def test_std_estimate_works_with_arrays(self):
num_dims = 16
mean_est = np.ones(num_dims)
mean_sq_est = np.ones(num_dims)
stddev_est = util.stddev_est(mean_est, mean_sq_est)
self.assertAllEqual(stddev_est, np.zeros(num_dims))
def test_std_estimate_works_with_tensors(self):
num_dims = 16
mean_est = tf.ones(num_dims)
mean_sq_est = tf.ones(num_dims)
stddev_est = util.stddev_est(mean_est, mean_sq_est)
with self.test_session() as session:
stddev_est_eval = session.run(stddev_est)
self.assertAllEqual(stddev_est_eval, np.zeros(num_dims))
def _run_mc_step():
"""Run one mini-batch step of the Monte-Carlo method."""
feed_dict.update({key_placeholder: num_steps})
batch_mean_est, batch_mean_sq_est = tf_session.run(
(mean_est, mean_sq_est), feed_dict=feed_dict)
new_mean_est_eval = util.running_mean_estimate(mean_est_eval,
batch_mean_est,
num_samples, batch_size)
new_mean_sq_est_eval = util.running_mean_estimate(
mean_sq_est_eval, batch_mean_sq_est, num_samples, batch_size)
std_est_eval = util.stddev_est(new_mean_est_eval, new_mean_sq_est_eval)
half_conf_interval = util.half_clt_conf_interval(
confidence, num_samples + batch_size, std_est_eval)
return new_mean_est_eval, new_mean_sq_est_eval, half_conf_interval
def test_european_call_log_euler_mc_close_to_black_scholes(self):
current_price = 100.0
r = interest_rate = 0.05
vol = 0.2
strike = 120.0
maturity = 0.5
dt = 0.01
discount = tf.exp(-r * maturity)
bs_call_price = util.black_scholes_call_price(current_price,
interest_rate, vol,
strike, maturity)
num_samples = int(1e4)
initial_state = tf.constant(current_price)
dynamics_op = lambda s, t, dt: dynamics.gbm_log_euler_step(
s, r, vol, t, dt)
payoff_fn = lambda s: discount * payoffs.call_payoff(tf.exp(s), strike)
(mean_outcome, mean_sq_outcome,
_) = monte_carlo_manager.non_callable_price_mc(
tf.log(initial_state), dynamics_op, payoff_fn, maturity,
num_samples, dt)
std_outcomes = util.stddev_est(mean_outcome, mean_sq_outcome)
with self.test_session() as session:
bs_call_price_eval = session.run(bs_call_price)
mean_outcome_eval, std_outcomes_eval = session.run(
(mean_outcome, std_outcomes))
self.assertLessEqual(
mean_outcome_eval, bs_call_price_eval +
3.0 * std_outcomes_eval / np.sqrt(num_samples))
self.assertGreaterEqual(
mean_outcome_eval, bs_call_price_eval -
3.0 * std_outcomes_eval / np.sqrt(num_samples))
