def test_call_payoff_is_correct(self):
np.random.seed(0)
num_samples = 8
price = 100.0
strike = 100.0
price_samples = price * np.exp(
np.random.normal(size=[num_samples]).astype(np.float32))
payoff_samples = payoffs.call_payoff(price_samples, strike)
with self.session() as session:
payoff_samples_eval = session.run(payoff_samples)
for i in range(num_samples):
self.assertEqual(payoff_samples_eval[i],
(price_samples[i] -
strike) if price_samples[i] > strike else 0.0)
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))
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))
def _payoff_fn(log_s):
return tf.exp(-r * maturity) * payoffs.call_payoff(
tf.exp(log_s), strike)
