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# coding=utf-8-unix
"""
Copyright (C) 2017 Wojciech Ślusarski
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
class BlackFormulaTest(unittest.TestCase):
def setUp(self):
# define the market and option parameters
self.option_type = ql.Option.Call
self.spot = 100.0
self.strike = 100.0
self.risk_free_rate = 0.05
self.expiry = 1.0
self.forward = self.spot * math.exp(self.risk_free_rate * self.expiry)
self.df = math.exp(-self.risk_free_rate * self.expiry)
self.vol = 0.2 * math.sqrt(self.expiry)
self.displacement = 0.0
def test_blackFormula(self):
"""Testing blackFormula in a simple Black-Scholes World..."""
#Anyone interested, feel free to provide more accurate number
expected = 10.4506
res = ql.blackFormula(self.option_type,
self.strike,
self.forward,
self.vol,
self.df,
self.displacement)
self.assertAlmostEqual(expected, res, delta=1e-4,
msg="Failed to calculate simple "
"Black-Scholes-Merton price rounded to "
"four decimal places.")
def test_black_formula_implied_stdev(self):
"""Testing implied volatility calculator"""
expected = 0.2 * math.sqrt(self.expiry)
black_price = 10.4506
res = ql.blackFormulaImpliedStdDev(self.option_type,
self.strike,
self.forward,
black_price,
self.df)
self.assertAlmostEqual(expected, res, delta=1e-4,
msg="Failed to determine Implied Vol rounded "
"to a single vol bps.")
class BlackDeltaCalculatorTest(unittest.TestCase):
def setUp(self):
self.todaysDate = ql.Date(5, ql.September, 2017)
ql.Settings.instance().evaluationDate = self.todaysDate
self.spotDate = ql.Date(7, ql.September, 2017)
self.domestic_rate = ql.FlatForward(self.spotDate, 0.017,
ql.Actual365Fixed())
self.foreign_rate = ql.FlatForward(self.spotDate, 0.013,
ql.Actual365Fixed())
def tearDown(self):
ql.Settings.instance().evaluationDate = ql.Date()
def test_single_spot_delta(self):
"""Test for a single strike for call spot delta 75"""
volatility = 0.2
expiry = 2
spot_price = 3.6
domDf = self.domestic_rate.discount(expiry)
forDf = self.foreign_rate.discount(expiry)
forward = spot_price * forDf / domDf
spot_delta_level = 0.75
stDev = volatility * expiry ** 0.5
inv_norm_dist = ql.InverseCumulativeNormal()
expected_strike = inv_norm_dist(spot_delta_level / forDf)
expected_strike *= stDev
expected_strike -= 0.5 * stDev ** 2
expected_strike = math.exp(expected_strike) / forward
expected_strike = 1 / expected_strike
option_type = ql.Option.Call
delta_type = ql.DeltaVolQuote.Spot
black_calculator = ql.BlackDeltaCalculator(option_type,
delta_type,
spot_price,
domDf,
forDf,
stDev)
strike = black_calculator.strikeFromDelta(spot_delta_level)
self.assertAlmostEqual(expected_strike, strike, delta=1e-4)
def test_spot_atm_delta_calculator(self):
"""Test for 0-delta straddle strike"""
volatility = 0.2
expiry = 2
spot_price = 3.6
domDf = self.domestic_rate.discount(expiry)
forDf = self.foreign_rate.discount(expiry)
forward = spot_price * forDf / domDf
expected_strike = forward * math.exp(-0.5 * volatility ** 2 * expiry)
option_type = ql.Option.Call
delta_type = ql.DeltaVolQuote.AtmDeltaNeutral
stDev = volatility * expiry ** 0.5
black_calculator = ql.BlackDeltaCalculator(option_type,
delta_type,
spot_price,
domDf,
forDf,
stDev)
strike = black_calculator.atmStrike(ql.DeltaVolQuote.AtmDeltaNeutral)
self.assertAlmostEqual(expected_strike, strike, delta=1e-4)
if __name__ == '__main__':
print("testing QuantLib", ql.__version__)
unittest.main(verbosity=2)
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