<gh_stars>0
# coding=utf-8-unix
"""
 Copyright (C) 2017 <NAME>

 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
 <<EMAIL>>. The license is also available online at
 <http://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.assertAlmostEquals(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.assertAlmostEquals(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 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.assertAlmostEquals(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.assertAlmostEquals(expected_strike, strike, delta=1e-4)


if __name__ == '__main__':
    unittest.main()
