def test_cfinverse(self):
"""Test Fourier inversion."""
riskfree, maturity = 0, 30 / 365
sigma = .15
points = int(1e5)
model = GBM(GBMParam(sigma=sigma), riskfree, maturity)
grid, density = cfinverse(model.charfun,
points=points,
alim=-1e5,
blim=1e5)
loc = (riskfree - sigma**2 / 2) * maturity
scale = sigma**2 * maturity
norm_density = scs.norm.pdf(grid, loc=loc, scale=scale**.5)
self.assertEqual(grid.shape, (points, ))
self.assertEqual(density.shape, (points, ))
good = np.abs(grid) < 2
np.testing.assert_array_almost_equal(density[good],
norm_density[good],
decimal=2)
def single_premium():
"""Test COS method for floats.
"""
price, strike = 100, 90
riskfree, maturity = 0, 30 / 365
sigma = .15
moneyness = np.log(strike / price) - riskfree * maturity
model = GBM(GBMParam(sigma=sigma), riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
nu = .2
theta = -.14
sigma = .25
param = VarGammaParam(theta=theta, nu=nu, sigma=sigma)
model = VarGamma(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
lm = 1.5768
mu = .12**2
eta = .5751
rho = -.0
sigma = .12**2
param = HestonParam(lm=lm, mu=mu, eta=eta, rho=rho, sigma=sigma)
model = Heston(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
rho = .55
delta = .75
mu = .2**2 / 365
sigma = .2**2 / 365
phi = -.0
theta1 = -16.0
theta2 = 20.95
param = ARGParam(rho=rho,
delta=delta,
mu=mu,
sigma=sigma,
phi=phi,
theta1=theta1,
theta2=theta2)
model = ARG(param, riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=True)
print(premium)
def multiple_premia_gbm(nobs=2000):
"""Test COS method on the grid.
"""
sigma = .15
price = 1
strike = np.exp(np.linspace(-.1, .1, nobs))
riskfree, maturity = 0, 30 / 365
moneyness = np.log(strike / price) - riskfree * maturity
call = np.ones_like(moneyness).astype(bool)
call[moneyness < 0] = False
model = GBM(GBMParam(sigma=sigma), riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=call)
plt.plot(strike, premium)
plt.show()
def test_gbm(self):
"""Test GBM model."""
price, strike = 100, 110
riskfree, maturity = .01, 30 / 365
call = True
put = np.logical_not(call)
moneyness = lfmoneyness(price, strike, riskfree, maturity)
sigma = .15
model = GBM(GBMParam(sigma=sigma), riskfree, maturity)
premium = cosmethod(model, moneyness=moneyness, call=call)
premium_true = blackscholes_norm(moneyness, maturity, sigma, call)
impvol_model = impvol_bisection(moneyness, maturity, premium, call)
self.assertEqual(premium.shape, (1, ))
np.testing.assert_array_almost_equal(premium, premium_true, 3)
np.testing.assert_array_almost_equal(impvol_model, sigma, 2)
moneyness = np.linspace(0, .1, 10)
premium = cosmethod(model, moneyness=moneyness, call=call)
premium_true = blackscholes_norm(moneyness, maturity, sigma, call)
impvol_model = impvol_bisection(moneyness, maturity, premium, call)
impvol_true = np.ones_like(impvol_model) * sigma
self.assertEqual(premium.shape, moneyness.shape)
np.testing.assert_array_almost_equal(premium, premium_true, 2)
np.testing.assert_array_almost_equal(impvol_model, impvol_true, 2)
riskfree = np.zeros_like(moneyness)
premium = cosmethod(model, moneyness=moneyness, call=call)
premium_true = blackscholes_norm(moneyness, maturity, sigma, call)
impvol_model = impvol_bisection(moneyness, maturity, premium, call)
self.assertEqual(premium.shape, moneyness.shape)
np.testing.assert_array_almost_equal(premium, premium_true, 3)
np.testing.assert_array_almost_equal(impvol_model, sigma, 2)
moneyness = np.linspace(-.1, 0, 10)
premium = cosmethod(model, moneyness=moneyness, call=put)
premium_true = blackscholes_norm(moneyness, maturity, sigma, put)
impvol_model = impvol_bisection(moneyness, maturity, premium, put)
np.testing.assert_array_almost_equal(premium, premium_true, 2)
np.testing.assert_array_almost_equal(impvol_model, impvol_true, 2)