def test_gbm_euler_step_running_max_bridge_changes_with_key(self):
drift = 0.2
vol = 0.1
t = 0.2
dt = 0.01
num_samples = 8
key_0 = 74
key_1 = 75
states_and_max = [tf.ones([num_samples])] * 2
next_states_and_max_0 = dynamics.gbm_euler_step_running_max(
states_and_max, drift, vol, t, dt, key=key_0, simulate_bridge=True)
next_states_and_max_1 = dynamics.gbm_euler_step_running_max(
states_and_max, drift, vol, t, dt, key=key_1, simulate_bridge=True)
with self.session() as session:
next_states_and_max_0_eval, next_states_and_max_1_eval = session.run(
(next_states_and_max_0, next_states_and_max_1))
next_states_0_eval, next_max_0_eval = next_states_and_max_0_eval
next_states_1_eval, next_max_1_eval = next_states_and_max_1_eval
self.assertEqual(next_states_0_eval.shape, (num_samples, ))
self.assertEqual(next_states_1_eval.shape, (num_samples, ))
self.assertEqual(next_max_0_eval.shape, (num_samples, ))
self.assertEqual(next_max_1_eval.shape, (num_samples, ))
# The step is a bijection w.r.t. dw_t, all terms should be different.
# However there is no such guarantee for the running maxima.
self.assertAllDistinct(next_states_0_eval, next_states_1_eval)
def test_gbm_euler_step_running_max_expects_static_shape_both_members(self):
drift = 0.2
vol = 0.1
t = 0.2
dt = 0.01
states_and_max = [
tf.placeholder(dtype=tf.float32, shape=[None]),
tf.placeholder(dtype=tf.float32, shape=[None])]
with self.assertRaises(ValueError):
dynamics.gbm_euler_step_running_max(states_and_max, drift, vol, t, dt)
def test_gbm_euler_step_running_max_bridge_is_deterministic(self):
drift = 0.2
vol = 0.1
t = 0.2
dt = 0.01
num_samples = 8
key = 1337
states_and_max = [tf.ones([num_samples])] * 2
eps_t = contrib_stateless.stateless_random_normal(
shape=[num_samples], seed=[2 * key, int(t / dt)])
u_t = contrib_stateless.stateless_random_uniform(
shape=[num_samples], seed=[2 * key + 1, int(t / dt)])
next_states_and_max = dynamics.gbm_euler_step_running_max(
states_and_max,
drift,
vol,
t,
dt,
simulate_bridge=True,
random_normal_op=lambda: eps_t,
random_uniform_op=lambda: u_t)
next_states_and_max_bis = dynamics.gbm_euler_step_running_max(
states_and_max, drift, vol, t, dt, simulate_bridge=True, key=key)
with self.session() as session:
next_states_and_max_eval, next_states_and_max_bis_eval = session.run(
(next_states_and_max, next_states_and_max_bis))
next_states_eval, next_max_eval = next_states_and_max_eval
next_states_bis_eval, next_max_bis_eval = next_states_and_max_bis_eval
self.assertEqual(next_states_eval.shape, (num_samples, ))
self.assertEqual(next_states_bis_eval.shape, (num_samples, ))
self.assertEqual(next_max_eval.shape, (num_samples, ))
self.assertEqual(next_max_bis_eval.shape, (num_samples, ))
self.assertAllClose(next_states_eval, next_states_bis_eval)
self.assertAllClose(next_max_eval, next_max_bis_eval)
def test_gbm_euler_step_running_max_bridge_output_is_correct(self):
np.random.seed(0)
drift = 0.2
vol = 0.1
t = 0.0
dt = 0.01
num_samples = 8
initial_states = np.ones([num_samples], dtype=np.float32)
states_and_max = [tf.constant(initial_states)] * 2
eps_t = np.ndarray.astype(np.random.normal(size=[num_samples]),
dtype=np.float32)
u_t = np.ndarray.astype(np.random.uniform(size=[num_samples]),
dtype=np.float32)
(next_states, next_max) = dynamics.gbm_euler_step_running_max(
states_and_max,
drift,
vol,
t,
dt,
simulate_bridge=True,
random_normal_op=lambda: eps_t,
random_uniform_op=lambda: u_t)
with self.session() as session:
(next_states_eval, next_max_eval) = session.run(
(next_states, next_max))
self.assertEqual(next_states_eval.shape, (num_samples, ))
self.assertEqual(next_max_eval.shape, (num_samples, ))
expected_next_states = initial_states * (1.0 + drift * dt +
vol * eps_t * np.sqrt(dt))
expected_bridge_max = 0.5 * (
initial_states + expected_next_states +
np.sqrt((initial_states - expected_next_states)**2 - 2.0 * dt *
(vol * initial_states)**2 * np.log(u_t)))
expected_next_max = np.maximum(expected_next_states,
expected_bridge_max)
# Here the maximum discrepancy is 1.17e-7 due to differences in
# numerical implementations between tf and np so we set delta to 1.2e-7.
self.assertAllClose(next_states_eval,
expected_next_states,
atol=1.2e-7)
self.assertAllClose(next_max_eval, expected_next_max, atol=1.2e-7)
