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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 Dimitri Reiswich
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.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/pricingengines/blackdeltacalculator.hpp>
#include <ql/quotes/deltavolquote.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/quotes/simplequote.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
using std::sqrt;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(BlackDeltaCalculatorTests)
struct DeltaData {
Option::Type ot;
DeltaVolQuote::DeltaType dt;
Real spot;
DiscountFactor dDf; // domestic discount
DiscountFactor fDf; // foreign discount
Real stdDev;
Real strike;
Real value;
};
struct EuropeanOptionData {
Option::Type type;
Real strike;
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Time t; // time to maturity
Volatility v; // volatility
Real result; // expected result
Real tol; // tolerance
};
BOOST_AUTO_TEST_CASE(testDeltaValues){
BOOST_TEST_MESSAGE("Testing delta calculator values...");
DeltaData values[] = {
// Values taken from parallel implementation in R
{Option::Call, DeltaVolQuote::Spot, 1.421, 0.997306, 0.992266, 0.1180654, 1.608080, 0.15},
{Option::Call, DeltaVolQuote::PaSpot, 1.421, 0.997306, 0.992266, 0.1180654, 1.600545, 0.15},
{Option::Call, DeltaVolQuote::Fwd, 1.421, 0.997306, 0.992266, 0.1180654, 1.609029, 0.15},
{Option::Call, DeltaVolQuote::PaFwd, 1.421, 0.997306, 0.992266, 0.1180654, 1.601550, 0.15},
{Option::Call, DeltaVolQuote::Spot, 122.121, 0.9695434,0.9872347, 0.0887676, 119.8031, 0.67},
{Option::Call, DeltaVolQuote::PaSpot, 122.121, 0.9695434,0.9872347, 0.0887676, 117.7096, 0.67},
{Option::Call, DeltaVolQuote::Fwd, 122.121, 0.9695434,0.9872347, 0.0887676, 120.0592, 0.67},
{Option::Call, DeltaVolQuote::PaFwd, 122.121, 0.9695434,0.9872347, 0.0887676, 118.0532, 0.67},
{Option::Put, DeltaVolQuote::Spot, 3.4582, 0.99979, 0.9250616, 0.3199034, 4.964924, -0.821},
{Option::Put, DeltaVolQuote::PaSpot, 3.4582, 0.99979, 0.9250616, 0.3199034, 3.778327, -0.821},
{Option::Put, DeltaVolQuote::Fwd, 3.4582, 0.99979, 0.9250616, 0.3199034, 4.51896, -0.821},
{Option::Put, DeltaVolQuote::PaFwd, 3.4582, 0.99979, 0.9250616, 0.3199034, 3.65728, -0.821},
// JPYUSD Data taken from Castagnas "FX Options and Smile Risk" (Wiley 2009)
{Option::Put, DeltaVolQuote::Spot, 103.00, 0.99482, 0.98508, 0.07247845, 97.47, -0.25},
{Option::Put, DeltaVolQuote::PaSpot, 103.00, 0.99482, 0.98508, 0.07247845, 97.22, -0.25}
};
Option::Type currOt;
DeltaVolQuote::DeltaType currDt;
Real currSpot;
Real currdDf;
Real currfDf;
Real currStdDev;
Real currStrike;
Real expected;
Real currDelta;
Real calculated;
Real error;
Real tolerance;
for (Size i=0; i<std::size(values); i++) {
currOt =values[i].ot;
currDt =values[i].dt;
currSpot =values[i].spot;
currdDf =values[i].dDf;
currfDf =values[i].fDf;
currStdDev =values[i].stdDev;
currStrike =values[i].strike;
currDelta =values[i].value;
BlackDeltaCalculator myCalc(currOt, currDt, currSpot,
currdDf, currfDf, currStdDev);
tolerance=1.0e-3;
expected =currDelta;
calculated =myCalc.deltaFromStrike(currStrike);
error =std::fabs(calculated-expected);
if (error>tolerance) {
BOOST_ERROR("\n Delta-from-strike calculation failed for delta. \n"
<< "Iteration: "<< i << "\n"
<< "Calculated Strike:" << calculated << "\n"
<< "Expected Strike:" << expected << "\n"
<< "Error: " << error);
}
tolerance=1.0e-2;
// tolerance not that small, but sufficient for strikes in
// particular since they might be results of a numerical
// procedure
expected =currStrike;
calculated =myCalc.strikeFromDelta(currDelta);
error =std::fabs(calculated-expected);
if (error>tolerance) {
BOOST_ERROR("\n Strike-from-delta calculation failed for delta. \n"
<< "Iteration: "<< i << "\n"
<< "Calculated Strike:" << calculated << "\n"
<< "Expected Strike:" << expected << "\n"
<< "Error: " << error);
}
}
}
BOOST_AUTO_TEST_CASE(testDeltaPriceConsistency) {
BOOST_TEST_MESSAGE("Testing premium-adjusted delta price consistency...");
// This function tests for price consistencies with the standard
// Black Scholes calculator, since premium adjusted deltas can be calculated
// from spot deltas by adding/subtracting the premium.
// actually, value and tol won't be needed for testing
EuropeanOptionData values[] = {
// type, strike, spot, rd, rf, t, vol, value, tol
{ Option::Call, 0.9123, 1.2212, 0.0231, 0.0000, 0.25, 0.301, 0.0, 0.0},
{ Option::Call, 0.9234, 1.2212, 0.0231, 0.0000, 0.35, 0.111, 0.0, 0.0},
{ Option::Call, 0.9783, 1.2212, 0.0231, 0.0000, 0.45, 0.071, 0.0, 0.0},
{ Option::Call, 1.0000, 1.2212, 0.0231, 0.0000, 0.55, 0.082, 0.0, 0.0},
{ Option::Call, 1.1230, 1.2212, 0.0231, 0.0000, 0.65, 0.012, 0.0, 0.0},
{ Option::Call, 1.2212, 1.2212, 0.0231, 0.0000, 0.75, 0.129, 0.0, 0.0},
{ Option::Call, 1.3212, 1.2212, 0.0231, 0.0000, 0.85, 0.034, 0.0, 0.0},
{ Option::Call, 1.3923, 1.2212, 0.0131, 0.2344, 0.95, 0.001, 0.0, 0.0},
{ Option::Call, 1.3455, 1.2212, 0.0000, 0.0000, 1.00, 0.127, 0.0, 0.0},
{ Option::Put, 0.9123, 1.2212, 0.0231, 0.0000, 0.25, 0.301, 0.0, 0.0},
{ Option::Put, 0.9234, 1.2212, 0.0231, 0.0000, 0.35, 0.111, 0.0, 0.0},
{ Option::Put, 0.9783, 1.2212, 0.0231, 0.0000, 0.45, 0.071, 0.0, 0.0},
{ Option::Put, 1.0000, 1.2212, 0.0231, 0.0000, 0.55, 0.082, 0.0, 0.0},
{ Option::Put, 1.1230, 1.2212, 0.0231, 0.0000, 0.65, 0.012, 0.0, 0.0},
{ Option::Put, 1.2212, 1.2212, 0.0231, 0.0000, 0.75, 0.129, 0.0, 0.0},
{ Option::Put, 1.3212, 1.2212, 0.0231, 0.0000, 0.85, 0.034, 0.0, 0.0},
{ Option::Put, 1.3923, 1.2212, 0.0131, 0.2344, 0.95, 0.001, 0.0, 0.0},
{ Option::Put, 1.3455, 1.2212, 0.0000, 0.0000, 1.00, 0.127, 0.0, 0.0},
// extreme case: zero vol
{ Option::Put, 1.3455, 1.2212, 0.0000, 0.0000, 0.50, 0.000, 0.0, 0.0},
// extreme case: zero strike
{ Option::Put, 0.0000, 1.2212, 0.0000, 0.0000, 1.50, 0.133, 0.0, 0.0},
// extreme case: zero strike+zero vol
{ Option::Put, 0.0000, 1.2212, 0.0000, 0.0000, 1.00, 0.133, 0.0, 0.0},
};
DayCounter dc = Actual360();
Calendar calendar = TARGET();
Date today = Date::todaysDate();
// Start setup of market data
Real discFor =0.0;
Real discDom =0.0;
Real implVol =0.0;
Real expectedVal =0.0;
Real calculatedVal =0.0;
Real error =0.0;
ext::shared_ptr<SimpleQuote> spotQuote(new SimpleQuote(0.0));
Handle<Quote> spotHandle(spotQuote);
ext::shared_ptr<SimpleQuote> qQuote(new SimpleQuote(0.0));
Handle<Quote> qHandle(qQuote);
ext::shared_ptr<YieldTermStructure> qTS(
new FlatForward(today, qHandle, dc));
ext::shared_ptr<SimpleQuote> rQuote(new SimpleQuote(0.0));
Handle<Quote> rHandle(qQuote);
ext::shared_ptr<YieldTermStructure> rTS(
new FlatForward(today, rHandle, dc));
ext::shared_ptr<SimpleQuote> volQuote(new SimpleQuote(0.0));
Handle<Quote> volHandle(volQuote);
ext::shared_ptr<BlackVolTermStructure> volTS(
new BlackConstantVol(today, calendar, volHandle, dc));
ext::shared_ptr<BlackScholesMertonProcess> stochProcess;
ext::shared_ptr<PricingEngine> engine;
ext::shared_ptr<StrikedTypePayoff> payoff;
Date exDate;
ext::shared_ptr<Exercise> exercise;
// Setup of market data finished
Real tolerance=1.0e-10;
for (auto& value : values) {
payoff =
ext::shared_ptr<StrikedTypePayoff>(new PlainVanillaPayoff(value.type, value.strike));
exDate = today + timeToDays(value.t);
exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
spotQuote->setValue(value.s);
volQuote->setValue(value.v);
rQuote->setValue(value.r);
qQuote->setValue(value.q);
discDom =rTS->discount(exDate);
discFor =qTS->discount(exDate);
implVol =sqrt(volTS->blackVariance(exDate,0.0));
BlackDeltaCalculator myCalc(value.type, DeltaVolQuote::PaSpot, spotQuote->value(), discDom,
discFor, implVol);
stochProcess=ext::make_shared<BlackScholesMertonProcess> (spotHandle,
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS));
engine = ext::shared_ptr<PricingEngine>(
new AnalyticEuropeanEngine(stochProcess));
EuropeanOption option(payoff, exercise);
option.setPricingEngine(engine);
calculatedVal = myCalc.deltaFromStrike(value.strike);
Real delta = 0.0;
if (implVol > 0.0) {
delta = option.delta();
}
else {
const Real fwd = spotQuote->value()*discFor/discDom;
if (payoff->optionType() == Option::Call && fwd > payoff->strike())
delta = 1.0;
else if (payoff->optionType() == Option::Put && fwd < payoff->strike())
delta = -1.0;
}
expectedVal=delta-option.NPV()/spotQuote->value();
error=std::fabs(expectedVal-calculatedVal);
if(error>tolerance){
BOOST_ERROR("\n Premium-adjusted spot delta test failed. \n" \
<< "Calculated Delta: " << calculatedVal << "\n"
<< "Expected Value: " << expectedVal << "\n"
<< "Error: "<< error);
}
myCalc.setDeltaType(DeltaVolQuote::PaFwd);
calculatedVal = myCalc.deltaFromStrike(value.strike);
expectedVal=expectedVal/discFor; // Premium adjusted Fwd Delta is PA spot without discount
error=std::fabs(expectedVal-calculatedVal);
if(error>tolerance){
BOOST_ERROR("\n Premium-adjusted forward delta test failed. \n"
<< "Calculated Delta: " << calculatedVal << "\n"
<< "Expected Value: " << expectedVal << "\n"
<< "Error: "<< error);
}
// Test consistency with BlackScholes Calculator for Spot Delta
myCalc.setDeltaType(DeltaVolQuote::Spot);
calculatedVal = myCalc.deltaFromStrike(value.strike);
expectedVal=delta;
error=std::fabs(calculatedVal-expectedVal);
if(error>tolerance){
BOOST_ERROR("\n spot delta in BlackDeltaCalculator differs "
"from delta in BlackScholesCalculator. \n"
<< "Calculated Value: " << calculatedVal << "\n"
<< "Expected Value: " << expectedVal << "\n"
<< "Error: " << error);
}
}
}
BOOST_AUTO_TEST_CASE(testPutCallParity){
BOOST_TEST_MESSAGE("Testing put-call parity for deltas...");
// Test for put call parity between put and call deltas.
/* The data below are from
"Option pricing formulas", E.G. Haug, McGraw-Hill 1998
pag 11-16
*/
EuropeanOptionData values[] = {
// pag 2-8
// type, strike, spot, q, r, t, vol, value, tol
{ Option::Call, 65.00, 60.00, 0.00, 0.08, 0.25, 0.30, 2.1334, 1.0e-4},
{ Option::Put, 95.00, 100.00, 0.05, 0.10, 0.50, 0.20, 2.4648, 1.0e-4},
{ Option::Put, 19.00, 19.00, 0.10, 0.10, 0.75, 0.28, 1.7011, 1.0e-4},
{ Option::Call, 19.00, 19.00, 0.10, 0.10, 0.75, 0.28, 1.7011, 1.0e-4},
{ Option::Call, 1.60, 1.56, 0.08, 0.06, 0.50, 0.12, 0.0291, 1.0e-4},
{ Option::Put, 70.00, 75.00, 0.05, 0.10, 0.50, 0.35, 4.0870, 1.0e-4},
// pag 24
{ Option::Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 0.0205, 1.0e-4},
{ Option::Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8734, 1.0e-4},
{ Option::Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 9.9413, 1.0e-4},
{ Option::Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 0.3150, 1.0e-4},
{ Option::Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1217, 1.0e-4},
{ Option::Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 10.3556, 1.0e-4},
{ Option::Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 0.9474, 1.0e-4},
{ Option::Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3693, 1.0e-4},
{ Option::Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 11.1381, 1.0e-4},
{ Option::Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 0.8069, 1.0e-4},
{ Option::Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0232, 1.0e-4},
{ Option::Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 10.5769, 1.0e-4},
{ Option::Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 2.7026, 1.0e-4},
{ Option::Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.6997, 1.0e-4},
{ Option::Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 12.7857, 1.0e-4},
{ Option::Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 4.9329, 1.0e-4},
{ Option::Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.3679, 1.0e-4},
{ Option::Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 15.3086, 1.0e-4},
{ Option::Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 9.9210, 1.0e-4},
{ Option::Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8734, 1.0e-4},
{ Option::Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 0.0408, 1.0e-4},
{ Option::Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 10.2155, 1.0e-4},
{ Option::Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1217, 1.0e-4},
{ Option::Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 0.4551, 1.0e-4},
{ Option::Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 10.8479, 1.0e-4},
{ Option::Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3693, 1.0e-4},
{ Option::Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 1.2376, 1.0e-4},
{ Option::Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 10.3192, 1.0e-4},
{ Option::Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0232, 1.0e-4},
{ Option::Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 1.0646, 1.0e-4},
{ Option::Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 12.2149, 1.0e-4},
{ Option::Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.6997, 1.0e-4},
{ Option::Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 3.2734, 1.0e-4},
{ Option::Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 14.4452, 1.0e-4},
{ Option::Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.3679, 1.0e-4},
{ Option::Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 5.7963, 1.0e-4},
// pag 27
{ Option::Call, 40.00, 42.00, 0.08, 0.04, 0.75, 0.35, 5.0975, 1.0e-4}
};
DayCounter dc = Actual360();
Calendar calendar = TARGET();
Date today = Date::todaysDate();
Real discFor =0.0;
Real discDom =0.0;
Real implVol =0.0;
Real deltaCall =0.0;
Real deltaPut =0.0;
Real expectedDiff =0.0;
Real calculatedDiff =0.0;
Real error =0.0;
Real forward =0.0;
ext::shared_ptr<SimpleQuote> spotQuote(new SimpleQuote(0.0));
ext::shared_ptr<SimpleQuote> qQuote(new SimpleQuote(0.0));
Handle<Quote> qHandle(qQuote);
ext::shared_ptr<YieldTermStructure> qTS(
new FlatForward(today, qHandle, dc));
ext::shared_ptr<SimpleQuote> rQuote(new SimpleQuote(0.0));
Handle<Quote> rHandle(qQuote);
ext::shared_ptr<YieldTermStructure> rTS(
new FlatForward(today, rHandle, dc));
ext::shared_ptr<SimpleQuote> volQuote(new SimpleQuote(0.0));
Handle<Quote> volHandle(volQuote);
ext::shared_ptr<BlackVolTermStructure> volTS(
new BlackConstantVol(today, calendar, volHandle, dc));
ext::shared_ptr<StrikedTypePayoff> payoff;
Date exDate;
ext::shared_ptr<Exercise> exercise;
Real tolerance=1.0e-10;
for (auto& value : values) {
payoff =
ext::shared_ptr<StrikedTypePayoff>(new PlainVanillaPayoff(Option::Call, value.strike));
exDate = today + timeToDays(value.t);
exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
spotQuote->setValue(value.s);
volQuote->setValue(value.v);
rQuote->setValue(value.r);
qQuote->setValue(value.q);
discDom=rTS->discount(exDate);
discFor=qTS->discount(exDate);
implVol=sqrt(volTS->blackVariance(exDate,0.0));
forward=spotQuote->value()*discFor/discDom;
BlackDeltaCalculator myCalc(Option::Call, DeltaVolQuote::Spot,
spotQuote->value(),
discDom, discFor, implVol);
deltaCall = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Put);
deltaPut = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Call);
expectedDiff=discFor;
calculatedDiff=deltaCall-deltaPut;
error=std::fabs(expectedDiff-calculatedDiff);
if(error>tolerance){
BOOST_ERROR("\n Put-call parity failed for spot delta. \n"
<< "Calculated Call Delta: " << deltaCall << "\n"
<< "Calculated Put Delta: " << deltaPut << "\n"
<< "Expected Difference: " << expectedDiff << "\n"
<< "Calculated Difference: " << calculatedDiff);
}
myCalc.setDeltaType(DeltaVolQuote::Fwd);
deltaCall = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Put);
deltaPut = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Call);
expectedDiff=1.0;
calculatedDiff=deltaCall-deltaPut;
error=std::fabs(expectedDiff-calculatedDiff);
if(error>tolerance){
BOOST_ERROR("\n Put-call parity failed for forward delta. \n"
<< "Calculated Call Delta: " << deltaCall << "\n"
<< "Calculated Put Delta: " << deltaPut << "\n"
<< "Expected Difference: " << expectedDiff << "\n"
<< "Calculated Difference: " << calculatedDiff );
}
myCalc.setDeltaType(DeltaVolQuote::PaSpot);
deltaCall = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Put);
deltaPut = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Call);
expectedDiff = discFor * value.strike / forward;
calculatedDiff=deltaCall-deltaPut;
error=std::fabs(expectedDiff-calculatedDiff);
if(error>tolerance){
BOOST_ERROR("\n Put-call parity failed for "
"premium-adjusted spot delta. \n"
<< "Calculated Call Delta: " << deltaCall << "\n"
<< "Calculated Put Delta: " << deltaPut << "\n"
<< "Expected Difference: " << expectedDiff << "\n"
<< "Calculated Difference: " << calculatedDiff);
}
myCalc.setDeltaType(DeltaVolQuote::PaFwd);
deltaCall = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Put);
deltaPut = myCalc.deltaFromStrike(value.strike);
;
myCalc.setOptionType(Option::Call);
expectedDiff = value.strike / forward;
calculatedDiff=deltaCall-deltaPut;
error=std::fabs(expectedDiff-calculatedDiff);
if(error>tolerance){
BOOST_ERROR("\n Put-call parity failed for premium-adjusted "
"forward delta. \n"
<< "Calculated Call Delta: " << deltaCall << "\n"
<< "Calculated Put Delta: " << deltaPut << "\n"
<< "Expected Difference: " << expectedDiff << "\n"
<< "Calculated Difference: " << calculatedDiff);
}
}
}
BOOST_AUTO_TEST_CASE(testAtmCalcs){
BOOST_TEST_MESSAGE("Testing delta-neutral ATM quotations...");
DeltaData values[] = {
{Option::Call, DeltaVolQuote::Spot, 1.421, 0.997306, 0.992266, 0.1180654, 1.608080, 0.15},
{Option::Call, DeltaVolQuote::PaSpot, 1.421, 0.997306, 0.992266, 0.1180654, 1.600545, 0.15},
{Option::Call, DeltaVolQuote::Fwd, 1.421, 0.997306, 0.992266, 0.1180654, 1.609029, 0.15},
{Option::Call, DeltaVolQuote::PaFwd, 1.421, 0.997306, 0.992266, 0.1180654, 1.601550, 0.15},
{Option::Call, DeltaVolQuote::Spot, 122.121, 0.9695434,0.9872347, 0.0887676, 119.8031, 0.67},
{Option::Call, DeltaVolQuote::PaSpot, 122.121, 0.9695434,0.9872347, 0.0887676, 117.7096, 0.67},
{Option::Call, DeltaVolQuote::Fwd, 122.121, 0.9695434,0.9872347, 0.0887676, 120.0592, 0.67},
{Option::Call, DeltaVolQuote::PaFwd, 122.121, 0.9695434,0.9872347, 0.0887676, 118.0532, 0.67},
{Option::Put, DeltaVolQuote::Spot, 3.4582, 0.99979, 0.9250616, 0.3199034, 4.964924, -0.821},
{Option::Put, DeltaVolQuote::PaSpot, 3.4582, 0.99979, 0.9250616, 0.3199034, 3.778327, -0.821},
{Option::Put, DeltaVolQuote::Fwd, 3.4582, 0.99979, 0.9250616, 0.3199034, 4.51896, -0.821},
{Option::Put, DeltaVolQuote::PaFwd, 3.4582, 0.99979, 0.9250616, 0.3199034, 3.65728, -0.821},
// Data taken from Castagnas "FX Options and Smile Risk" (Wiley 2009)
{Option::Put, DeltaVolQuote::Spot, 103.00, 0.99482, 0.98508, 0.07247845, 97.47, -0.25},
{Option::Put, DeltaVolQuote::PaSpot, 103.00, 0.99482, 0.98508, 0.07247845, 97.22, -0.25},
// Extreme case: zero vol, ATM Fwd strike
{Option::Call, DeltaVolQuote::Fwd, 103.00, 0.99482, 0.98508, 0.0, 101.0013,0.5},
{Option::Call, DeltaVolQuote::Spot, 103.00, 0.99482, 0.98508, 0.0, 101.0013,0.99482*0.5}
};
DeltaVolQuote::DeltaType currDt;
Real currSpot;
Real currdDf;
Real currfDf;
Real currStdDev;
Real expected;
Real calculated;
Real error;
Real tolerance=1.0e-2; // not that small, but sufficient for strikes
Real currAtmStrike;
Real currCallDelta;
Real currPutDelta;
Real currFwd;
for (Size i=0; i<std::size(values); i++) {
currDt =values[i].dt;
currSpot =values[i].spot;
currdDf =values[i].dDf;
currfDf =values[i].fDf;
currStdDev =values[i].stdDev;
currFwd =currSpot*currfDf/currdDf;
BlackDeltaCalculator myCalc(Option::Call, currDt, currSpot, currdDf,
currfDf, currStdDev);
currAtmStrike=myCalc.atmStrike(DeltaVolQuote::AtmDeltaNeutral);
currCallDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Put);
currPutDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Call);
expected =0.0;
calculated =currCallDelta+currPutDelta;
error =std::fabs(calculated-expected);
if(error>tolerance){
BOOST_ERROR("\n Delta neutrality failed for spot delta "
"in Delta Calculator. \n"
<< "Iteration: "<< i << "\n"
<< "Calculated Delta Sum: " << calculated << "\n"
<< "Expected Delta Sum: " << expected << "\n"
<< "Error: " << error);
}
myCalc.setDeltaType(DeltaVolQuote::Fwd);
currAtmStrike=myCalc.atmStrike(DeltaVolQuote::AtmDeltaNeutral);
currCallDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Put);
currPutDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Call);
expected =0.0;
calculated =currCallDelta+currPutDelta;
error =std::fabs(calculated-expected);
if(error>tolerance){
BOOST_ERROR("\n Delta neutrality failed for forward delta "
"in Delta Calculator. \n"
<< "Iteration: " << i << "\n"
<< "Calculated Delta Sum: " << calculated << "\n"
<< "Expected Delta Sum: " << expected << "\n"
<< "Error: " << error);
}
myCalc.setDeltaType(DeltaVolQuote::PaSpot);
currAtmStrike=myCalc.atmStrike(DeltaVolQuote::AtmDeltaNeutral);
currCallDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Put);
currPutDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Call);
expected =0.0;
calculated =currCallDelta+currPutDelta;
error =std::fabs(calculated-expected);
if(error>tolerance){
BOOST_ERROR("\n Delta neutrality failed for premium-adjusted "
"spot delta in Delta Calculator. \n"
<< "Iteration: " << i << "\n"
<< "Calculated Delta Sum: " << calculated << "\n"
<< "Expected Delta Sum: " << expected << "\n"
<< "Error: " << error);
}
myCalc.setDeltaType(DeltaVolQuote::PaFwd);
currAtmStrike=myCalc.atmStrike(DeltaVolQuote::AtmDeltaNeutral);
currCallDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Put);
currPutDelta=myCalc.deltaFromStrike(currAtmStrike);
myCalc.setOptionType(Option::Call);
expected =0.0;
calculated =currCallDelta+currPutDelta;
error =std::fabs(calculated-expected);
if(error>tolerance){
BOOST_ERROR("\n Delta neutrality failed for premium-adjusted "
"forward delta in Delta Calculator. \n"
<< "Iteration: " << i << "\n"
<< "Calculated Delta Sum: " << calculated << "\n"
<< "Expected Delta Sum: " << expected << "\n"
<< "Error: " << error);
}
// Test ATM forward Calculations
calculated=myCalc.atmStrike(DeltaVolQuote::AtmFwd);
expected=currFwd;
error=std::fabs(expected-calculated);
if(error>tolerance){
BOOST_ERROR("\n Atm forward test failed. \n"
<< "Calculated Value: " << calculated << "\n"
<< "Expected Value: " << expected << "\n"
<< "Error: " << error);
}
// Test ATM 0.50 delta calculations
myCalc.setDeltaType(DeltaVolQuote::Fwd);
Real atmFiftyStrike=myCalc.atmStrike(DeltaVolQuote::AtmPutCall50);
calculated=std::fabs(myCalc.deltaFromStrike(atmFiftyStrike));
expected=0.50;
error=std::fabs(expected-calculated);
if(error>tolerance){
BOOST_ERROR("\n Atm 0.50 delta strike test failed. \n"
<< "Iteration:" << i << "\n"
<< "Calculated Value: " << calculated << "\n"
<< "Expected Value: " << expected << "\n"
<< "Error: " << error);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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