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"""
Copyright (C) 2020 Marcin Rybacki
Copyright (C) 2022 Skandinaviska Enskilda Banken AB (publ)
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
"""
import unittest
import math
import QuantLib as ql
TOLERANCE = 1e-10 if ql.IborCoupon.usingAtParCoupons() else 1e-6
SABR_ATM_TOLERANCE = 3.0e-4
SABR_SPREAD_TOLERANCE = 12.0e-4
CAL = ql.TARGET()
# Data source:
# https://quantlib-python-docs.readthedocs.io/en/latest/termstructures.html#swaption-volatility
ATM_NORM_VOLS = (
(0.0086, 0.00128, 0.00195, 0.00269, 0.00327, 0.00361, 0.00387,
0.00409, 0.00427, 0.00443, 0.00488, 0.00504, 0.00508, 0.00504),
(0.0092, 0.00134, 0.00197, 0.00264, 0.00319, 0.00352, 0.00383,
0.00402, 0.00419, 0.00431, 0.00478, 0.00499, 0.00507, 0.00503),
(0.00112, 0.00153, 0.00210, 0.00276, 0.00327, 0.00353, 0.00384,
0.00408, 0.00426, 0.00445, 0.00486, 0.00505, 0.00509, 0.00510),
(0.00129, 0.00171, 0.00226, 0.00288, 0.00335, 0.00360, 0.00388,
0.00410, 0.00430, 0.00446, 0.00487, 0.00506, 0.00511, 0.00510),
(0.00146, 0.00187, 0.00246, 0.00301, 0.00342, 0.00369, 0.00393,
0.00413, 0.00432, 0.00449, 0.00489, 0.00510, 0.00513, 0.00515),
(0.00165, 0.00209, 0.00263, 0.00313, 0.00350, 0.00376, 0.00400,
0.00420, 0.00437, 0.00453, 0.00488, 0.00509, 0.00514, 0.00517),
(0.00209, 0.00253, 0.00300, 0.00340, 0.00370, 0.00395, 0.00419,
0.00434, 0.00450, 0.00464, 0.00493, 0.00510, 0.00513, 0.00519),
(0.00251, 0.00289, 0.00332, 0.00362, 0.00392, 0.00412, 0.00432,
0.00447, 0.00460, 0.00473, 0.00496, 0.00510, 0.00513, 0.00516),
(0.00340, 0.00366, 0.00392, 0.00411, 0.00432, 0.00445, 0.00461,
0.00472, 0.00480, 0.00490, 0.00503, 0.00513, 0.00513, 0.00512),
(0.00403, 0.00418, 0.00436, 0.00449, 0.00461, 0.00471, 0.00482,
0.00492, 0.00499, 0.00505, 0.00512, 0.00513, 0.00509, 0.00507),
(0.00440, 0.00448, 0.00460, 0.00471, 0.00484, 0.00491, 0.00499,
0.00507, 0.00514, 0.00519, 0.00516, 0.00514, 0.00506, 0.00502),
(0.00496, 0.00497, 0.00504, 0.00512, 0.00518, 0.00522, 0.00526,
0.00529, 0.00533, 0.00538, 0.00526, 0.00517, 0.00504, 0.00496),
(0.00539, 0.00537, 0.00540, 0.00542, 0.00544, 0.00545, 0.00545,
0.00544, 0.00544, 0.00549, 0.00531, 0.00518, 0.00501, 0.00491),
(0.00540, 0.00537, 0.00538, 0.00537, 0.00535, 0.00536, 0.00535,
0.00533, 0.00535, 0.00537, 0.00514, 0.00498, 0.00479, 0.00466),
(0.00528, 0.00524, 0.00526, 0.00523, 0.00522, 0.00523, 0.00520,
0.00519, 0.00518, 0.00518, 0.00495, 0.00474, 0.00454, 0.00438),
(0.00514, 0.00512, 0.00513, 0.00510, 0.00508, 0.00507, 0.00503,
0.00499, 0.00498, 0.00497, 0.00476, 0.00453, 0.00431, 0.00414),
(0.00496, 0.00496, 0.00497, 0.00495, 0.00495, 0.00492, 0.00486,
0.00479, 0.00474, 0.00471, 0.00451, 0.00429, 0.00408, 0.00392))
ATM_NORM_VOL_OPT_TENORS = (ql.Period(1, ql.Months), ql.Period(2, ql.Months),
ql.Period(3, ql.Months), ql.Period(6, ql.Months),
ql.Period(9, ql.Months), ql.Period(1, ql.Years),
ql.Period(18, ql.Months), ql.Period(2, ql.Years),
ql.Period(3, ql.Years), ql.Period(4, ql.Years),
ql.Period(5, ql.Years), ql.Period(7, ql.Years),
ql.Period(10, ql.Years), ql.Period(15, ql.Years),
ql.Period(20, ql.Years), ql.Period(25, ql.Years),
ql.Period(30, ql.Years))
ATM_NORM_VOL_SWAP_TENORS = (ql.Period(1, ql.Years), ql.Period(2, ql.Years),
ql.Period(3, ql.Years), ql.Period(4, ql.Years),
ql.Period(5, ql.Years), ql.Period(6, ql.Years),
ql.Period(7, ql.Years), ql.Period(8, ql.Years),
ql.Period(9, ql.Years), ql.Period(10, ql.Years),
ql.Period(15, ql.Years), ql.Period(20, ql.Years),
ql.Period(25, ql.Years), ql.Period(30, ql.Years))
ATM_LOGNORM_VOLS = (
(0.1300, 0.1560, 0.1390, 0.1220),
(0.1440, 0.1580, 0.1460, 0.1260),
(0.1600, 0.1590, 0.1470, 0.1290),
(0.1640, 0.1470, 0.1370, 0.1220),
(0.1400, 0.1300, 0.1250, 0.1100),
(0.1130, 0.1090, 0.1070, 0.0930))
ATM_LOGNORM_VOL_OPT_TENORS = (ql.Period(1, ql.Months),
ql.Period(6, ql.Months),
ql.Period(3, ql.Years),
ql.Period(5, ql.Years),
ql.Period(10, ql.Years),
ql.Period(25, ql.Years))
ATM_LOGNORM_VOL_SWAP_TENORS = (ql.Period(1, ql.Years),
ql.Period(3, ql.Years),
ql.Period(10, ql.Years),
ql.Period(25, ql.Years))
SMILE_OPT_TENORS = (ql.Period(1, ql.Years),
ql.Period(10, ql.Years),
ql.Period(30, ql.Years))
SMILE_SWAP_TENORS = (ql.Period(2, ql.Years),
ql.Period(10, ql.Years),
ql.Period(30, ql.Years))
STRIKE_SPREADS = (-0.02, -0.005, 0.0, 0.005, 0.02)
NORM_VOL_SPREADS = (
(-0.0006, 0.0005, 0.0, 0.0006, 0.0006),
(-0.0006, 0.0005, 0.0, 0.00065, 0.0006),
(-0.0006, 0.0001, 0.0, 0.0006, 0.0006),
(-0.0006, 0.0005, 0.0, 0.0006, 0.0006),
(-0.0006, 0.0005, 0.0, 0.0006, 0.0006),
(-0.0003, 0.0005, 0.0, 0.0003, 0.0003),
(-0.0006, 0.0005, 0.0, 0.0006, 0.0006),
(-0.0006, 0.0005, 0.0, 0.0006, 0.0006),
(-0.0003, 0.0005, 0.0, 0.0003, 0.0003))
LOGNORM_VOL_SPREADS = (
(0.0599, 0.0049, 0.0000, -0.0001, 0.0127),
(0.0729, 0.0086, 0.0000, -0.0024, 0.0098),
(0.0738, 0.0102, 0.0000, -0.0039, 0.0065),
(0.0465, 0.0063, 0.0000, -0.0032, -0.0010),
(0.0558, 0.0084, 0.0000, -0.0050, -0.0057),
(0.0576, 0.0083, 0.0000, -0.0043, -0.0014),
(0.0437, 0.0059, 0.0000, -0.0030, -0.0006),
(0.0533, 0.0078, 0.0000, -0.0045, -0.0046),
(0.0545, 0.0079, 0.0000, -0.0042, -0.0020))
ZERO_COUPON_DATA = (
(ql.Period(1, ql.Days), 0.013),
(ql.Period(1, ql.Years), 0.013),
(ql.Period(2, ql.Years), 0.015),
(ql.Period(3, ql.Years), 0.016),
(ql.Period(4, ql.Years), 0.017),
(ql.Period(5, ql.Years), 0.019),
(ql.Period(10, ql.Years), 0.021),
(ql.Period(15, ql.Years), 0.024),
(ql.Period(20, ql.Years), 0.026),
(ql.Period(30, ql.Years), 0.029))
NORM_VOL_MATRIX = ql.SwaptionVolatilityMatrix(
CAL,
ql.ModifiedFollowing,
ATM_NORM_VOL_OPT_TENORS,
ATM_NORM_VOL_SWAP_TENORS,
ql.Matrix(ATM_NORM_VOLS),
ql.Actual365Fixed(),
False,
ql.Normal)
LOGNORM_VOL_MATRIX = ql.SwaptionVolatilityMatrix(
CAL,
ql.ModifiedFollowing,
ATM_LOGNORM_VOL_OPT_TENORS,
ATM_LOGNORM_VOL_SWAP_TENORS,
ql.Matrix(ATM_LOGNORM_VOLS),
ql.Actual365Fixed(),
False,
ql.ShiftedLognormal)
def build_euribor_swap_idx(
projection_curve_handle):
return ql.EuriborSwapIsdaFixA(ql.Period(1, ql.Years),
projection_curve_handle)
def build_nominal_term_structure(valuation_date, nominal_quotes):
dates, rates = zip(*[(CAL.advance(valuation_date, x[0]), x[1])
for x in nominal_quotes])
crv = ql.ZeroCurve(dates, rates, ql.Actual365Fixed())
crv.enableExtrapolation()
return crv
def build_linear_swaption_cube(
volatility_matrix,
spread_opt_tenors,
spread_swap_tenors,
strike_spreads,
vol_spreads,
swap_index_base,
short_swap_index_base=None,
vega_weighted_smile_fit=False):
vol_spreads = [[ql.makeQuoteHandle(v) for v in row]
for row in vol_spreads]
cube = ql.InterpolatedSwaptionVolatilityCube(
ql.SwaptionVolatilityStructureHandle(volatility_matrix),
spread_opt_tenors,
spread_swap_tenors,
strike_spreads,
vol_spreads,
swap_index_base,
short_swap_index_base if short_swap_index_base else swap_index_base,
vega_weighted_smile_fit)
cube.enableExtrapolation()
return cube
def sabr_parameters_guess(number_of_options, number_of_swaps):
n_elements = number_of_options * number_of_swaps
guess = n_elements * [0]
for n in range(n_elements):
guess[n] = (ql.makeQuoteHandle(0.2),
ql.makeQuoteHandle(0.5),
ql.makeQuoteHandle(0.4),
ql.makeQuoteHandle(0.0))
return guess
def build_sabr_swaption_cube(
volatility_matrix,
spread_opt_tenors,
spread_swap_tenors,
strike_spreads,
vol_spreads,
swap_index_base,
short_swap_index_base=None,
vega_weighted_smile_fit=False,
is_parameter_fixed=(False, False, False, False),
is_atm_calibrated=True):
v_spreads = [[ql.makeQuoteHandle(v) for v in row]
for row in vol_spreads]
guess = sabr_parameters_guess(
len(spread_opt_tenors), len(spread_swap_tenors))
cube = ql.SabrSwaptionVolatilityCube(
ql.SwaptionVolatilityStructureHandle(volatility_matrix),
spread_opt_tenors,
spread_swap_tenors,
strike_spreads,
v_spreads,
swap_index_base,
short_swap_index_base if short_swap_index_base else swap_index_base,
vega_weighted_smile_fit,
guess,
is_parameter_fixed,
is_atm_calibrated)
cube.enableExtrapolation()
return cube
class SwaptionVolatilityCubeTest(unittest.TestCase):
def setUp(self):
self.today = CAL.adjust(ql.Date.todaysDate())
ql.Settings.instance().evaluationDate = self.today
curve_handle = ql.RelinkableYieldTermStructureHandle()
curve = build_nominal_term_structure(self.today, ZERO_COUPON_DATA)
curve_handle.linkTo(curve)
self.idx = ql.Euribor6M(curve_handle)
self.swap_idx = build_euribor_swap_idx(curve_handle)
self.swap_engine = ql.DiscountingSwapEngine(curve_handle)
def tearDown(self):
ql.Settings.instance().evaluationDate = ql.Date()
def _get_fair_rate(self, exercise_date, swap_tenor):
start_date = CAL.advance(exercise_date, ql.Period(2, ql.Days))
underlying = ql.MakeVanillaSwap(
swap_tenor, self.idx, 0.0, ql.Period(0, ql.Days),
effectiveDate=start_date,
fixedLegTenor=ql.Period(1, ql.Years),
fixedLegDayCount=ql.Thirty360(ql.Thirty360.BondBasis),
floatingLegSpread=0.0,
swapType=ql.Swap.Receiver)
underlying.setPricingEngine(self.swap_engine)
return underlying.fairRate()
def _assert_atm_strike(
self, cube, interpolation, vol_type):
opt_tenor = ql.Period(1, ql.Years)
swap_tenor = ql.Period(10, ql.Years)
exercise_date = cube.optionDateFromTenor(opt_tenor)
expected_atm_strike = self._get_fair_rate(exercise_date, swap_tenor)
actual_atm_strike = cube.atmStrike(exercise_date, swap_tenor)
fail_msg = """ ATM strike test failed for:
cube interpolation: {interpolation}
volatility_type: {vol_type}
option tenor: {option_tenor}
swap tenor: {swap_tenor}
strike: {strike}
replicated strike: {replicated_strike}
""".format(interpolation=interpolation,
vol_type=vol_type,
option_tenor=opt_tenor,
swap_tenor=swap_tenor,
strike=actual_atm_strike,
replicated_strike=expected_atm_strike)
self.assertAlmostEqual(
first=actual_atm_strike,
second=expected_atm_strike,
delta=TOLERANCE,
msg=fail_msg)
def _assert_atm_vol(
self,
cube,
opt_tenor,
swap_tenor,
expected_vol,
interpolation,
vol_type,
epsilon=TOLERANCE):
option_date = cube.optionDateFromTenor(opt_tenor)
strike = cube.atmStrike(option_date, swap_tenor)
actual_vol = cube.volatility(option_date, swap_tenor, strike)
fail_msg = """ ATM vol test failed for:
cube interpolation: {interpolation}
volatility_type: {vol_type}
option tenor: {option_tenor}
swap tenor: {swap_tenor}
strike: {strike}
volatility: {vol}
expected volatility: {expected_vol}
epsilon: {eps}
""".format(interpolation=interpolation,
vol_type=vol_type,
option_tenor=opt_tenor,
swap_tenor=swap_tenor,
strike=strike,
vol=actual_vol,
expected_vol=expected_vol,
eps=epsilon)
self.assertAlmostEqual(
first=actual_vol,
second=expected_vol,
delta=epsilon,
msg=fail_msg)
def _assert_vol_spread(
self,
cube,
opt_tenor,
swap_tenor,
strike_spread,
expected_vol,
interpolation,
vol_type,
epsilon=TOLERANCE):
option_date = cube.optionDateFromTenor(opt_tenor)
strike = cube.atmStrike(option_date, swap_tenor) + strike_spread
actual_vol = cube.volatility(option_date, swap_tenor, strike)
fail_msg = """ Vol spread test failed for:
cube interpolation: {interpolation}
volatility_type: {vol_type}
option tenor: {option_tenor}
swap tenor: {swap_tenor}
strike: {strike}
volatility: {vol}
expected volatility: {expected_vol}
epsilon: {eps}
""".format(interpolation=interpolation,
vol_type=vol_type,
option_tenor=opt_tenor,
swap_tenor=swap_tenor,
strike=strike,
vol=actual_vol,
expected_vol=expected_vol,
eps=epsilon)
self.assertAlmostEqual(
first=actual_vol,
second=expected_vol,
delta=epsilon,
msg=fail_msg)
def test_linear_normal_cube_at_the_money_strike(self):
"""Testing ATM strike for linearly interpolated normal vol cube"""
linear_cube = build_linear_swaption_cube(
NORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
NORM_VOL_SPREADS,
self.swap_idx)
self._assert_atm_strike(
cube=linear_cube,
interpolation='linear',
vol_type='normal')
def test_linear_lognormal_cube_at_the_money_strike(self):
"""Testing ATM strike for linearly interpolated log-normal vol cube"""
linear_cube = build_linear_swaption_cube(
LOGNORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
LOGNORM_VOL_SPREADS,
self.swap_idx)
self._assert_atm_strike(
cube=linear_cube,
interpolation='linear',
vol_type='log-normal')
def test_sabr_lognormal_cube_at_the_money_strike(self):
"""Testing ATM strike for SABR interpolated log-normal vol cube"""
sabr_cube = build_sabr_swaption_cube(
LOGNORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
LOGNORM_VOL_SPREADS,
self.swap_idx)
self._assert_atm_strike(
cube=sabr_cube,
interpolation='SABR',
vol_type='log-normal')
def test_linear_normal_cube_at_the_money_vol(self):
"""Testing ATM volatility for linearly interpolated normal vol cube"""
linear_cube = build_linear_swaption_cube(
NORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
NORM_VOL_SPREADS,
self.swap_idx)
self._assert_atm_vol(
cube=linear_cube,
opt_tenor=ql.Period(1, ql.Years),
swap_tenor=ql.Period(10, ql.Years),
expected_vol=0.00453,
interpolation='linear',
vol_type='normal')
def test_linear_lognormal_cube_at_the_money_vol(self):
"""Testing ATM volatility for linearly interpolated log-normal vol cube"""
linear_cube = build_linear_swaption_cube(
LOGNORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
LOGNORM_VOL_SPREADS,
self.swap_idx)
self._assert_atm_vol(
cube=linear_cube,
opt_tenor=ql.Period(10, ql.Years),
swap_tenor=ql.Period(10, ql.Years),
expected_vol=0.1250,
interpolation='linear',
vol_type='log-normal')
def test_sabr_lognormal_cube_at_the_money_vol(self):
"""Testing ATM volatility for SABR interpolated log-normal vol cube"""
sabr_cube = build_sabr_swaption_cube(
LOGNORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
LOGNORM_VOL_SPREADS,
self.swap_idx)
self._assert_atm_vol(
cube=sabr_cube,
opt_tenor=ql.Period(10, ql.Years),
swap_tenor=ql.Period(10, ql.Years),
expected_vol=0.1250,
interpolation='SABR',
vol_type='log-normal',
epsilon=SABR_ATM_TOLERANCE)
def test_linear_normal_cube_spread_vol(self):
"""Testing spread volatility for linearly interpolated normal cube"""
linear_cube = build_linear_swaption_cube(
NORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
NORM_VOL_SPREADS,
self.swap_idx)
self._assert_vol_spread(
cube=linear_cube,
opt_tenor=ql.Period(1, ql.Years),
swap_tenor=ql.Period(10, ql.Years),
strike_spread=-0.02,
expected_vol=0.00453 - 0.0006,
interpolation='linear',
vol_type='normal')
def test_linear_lognormal_cube_spread_vol(self):
"""Testing spread volatility for linearly interpolated log-normal cube"""
linear_cube = build_linear_swaption_cube(
LOGNORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
LOGNORM_VOL_SPREADS,
self.swap_idx)
self._assert_vol_spread(
cube=linear_cube,
opt_tenor=ql.Period(10, ql.Years),
swap_tenor=ql.Period(10, ql.Years),
strike_spread=-0.02,
expected_vol=0.125 + 0.0558,
interpolation='linear',
vol_type='log-normal')
def test_sabr_lognormal_cube_spread_vol(self):
"""Testing spread volatility for SABR interpolated log-normal cube"""
sabr_cube = build_sabr_swaption_cube(
LOGNORM_VOL_MATRIX,
SMILE_OPT_TENORS,
SMILE_SWAP_TENORS,
STRIKE_SPREADS,
LOGNORM_VOL_SPREADS,
self.swap_idx)
self._assert_vol_spread(
cube=sabr_cube,
opt_tenor=ql.Period(10, ql.Years),
swap_tenor=ql.Period(10, ql.Years),
strike_spread=-0.02,
expected_vol=0.125 + 0.0558,
interpolation='SABR',
vol_type='log-normal',
epsilon=SABR_SPREAD_TOLERANCE)
class SviSmileSectionTest(unittest.TestCase):
def setUp(self):
ql.Settings.instance().evaluationDate = ql.Date(3, ql.May, 2022)
def tearDown(self):
# The objects created in this test are not immediately garbage-collected
# by PyPy, and can throw errors when the global evaluation date changes.
# Thus, we need to force a collection when we're done with them.
import gc
gc.collect()
def test_svi_smile_section(self):
"""Testing the SviSmileSection against already fitted parameters"""
expiry_date = ql.Date(16, ql.December, 2022)
forward = 100
atm_vol = 0.325819
# parameters = a, b, sigma, rho, m
svi_parameters = [-0.651304, 0.986546, 0.838493, 0.520853, 0.695177]
smile = ql.SviSmileSection(expiry_date, forward, svi_parameters)
self.assertAlmostEqual(smile.volatility(forward), atm_vol, places=5)
self.assertAlmostEqual(smile.volatility(257.328), 0.739775, places=5)
def test_svi_interpolated_smile_section(self):
"""Testing the SviInterpolatedSmileSection's parameter fitting against given vols"""
expiry_date = ql.Date(16, ql.December, 2022)
forward = 100
strikes = [25.6134, 48.5585, 71.5027, 94.4478, 117.3920, 140.3372, 163.2814, 186.2265, 209.1707, 232.1149]
has_floating_strikes = False
atm_vol = 0.325819
vols = [0.881504, 0.627807, 0.456964, 0.343740, 0.297482, 0.321816, 0.390772, 0.476758, 0.565635, 0.651507]
a = -0.6
b = 0.9
sigma = 0.8
rho = 0.5
m = 0.6
interpolated_smile = ql.SviInterpolatedSmileSection(
expiry_date, forward, strikes, has_floating_strikes, atm_vol, vols,
a, b, sigma, rho, m,
False, False, False, False, False
)
self.assertAlmostEqual(interpolated_smile.volatility(forward), atm_vol, places=5)
self.assertAlmostEqual(interpolated_smile.volatility(257.328), 0.739775, places=5)
class AndreasenHugeVolatilityTest(unittest.TestCase):
def testLocalVolCalibration(self):
""" Testing Andreasen-Huge Local Volatility calibration"""
today = ql.Settings.instance().evaluationDate
spot = ql.makeQuoteHandle(100)
dc = ql.Actual365Fixed()
qTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.025, dc))
rTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, dc))
vol_data = [
# maturity in days, strike, volatility
(30, 75, 0.13),
(30, 100, 0.26),
(30, 125, 0.3),
(180, 80, 0.4),
(180, 150, 0.6),
(365, 110, 0.5)]
calibration_set = ql.CalibrationSet(
[(
ql.VanillaOption(
ql.PlainVanillaPayoff(ql.Option.Call, strike),
ql.EuropeanExercise(today + ql.Period(maturity_in_days, ql.Days))
),
ql.SimpleQuote(volatility)
) for maturity_in_days, strike, volatility in vol_data]
)
local_vol = ql.LocalVolTermStructureHandle(
ql.AndreasenHugeLocalVolAdapter(
ql.AndreasenHugeVolatilityInterpl(calibration_set, spot, rTS, qTS)
)
)
option = calibration_set[-2][0] # maturity in days: 180, strike: 150, vol: 0.6
dummy_vol = ql.BlackVolTermStructureHandle()
local_vol_process = ql.GeneralizedBlackScholesProcess(spot, qTS, rTS, dummy_vol, local_vol)
option.setPricingEngine(ql.MCEuropeanEngine(
local_vol_process, "lowdiscrepancy",
timeSteps=75, brownianBridge=True, requiredSamples=16000, seed=42)
)
t = dc.yearFraction(today, option.exercise().lastDate())
fwd = spot.value() * qTS.discount(t) / rTS.discount(t)
vol = calibration_set[-2][1].value()
expected = ql.BlackCalculator(
ql.as_plain_vanilla_payoff(option.payoff()), fwd, vol * math.sqrt(t), rTS.discount(t)).value()
self.assertAlmostEqual(expected, option.NPV(), delta=0.2)
if __name__ == "__main__":
print("testing QuantLib", ql.__version__)
unittest.main(verbosity=2)
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