def test_mc_estimator_converges_with_multiple_fixed_estimates_nd(self):
num_dims = 8
mean = np.arange(1.27, 1.349, 0.01)
stddev = 2.0
batch_size = int(1e5)
dummy_key_placeholder = tf.placeholder(shape=(), dtype=tf.int32)
mean_est = tf.constant(mean)
mean_sq_est = tf.ones([num_dims]) * (stddev**2)
tol = 5e-3
conf_level = 0.99
max_num_steps = (util.half_clt_conf_interval(conf_level, 1, stddev) /
(np.min(mean) * tol))**2 + 1
with self.test_session() as session:
(mean_est_eval, rel_half_conf_interval,
converged) = monte_carlo_manager.mc_estimator(
mean_est, mean_sq_est, batch_size, dummy_key_placeholder, {},
tol, conf_level, max_num_steps, session)
self.assertAllAlmostEqual(mean_est_eval, mean * np.ones([num_dims]))
self.assertTrue(converged)
self.assertAllGreaterEqual(
rel_half_conf_interval * mean,
util.half_clt_conf_interval(conf_level, max_num_steps * batch_size,
stddev))
def test_mc_estimator_converges_with_fixed_estimates(self):
mean = 1.3
stddev = 2.0
batch_size = int(1e5)
dummy_key_placeholder = tf.placeholder(shape=(), dtype=tf.int32)
mean_est = tf.constant(mean)
mean_sq_est = tf.constant(stddev**2)
tol = 5e-3
conf_level = 0.99
max_num_steps = (util.half_clt_conf_interval(conf_level, 1, stddev) /
(mean * tol))**2 + 1
with self.test_session() as session:
(mean_est_eval, rel_half_conf_interval,
converged) = monte_carlo_manager.mc_estimator(
mean_est, mean_sq_est, batch_size, dummy_key_placeholder, {},
tol, conf_level, max_num_steps, session)
self.assertAlmostEqual(mean_est_eval, mean)
self.assertTrue(converged)
self.assertGreaterEqual(
rel_half_conf_interval,
util.half_clt_conf_interval(conf_level, max_num_steps * batch_size,
stddev) / mean)
def test_european_call_estimator_converges_close_to_black_scholes(self):
current_price = 100.0
r = interest_rate = 0.05
vol = 0.2
strike = 120.0
maturity = 0.5
dt = 0.001
discount = tf.exp(-r * maturity)
tol = 5e-2
conf_level = 0.95
batch_size = int(1e4)
k = key_placeholder = tf.placeholder(shape=(), dtype=tf.int32)
max_num_steps = 1e5
bs_call_price = util.black_scholes_call_price(current_price,
interest_rate, vol,
strike, maturity)
initial_state = tf.constant(current_price)
dynamics_op = lambda s, t, dt: dynamics.gbm_euler_step(
s, r, vol, t, dt, k)
payoff_fn = lambda s: discount * payoffs.call_payoff(s, strike)
(mean_est, mean_sq_est, _) = monte_carlo_manager.non_callable_price_mc(
initial_state, dynamics_op, payoff_fn, maturity, batch_size, dt)
with self.test_session() as session:
(mean_est_eval, _, converged) = monte_carlo_manager.mc_estimator(
mean_est, mean_sq_est, batch_size, key_placeholder, {}, tol,
conf_level, max_num_steps, session)
bs_call_price_eval = session.run(bs_call_price)
self.assertTrue(converged)
# Here the discretization bias would make these asserts fail with larger dt.
self.assertLessEqual(mean_est_eval, bs_call_price_eval * (1.0 + tol))
self.assertGreaterEqual(mean_est_eval,
bs_call_price_eval * (1.0 - tol))
