[0]
log_states = tf.placeholder(dtype=tf.float32, shape=[None, num_dims])
with self.assertRaises(ValueError):
dynamics.gbm_log_euler_step_nd(log_states, drift, vol_matrix, t, dt)
def test_gbm_log_euler_step_nd_output_is_correct(self):
drift = np.asarray([0.1, 0.3, -0.05], dtype=np.float32)
vol_matrix = 0.2 * np.asarray(
[[1.5, 0.2, 0.3], [0.2, 1.1, -0.1], [0.3, -0.1, 0.8]],
dtype=np.float32)
dt = 0.01
t = 0.0
num_samples = 8
num_dims = drift.shape[0]
log_states = tf.zeros([num_samples, num_dims])
eps_t = np.ndarray.astype(
np.random.normal(size=[num_samples, num_dims]), dtype=np.float32)
next_log_states = dynamics.gbm_log_euler_step_nd(
log_states,
drift,
vol_matrix,
t,
dt,
random_normal_op=lambda: eps_t)
with self.session() as session:
next_log_states_eval = session.run(next_log_states)
self.assertEqual(next_log_states_eval.shape, (num_samples, num_dims))
for i in range(num_samples):
self.assertAllClose(
next_log_states_eval[i],
np.zeros([num_dims], dtype=np.float32) +
(drift - 0.5 * np.sum(vol_matrix**2, axis=0)) * dt +
np.matmul(vol_matrix, eps_t[i] * np.sqrt(dt)))
def _dynamics_op(log_s, t, dt):
return dynamics.gbm_log_euler_step_nd(log_s, r, vol, t, dt, key=1)
def _dynamics_op(log_s, t, dt):
return gbm_log_euler_step_nd(log_s, sim_drift, sim_vol_matrix, t, dt)
