def test_ExpectedShortfall(self):
alpha = 0.95
risk_measure = hedge_models.ExpectedShortfall(alpha)
# ES is known in closed form for uniform.
loss = tf.math.sobol_sample(1, 2**19, dtype=FLOAT_DTYPE)
var = alpha
risk_measure.w.assign(var)
result_fitted = risk_measure(-loss)
result_evaluate = risk_measure.evaluate(-loss)
expected = tf.constant([(1 + var) / 2.], FLOAT_DTYPE)
tf.debugging.assert_near(result_fitted, expected, atol=1e-3)
tf.debugging.assert_near(result_evaluate, expected, atol=1e-3)
def test_cost_gradient(self):
timesteps = 3
dimension = 2
num = 1
cost = True
init_instruments, init_numeraire, book = books.random_put_call_book(
timesteps / 250, dimension * 2, dimension, dimension, num)
time, instruments, numeraire = book.sample_paths(
init_instruments, init_numeraire, int(2**10), timesteps, True)
martingales = instruments / numeraire
features = tf.unstack(book.delta(time, instruments, numeraire) \
* numeraire,
axis=-1)[:-1]
payoff = book.payoff(time, instruments, numeraire)
model = hedge_models.LinearFeatureHedge(
timesteps=timesteps,
instrument_dim=book.instrument_dim,
mappings=[approximators.IdentityFeatureMap] * (1 + cost))
model.add_cost(1 / 100)
model.compile(risk_measure=hedge_models.ExpectedShortfall(0.95))
with tf.GradientTape() as tape:
value, costs = model([features, martingales], training=True)
wealth = value - costs - payoff
loss = model.risk_measure(wealth)
trainable_vars = [model.risk_measure.w] + model.trainable_variables
gradient_expected = tape.gradient(loss, trainable_vars)
gradient_result, wealth = model.cost_gradient(
([features, martingales, payoff], ))
for x1, x2 in zip(gradient_result, gradient_expected):
tf.debugging.assert_near(x1, x2)
cost=1 / 100 if cost else None,
risk_neutral=True,
learning_rate=1e-1)
driver.verbose = 2
risklevels = [0.05, 0.5, 0.95] if not cost else [0.95]
for alpha in risklevels:
driver.add_testcase(f"deep network {alpha}",
hedge_models.NeuralHedge(
timesteps=timesteps,
instrument_dim=book.instrument_dim,
internal_dim=0,
num_layers=4,
num_units=5,
activation=tf.keras.activations.softplus),
risk_measure=hedge_models.ExpectedShortfall(alpha),
normaliser=preprocessing.MeanVarianceNormaliser(),
feature_function="log_martingale",
price_type="arbitrage")
if driver.cost is not None or not driver.risk_neutral:
driver.add_liability_free(
hedge_models.LinearFeatureHedge(
timesteps=timesteps,
instrument_dim=book.instrument_dim,
mappings=[approximators.IdentityFeatureMap] \
* (1 + (driver.cost is not None))),
risk_measure=hedge_models.ExpectedShortfall(alpha),
normaliser=preprocessing.MeanVarianceNormaliser(),
feature_function="log_martingale")