def test_american_option_put(self):
"""Tests that LSM price of American put option is computed as expected."""
# This is the same example as in Section 1 of
# Longstaff, F.A. and Schwartz, E.S., 2001. Valuing American options by
# simulation: a simple least-squares approach. The review of financial
# studies, 14(1), pp.113-147.
basis_fn = lsm.make_polynomial_basis(2)
for dtype in (np.float32, np.float64):
payoff_fn = payoff.make_basket_put_payoff([1.1], dtype=dtype)
# Option price
american_put_price = lsm.least_square_mc(
self.samples, [1, 2, 3],
payoff_fn,
basis_fn,
discount_factors=self.discount_factors,
dtype=dtype)
self.assertAllClose(american_put_price, [0.1144],
rtol=1e-4,
atol=1e-4)
def test_american_basket_option_put(self):
"""Tests the LSM price of American Basket put option."""
# This is the same example as in Section 1 of
# Longstaff, F.A. and Schwartz, E.S., 2001. Valuing American options by
# simulation: a simple least-squares approach. The review of financial
# studies, 14(1), pp.113-147.
# This is the minimum number of basis functions for the tests to pass.
basis_fn = lsm.make_polynomial_basis(10)
exercise_times = [1, 2, 3]
dtype = np.float64
payoff_fn = payoff.make_basket_put_payoff([1.1, 1.2, 1.3], dtype=dtype)
# Create a 2-d process which is simply follows the `samples` paths:
samples = tf.convert_to_tensor(self.samples, dtype=dtype)
samples_2d = tf.concat([samples, samples], -1)
# Price American basket option
american_basket_put_price = lsm.least_square_mc(
samples_2d,
exercise_times,
payoff_fn,
basis_fn,
discount_factors=self.discount_factors,
dtype=dtype)
# Since the marginal processes of `samples_2d` are 100% correlated, the
# price should be the same as of the American option computed for
# `samples`
american_put_price = lsm.least_square_mc(
self.samples,
exercise_times,
payoff_fn,
basis_fn,
discount_factors=self.discount_factors,
dtype=dtype)
self.assertAllClose(american_basket_put_price,
american_put_price,
rtol=1e-4,
atol=1e-4)
self.assertAllEqual(american_basket_put_price.shape, [3])