def test_vol_values(self):
"""Test values of implied volatility."""
premium = .024
price = 1
strike = 1
riskfree = .02
maturity = 30/365
call = True
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = imp_vol(moneyness, maturity, premium, call)
self.assertAlmostEqual(float(vol), .2, 2)
strike = [1, .95]
premium = [.024, .057]
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = imp_vol(moneyness, maturity, premium, call)
np.testing.assert_array_almost_equal(vol, [.2, .2], 2)
def test_vol_values(self):
"""Test values of implied volatility."""
premium = .024
price = 1
strike = 1
riskfree = .02
maturity = 30 / 365
call = True
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = imp_vol(moneyness, maturity, premium, call)
self.assertAlmostEqual(float(vol), .2, 2)
strike = [1, .95]
premium = [.024, .057]
moneyness = lfmoneyness(price, strike, riskfree, maturity)
vol = imp_vol(moneyness, maturity, premium, call)
np.testing.assert_array_almost_equal(vol, [.2, .2], 2)
def test_moneyness(self):
"""Test conversion to moneyness."""
price, strike, riskfree, time = 1, 1, 0, .5
moneyness = lfmoneyness(price, strike, riskfree, time)
self.assertEqual(moneyness, 0)
price, riskfree, time = 1, 0, .5
strike = [1, np.e]
moneyness = lfmoneyness(price, strike, riskfree, time)
np.testing.assert_array_equal(moneyness, np.array([0, 1]))
strike, riskfree, time = 1, 0, .5
price = [1, np.e]
moneyness = lfmoneyness(price, strike, riskfree, time)
np.testing.assert_array_equal(moneyness, np.array([0, -1]))
def test_moneyness(self):
"""Test conversion to moneyness."""
price, strike, riskfree, time = 1, 1, 0, .5
moneyness = lfmoneyness(price, strike, riskfree, time)
self.assertEqual(moneyness, 0)
price, riskfree, time = 1, 0, .5
strike = [1, np.e]
moneyness = lfmoneyness(price, strike, riskfree, time)
np.testing.assert_array_equal(moneyness, np.array([0, 1]))
strike, riskfree, time = 1, 0, .5
price = [1, np.e]
moneyness = lfmoneyness(price, strike, riskfree, time)
np.testing.assert_array_equal(moneyness, np.array([0, -1]))
def import_vol_surface():
"""Import volatility surface.
Infer risk-free rate directly from data.
"""
zf = zipfile.ZipFile(path + "SPX_surface.zip", "r")
name = zf.namelist()[0]
df = pd.read_csv(zf.open(name), converters={"date": convert_dates})
df.loc[:, "weekday"] = df["date"].apply(lambda x: x.weekday())
# Apply some filters
df = df[df["weekday"] == 2]
df = df[df["days"] <= 365]
df = df.drop("weekday", axis=1)
surface = df # .set_index(['cp_flag', 'date', 'days']).sort_index()
cols = {"impl_volatility": "imp_vol", "impl_strike": "strike", "impl_premium": "premium"}
surface.rename(columns=cols, inplace=True)
# TODO : who term structure should be imported and merged!
riskfree = load_riskfree().reset_index()
dividends = load_dividends().reset_index()
spx = load_spx().reset_index()
surface = pd.merge(surface, riskfree)
surface = pd.merge(surface, spx)
surface = pd.merge(surface, dividends)
# Adjust riskfree by dividend yield
surface["riskfree"] -= surface["rate"]
# Remove percentage point
surface["riskfree"] /= 100
# Replace 'cp_flag' with True/False 'call' variable
surface.loc[:, "call"] = True
surface.loc[surface["cp_flag"] == "P", "call"] = False
# Normalize maturity to being a share of the year
surface["maturity"] = surface["days"] / 365
# Rename columns
surface.rename(columns={"spx": "price"}, inplace=True)
# Compute lf-moneyness
surface["moneyness"] = lfmoneyness(surface["price"], surface["strike"], surface["riskfree"], surface["maturity"])
# Compute option Delta normalized by current price
surface["delta"] = delta(surface["moneyness"], surface["maturity"], surface["imp_vol"], surface["call"])
# Compute option Vega normalized by current price
surface["vega"] = vega(surface["moneyness"], surface["maturity"], surface["imp_vol"])
# Sort index
surface.sort_index(by=["date", "maturity", "moneyness"], inplace=True)
print(surface.head())
surface.to_hdf(path + "surface.h5", "surface")
def import_vol_surface_simple():
"""Import volatility surface. Simple version.
"""
zf = zipfile.ZipFile(path + "SPX_surface.zip", "r")
name = zf.namelist()[0]
df = pd.read_csv(zf.open(name), converters={"date": convert_dates})
df.loc[:, "weekday"] = df["date"].apply(lambda x: x.weekday())
# Apply some filters
df = df[df["weekday"] == 2]
df = df[df["days"] <= 365]
surface = df.drop("weekday", axis=1)
cols = {"impl_volatility": "imp_vol", "impl_strike": "strike", "impl_premium": "premium"}
surface.rename(columns=cols, inplace=True)
spx = load_spx().reset_index()
standard_options = load_standard_options()[["forward"]].reset_index()
surface = pd.merge(surface, standard_options)
surface = pd.merge(surface, spx)
# Normalize maturity to being a share of the year
surface["maturity"] = surface["days"] / 365
surface["riskfree"] = np.log(surface["forward"] / surface["spx"])
surface["riskfree"] /= surface["maturity"]
# Remove percentage point
# Replace 'cp_flag' with True/False 'call' variable
surface.loc[:, "call"] = True
surface.loc[surface["cp_flag"] == "P", "call"] = False
# Rename columns
surface.rename(columns={"spx": "price"}, inplace=True)
# Compute lf-moneyness
surface["moneyness"] = lfmoneyness(surface["price"], surface["strike"], surface["riskfree"], surface["maturity"])
# Compute option Delta normalized by current price
surface["delta"] = delta(surface["moneyness"], surface["maturity"], surface["imp_vol"], surface["call"])
# Compute option Vega normalized by current price
surface["vega"] = vega(surface["moneyness"], surface["maturity"], surface["imp_vol"])
# Take out-of-the-money options
calls = surface["call"] & (surface["moneyness"] >= 0)
puts = np.logical_not(surface["call"]) & (surface["moneyness"] < 0)
surface = pd.concat([surface[calls], surface[puts]])
# Sort index
surface.sort_index(by=["date", "maturity", "moneyness"], inplace=True)
print(surface.head())
surface.to_hdf(path + "surface.h5", "surface")
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)
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))
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))
