def plot(underlying, ivs, params, date):
time = pd.to_datetime(f"{date} 12:15:00")
ivs.columns.name = 'Side'
groups = ivs.xs(time, level='Time').stack().groupby('Expiry')
fig, axs = plt.subplots(len(groups), sharex=True, figsize=(8, 10))
strike_min = np.min(ivs.index.get_level_values('Strike').values)
strike_max = np.max(ivs.index.get_level_values('Strike').values)
strike_grid = np.linspace(strike_min, strike_max, 20)
for ax, (e, g) in zip(axs, groups):
g.index = g.index.droplevel(['Expiry', 'Side'])
g.xs('C').plot(ax=ax, linewidth=0, marker='_', markersize=3)
g.xs('P').plot(ax=ax, linewidth=0, marker='_', markersize=3, color='g')
heston_prices = heston.formula(underlying.loc[time], strike_grid,
_years_to_expiry(date, e), *params)
heston_ivs = pd.Series(
blackscholes.implied_vol(underlying.loc[time], strike_grid,
_years_to_expiry(date, e), heston_prices),
strike_grid)
heston_ivs.plot(ax=ax, color='gray').set_ylabel('Implied volatility')
ax.set_title("Expiry: {}".format(e.strftime('%Y-%m-%d')))
return fig
def test_blackscholes_impliedvol():
sigma = 0.2
underlying_price = 100.
strike = 90.
expiry = 0.5
option_price = blackscholes.formula(underlying_price, strike, expiry,
sigma)
iv = blackscholes.implied_vol(underlying_price, strike, expiry,
option_price)
assert abs(sigma - iv) < 1e-8
option_price = blackscholes.formula(underlying_price, strike, expiry,
sigma, True)
iv = blackscholes.implied_vol(underlying_price, strike, expiry,
option_price, True)
assert abs(sigma - iv) < 1e-8
def test_blackscholes_impliedvol_exception():
underlying_price = 100.
strike = 90.
expiry = 0.5
option_price = 9.
with raises(ValueError):
blackscholes.implied_vol(underlying_price, strike, expiry,
option_price)
option_price = 101.
with raises(ValueError):
blackscholes.implied_vol(underlying_price, strike, expiry,
option_price)
option_price = np.array([0.9, 20, np.nan])
with np.testing.suppress_warnings() as sup:
sup.filter(RuntimeWarning)
ivs = blackscholes.implied_vol(underlying_price,
strike,
expiry,
option_price,
assert_no_arbitrage=False)
assert np.isnan(ivs[0]) and not np.isnan(ivs[1]) and np.isnan(ivs[2])
def build(bbo, underlying, discount, date):
return bbo.transform(
lambda side: side.groupby(['Class', 'Expiry', 'Strike']).transform(
lambda o: blackscholes.implied_vol(
underlying, discount[o.name[1]]*o.name[2],
_years_to_expiry(date, o.name[1]), o, o.name[0] == 'P')))
import numpy as np
import pandas as pd
from fyne import blackscholes, heston
underlying_price = 100.
vol, kappa, theta, nu, rho = 0.0457, 5.07, 0.0457, 0.48, -0.767
strikes = pd.Index(np.linspace(80., 120., 40), name='Strike')
expiries = pd.Index([0.1, 0.3, 1.0], name='Expiry')
option_prices = heston.formula(underlying_price, strikes[:, None], expiries,
vol, kappa, theta, nu, rho)
implied_vols = pd.DataFrame(
blackscholes.implied_vol(underlying_price, strikes[:, None], expiries,
option_prices), strikes, expiries)
implied_vols.plot().set_ylabel('Implied volatility')