def test_put_payoff_function(self):
"""Tests the put payoff function returns the right numbers."""
# See Longstaff, F.A. and Schwartz, E.S., 2001. Valuing American options by
# simulation: a simple least-squares approach.
samples = [[1.0, 1.09, 1.08, 1.34],
[1.0, 1.16, 1.26, 1.54],
[1.0, 1.22, 1.07, 1.03],
[1.0, 0.93, 0.97, 0.92],
[1.0, 1.11, 1.56, 1.52],
[1.0, 0.76, 0.77, 0.90],
[1.0, 0.92, 0.84, 1.01],
[1.0, 0.88, 1.22, 1.34]]
# Expand dims to reflect that `samples` represent sample paths of
# a 1-dimensional process
for dtype in (np.float32, np.float64):
# Create payoff functions for 2 different strike values
payoff_fn = payoff_utils.make_basket_put_payoff([1.1, 1.2], dtype=dtype)
sample_paths = tf.convert_to_tensor(samples, dtype=dtype)
sample_paths = tf.expand_dims(sample_paths, -1)
# Actual payoff
payoff = payoff_fn(sample_paths, 3)
# Expected payoffs at the final time
expected_payoff = [[0, 0],
[0, 0],
[0.07, 0.17],
[0.18, 0.28],
[0, 0],
[0.2, 0.3],
[0.09, 0.19],
[0, 0]]
self.assertAllClose(expected_payoff, payoff, rtol=1e-8, atol=1e-8)
def test_put_payoff_function(self, dtype):
"""Tests the put payoff function for a batch of strikes."""
# Create payoff functions for 2 different strike values
payoff_fn = payoff_utils.make_basket_put_payoff([1.1, 1.2],
dtype=dtype)
sample_paths = tf.convert_to_tensor(_SAMPLES, dtype=dtype)
sample_paths = tf.expand_dims(sample_paths, -1)
# Actual payoff
payoff = payoff_fn(sample_paths, 3)
# Expected payoffs at the final time
expected_payoff = [[0, 0], [0, 0], [0.07, 0.17], [0.18, 0.28], [0, 0],
[0.2, 0.3], [0.09, 0.19], [0, 0]]
self.assertAllClose(expected_payoff, payoff, rtol=1e-6, atol=1e-6)
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])