def plot_outofthemoney():
"""Plot model-implied out-of-the-money premium.
"""
nobs = 200
moneyness = np.linspace(-.2, .2, nobs)
riskfree, maturity = .1/365, 30/365
call = np.ones_like(moneyness).astype(bool)
call[moneyness < 0] = False
current_vol = .2**2/365
rho = .9
delta = 1.1
phi = -.5
price_vol = -1000
price_ret = .6
param = ARGparams(mean=current_vol, rho=rho, delta=delta,
phi=phi, price_ret=price_ret, price_vol=price_vol)
argmodel = ARG(param=param)
premium = argmodel.option_premium(vol=current_vol, moneyness=moneyness,
maturity=maturity,
riskfree=riskfree, call=call)
vol = impvol_bisection(moneyness, maturity, premium, call)
fig, axes = plt.subplots(nrows=2, ncols=1)
axes[0].plot(moneyness, premium, label='premium')
axes[1].plot(moneyness, vol, label='impvol')
axes[0].legend()
axes[1].legend()
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)
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)
def test_bisection(self):
"""Test values of implied volatility (bisection method)."""
premium = .024
price = 1
strike = 1
riskfree = .02
maturity = 30/365
call = True
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = impvol_bisection(moneyness, maturity, premium, call)
self.assertAlmostEqual(float(vol), .2, 2)
strike = [1, .95]
premium = [.024, .057]
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = impvol_bisection(moneyness, maturity, premium, call)
np.testing.assert_array_almost_equal(vol, [.2, .2], 2)
def test_bisection(self):
"""Test values of implied volatility (bisection method)."""
premium = .024
price = 1
strike = 1
riskfree = .02
maturity = 30 / 365
call = True
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = impvol_bisection(moneyness, maturity, premium, call)
self.assertAlmostEqual(float(vol), .2, 2)
strike = [1, .95]
premium = [.024, .057]
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = impvol_bisection(moneyness, maturity, premium, call)
np.testing.assert_array_almost_equal(vol, [.2, .2], 2)
def test_bs_prices(self):
"""Test accuracy of back and forth BS conversion."""
count = int(1e3)
maturity = 30/365
call = True
sigma = np.random.uniform(.05, .8, count)
moneyness = np.random.uniform(-.1, .1, count)
premium = blackscholes_norm(moneyness, maturity, sigma, call)
vol = impvol_bisection(moneyness, maturity, premium, call)
np.testing.assert_array_almost_equal(vol, sigma, 3)
def test_bs_prices(self):
"""Test accuracy of back and forth BS conversion."""
count = int(1e3)
maturity = 30 / 365
call = True
sigma = np.random.uniform(.05, .8, count)
moneyness = np.random.uniform(-.1, .1, count)
premium = blackscholes_norm(moneyness, maturity, sigma, call)
vol = impvol_bisection(moneyness, maturity, premium, call)
np.testing.assert_array_almost_equal(vol, sigma, 3)
def plot_smiles(fname=None):
"""Plot model-implied volatility smiles.
"""
price = 1
nobs = 100
moneyness = np.linspace(-.1, .1, nobs)
riskfree, maturity = .0, 30/365
call = np.ones_like(moneyness).astype(bool)
call[moneyness < 0] = False
current_vol = .2**2/365
rho = .9
delta = 1.1
phi = -.5
price_vol = -1
price_ret = .5
points = 5
sns.set_palette(sns.color_palette("binary_r", desat=.5))
fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))
loc = 'upper center'
phis = np.linspace(0, -.5, points)
for phi in phis:
param = ARGparams(mean=current_vol, rho=rho, delta=delta,
phi=phi, price_ret=price_ret, price_vol=price_vol)
argmodel = ARG(param=param)
premium = argmodel.option_premium(vol=current_vol, moneyness=moneyness,
maturity=maturity,
riskfree=riskfree, call=call)
vol = impvol_bisection(moneyness, maturity, premium/price, call)
axes[0].plot(moneyness*100, vol*100, label=str(phi))
axes[0].legend(title='Leverage, $\phi$', loc=loc)
axes[0].set_xlabel('Log-forward moneyness, $\log(F/S)$, %')
axes[0].set_ylabel('Implied volatility, annualized %')
maturities = np.linspace(30, 90, points) / 365
phi = 0.
for matur in maturities:
param = ARGparams(mean=current_vol, rho=rho, delta=delta,
phi=phi, price_ret=price_ret, price_vol=price_vol)
argmodel = ARG(param=param)
premium = argmodel.option_premium(vol=current_vol, moneyness=moneyness,
maturity=matur,
riskfree=riskfree, call=call)
vol = impvol_bisection(moneyness, matur, premium/price, call)
axes[1].plot(moneyness*100, vol*100, label=str(int(matur*365)))
axes[1].legend(title='Maturity, $T$', loc=loc)
axes[1].set_xlabel('Log-forward moneyness, $\log(F/S)$, %')
axes[1].set_ylabel('Implied volatility, annualized %')
plt.tight_layout()
if fname is not None:
plt.savefig(fname)
plt.show()
import pandas as pd
from impvol import (imp_vol, impvol_bisection, lfmoneyness, blackscholes_norm,
impvol_table)
if __name__ == '__main__':
price = 1
strike = 1
riskfree = .02
maturity = 30/365
premium = .057
call = True
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = impvol_bisection(moneyness, maturity, premium, call)
count = int(1e2)
sigma = np.random.uniform(.05, .8, count)
moneyness = np.random.uniform(-.1, .1, count)
premium = blackscholes_norm(moneyness, maturity, sigma, call)
text = 'Time elapsed: %.2f seconds'
time_start = time.time()
# Based on SciPy root method
vol = imp_vol(moneyness, maturity, premium, call)
print(np.allclose(sigma, vol))
print(text % (time.time() - time_start))
time_start = time.time()
import numpy as np
import pandas as pd
from impvol import (imp_vol, impvol_bisection, lfmoneyness, blackscholes_norm,
impvol_table)
if __name__ == '__main__':
price = 1
strike = 1
riskfree = .02
maturity = 30 / 365
premium = .057
call = True
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = impvol_bisection(moneyness, maturity, premium, call)
count = int(1e2)
sigma = np.random.uniform(.05, .8, count)
moneyness = np.random.uniform(-.1, .1, count)
premium = blackscholes_norm(moneyness, maturity, sigma, call)
text = 'Time elapsed: %.2f seconds'
time_start = time.time()
# Based on SciPy root method
vol = imp_vol(moneyness, maturity, premium, call)
print(np.allclose(sigma, vol))
print(text % (time.time() - time_start))
time_start = time.time()
def impvol(self):
"""Implied Volatility.
"""
return impvol_bisection(self.data['moneyness'], self.data['maturity'],
self.premium(), self.data['call'])
def impvol(self):
"""Implied Volatility.
"""
return impvol_bisection(self.data['moneyness'], self.data['maturity'],
self.premium(), self.data['call'])