def test_price_vol_and_expiry_scaling(self):
"""Tests that the price is invariant under vol->k vol, T->T/k**2."""
np.random.seed(1234)
n = 20
forwards = np.exp(np.random.randn(n))
volatilities = np.exp(np.random.randn(n) / 2)
strikes = np.exp(np.random.randn(n))
expiries = np.exp(np.random.randn(n))
scaling = 5.0
base_prices = self.evaluate(
black_scholes.option_price(forwards, strikes, volatilities,
expiries))
scaled_prices = self.evaluate(
black_scholes.option_price(forwards, strikes,
volatilities * scaling,
expiries / scaling / scaling))
self.assertArrayNear(base_prices, scaled_prices, 1e-10)
def test_price_long_expiry_calls(self):
"""Tests that very long expiry call option behaves like the asset."""
forwards = np.array([1.0, 1.0, 1.0, 1.0])
strikes = np.array([1.1, 0.9, 1.1, 0.9])
volatilities = np.array([0.1, 0.2, 0.5, 0.9])
expiries = 1e10
expected_prices = forwards
computed_prices = self.evaluate(
black_scholes.option_price(forwards, strikes, volatilities,
expiries))
self.assertArrayNear(expected_prices, computed_prices, 1e-10)
def test_price_long_expiry_puts(self):
"""Tests that very long expiry put option is worth the strike."""
forwards = np.array([1.0, 1.0, 1.0, 1.0])
strikes = np.array([0.1, 10.0, 3.0, 0.0001])
volatilities = np.array([0.1, 0.2, 0.5, 0.9])
expiries = 1e10
expected_prices = strikes
computed_prices = self.evaluate(
black_scholes.option_price(forwards,
strikes,
volatilities,
expiries,
is_call_options=False))
self.assertArrayNear(expected_prices, computed_prices, 1e-10)
def test_option_prices(self):
"""Tests that the BS prices are correct."""
forwards = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
strikes = np.array([3.0, 3.0, 3.0, 3.0, 3.0])
volatilities = np.array([0.0001, 102.0, 2.0, 0.1, 0.4])
expiries = 1.0
computed_prices = self.evaluate(
black_scholes.option_price(forwards, strikes, volatilities,
expiries))
expected_prices = np.array([
0.0, 2.0, 2.0480684764112578, 1.0002029716043364,
2.0730313058959933
])
self.assertArrayNear(expected_prices, computed_prices, 1e-10)
def test_polya_implied_vol(self):
"""Basic test of the implied vol calculation."""
np.random.seed(6589)
n = 100
volatilities = np.exp(np.random.randn(n) / 2)
forwards = np.exp(np.random.randn(n))
strikes = forwards * (1 + (np.random.rand(n) - 0.5) * 0.2)
expiries = np.exp(np.random.randn(n))
prices = self.evaluate(
black_scholes.option_price(forwards, strikes, volatilities,
expiries))
implied_vols = self.evaluate(
approx_implied_vol.polya(prices, forwards, strikes, expiries))
self.assertArrayNear(volatilities, implied_vols, 0.6)
def test_price_zero_expiry(self):
"""Tests that zero expiry is correctly handled."""
# If the expiry is zero, the option's value should be correct.
forwards = np.array([1.0, 1.0, 1.0, 1.0])
strikes = np.array([1.1, 0.9, 1.1, 0.9])
volatilities = np.array([0.1, 0.2, 0.5, 0.9])
expiries = 0.0
is_call_options = np.array([True, True, False, False])
expected_prices = np.array([0.0, 0.1, 0.1, 0.0])
computed_prices = self.evaluate(
black_scholes.option_price(forwards,
strikes,
volatilities,
expiries,
is_call_options=is_call_options))
self.assertArrayNear(expected_prices, computed_prices, 1e-10)
def test_polya_implied_vol_validate(self):
"""Test the Radiocic-Polya approx doesn't raise where it shouldn't."""
np.random.seed(6589)
n = 100
volatilities = np.exp(np.random.randn(n) / 2)
forwards = np.exp(np.random.randn(n))
strikes = forwards * (1 + (np.random.rand(n) - 0.5) * 0.2)
expiries = np.exp(np.random.randn(n))
prices = self.evaluate(
black_scholes.option_price(forwards, strikes, volatilities,
expiries))
implied_vols = self.evaluate(
approx_implied_vol.polya(prices,
forwards,
strikes,
expiries,
validate_args=True))
self.assertArrayNear(volatilities, implied_vols, 0.6)