def __init__(self, sigma, vov=0, rho=0.0, beta=0.0, intr=0, divr=0):
self.sigma = sigma
self.vov = vov
self.rho = rho
self.intr = intr
self.divr = divr
self.normal_model = pf.Norm(sigma, intr=intr, divr=divr)
def test_norm_price(self):
bsm = pf.Norm(sigma=20, intr=0.05, divr=0.1)
result = bsm.price(strike=np.arange(80, 126, 5), spot=100, texp=1.2)
expect_result = np.array([
16.572334463, 13.264066668, 10.347114013, 7.849408092, 5.778270261,
4.119308420, 2.838573670, 1.887447196, 1.209104773, 0.745157542
])
np.testing.assert_almost_equal(result, expect_result)
def test_BsmDisp(self):
strike = np.arange(80, 126, 5)
dbs = pf.BsmDisp(sigma=0.2, beta=1, pivot=125, intr=0.05, divr=0.1)
# DBS = BSM if beta=1
bsm = pf.Bsm(sigma=dbs.sigma_disp, intr=0.05, divr=0.1)
r1 = bsm.price(strike, 100, 2.5, cp=-1)
r2 = dbs.price(strike, 100, 2.5, cp=-1)
np.testing.assert_almost_equal(r1, r2)
# DBS = Norm if beta=0
dbs.beta = 0.0001
dbs.is_fwd = True
norm = pf.Norm(sigma=dbs.sigma_disp * dbs.pivot,
intr=0.05,
divr=0.1,
is_fwd=True)
r1 = norm.price(strike, 100, 2.5, cp=-1)
r2 = dbs.price(strike, 100, 2.5, cp=-1)
np.testing.assert_almost_equal(r1 / r2, 1, decimal=4)
dbs.is_fwd = False
# Approximate BSM vol
dbs.beta = 0.2
v1 = dbs.vol_smile(strike, 100, 2.5, model='bsm')
v2 = dbs.vol_smile(strike, 100, 2.5, model='bsm-approx')
np.testing.assert_almost_equal(v1 / v2, 1, decimal=4)
p1 = dbs.price(strike, 100, 2.5)
p2 = pf.Bsm(v1, intr=0.05, divr=0.1).price(strike, 100, 2.5)
np.testing.assert_almost_equal(p1, p2)
# Approximate Bachelier vol
dbs.beta = 0.8
v1 = dbs.vol_smile(strike, 100, 2.5, model='norm')
v2 = dbs.vol_smile(strike, 100, 2.5, model='norm-approx')
np.testing.assert_almost_equal(v1 / v2, 1, decimal=4)
p1 = dbs.price(strike, 100, 2.5)
p2 = pf.Norm(v1, intr=0.05, divr=0.1).price(strike, 100, 2.5)
np.testing.assert_almost_equal(p1, p2)
class ModelNormalMC:
beta = 0.0 # fixed (not used)
vov, rho = 0.0, 0.0
sigma, intr, divr = None, None, None
normal_model = None
def __init__(self, sigma, vov=0, rho=0.0, beta=0.0, intr=0, divr=0, time_steps=1_000, n_samples=10_000):
self.sigma = sigma
self.vov = vov
self.rho = rho
self.intr = intr
self.divr = divr
self.time_steps = time_steps
self.n_samples = n_samples
self.normal_model = pf.Norm(sigma, intr=intr, divr=divr)
def test_norm_iv_greeks(self):
for k in range(100):
spot = np.random.uniform(80, 120)
strike = np.random.uniform(80, 120)
sigma = np.random.uniform(1, 100)
texp = np.random.uniform(0.1, 10)
intr = np.random.uniform(0, 0.3)
divr = np.random.uniform(0, 0.3)
cp = 1 if np.random.rand() > 0.5 else -1
is_fwd = (np.random.rand() > 0.5)
# print( spot, strike, vol, texp, intr, divr, cp)
m_norm = pf.Norm(sigma, intr=intr, divr=divr, is_fwd=is_fwd)
price = m_norm.price(strike, spot, texp, cp)
# get implied vol
iv = m_norm.impvol(price, strike, spot, texp=texp, cp=cp)
# now price option with the obtained implied vol
m_norm2 = copy.copy(m_norm)
m_norm2.sigma = iv
price_imp = m_norm2.price(strike, spot, texp, cp)
# compare the two prices
self.assertAlmostEqual(price,
price_imp,
delta=200 * m_norm.IMPVOL_TOL)
delta1 = m_norm.delta(strike=strike, spot=spot, texp=texp, cp=cp)
delta2 = m_norm.delta_numeric(strike=strike,
spot=spot,
texp=texp,
cp=cp)
self.assertAlmostEqual(delta1, delta2, delta=1e-4)
gamma1 = m_norm.delta(strike=strike, spot=spot, texp=texp, cp=cp)
gamma2 = m_norm.delta_numeric(strike=strike,
spot=spot,
texp=texp,
cp=cp)
self.assertAlmostEqual(gamma1, gamma2, delta=1e-4)
vega1 = m_norm.vega(strike=strike, spot=spot, texp=texp, cp=cp)
vega2 = m_norm.vega_numeric(strike=strike,
spot=spot,
texp=texp,
cp=cp)
self.assertAlmostEqual(vega1, vega2, delta=1e-3)