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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
<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.
*/
#include <ql/experimental/fx/blackdeltacalculator.hpp>
namespace QuantLib {
BlackDeltaCalculator::BlackDeltaCalculator(
Option::Type ot,
DeltaVolQuote::DeltaType dt,
Real spot,
DiscountFactor dDiscount, // domestic discount
DiscountFactor fDiscount, // foreign discount
Real stdDev):
dt_(dt), ot_(ot),
dDiscount_(dDiscount), fDiscount_(fDiscount),
stdDev_(stdDev), spot_(spot),
forward_(spot*fDiscount/dDiscount), phi_(Integer(ot)) {
QL_REQUIRE(spot_>0.0,
"positive spot value required: " <<
spot_ << " not allowed");
QL_REQUIRE(dDiscount_>0.0,
"positive domestic discount factor required: " <<
dDiscount_ << " not allowed");
QL_REQUIRE(fDiscount_>0.0,
"positive foreign discount factor required: " <<
fDiscount_ << " not allowed");
QL_REQUIRE(stdDev_>=0.0,
"non-negative standard deviation required: "
<< stdDev_ << " not allowed");
fExpPos_ =forward_*exp(0.5*stdDev_*stdDev_);
fExpNeg_ =forward_*exp(-0.5*stdDev_*stdDev_);
}
Real BlackDeltaCalculator::deltaFromStrike(Real strike) const {
QL_REQUIRE(strike >=0.0,
"positive strike value required: " <<
strike << " not allowed");
Real res=0.0;
switch(dt_){
case DeltaVolQuote::Spot:
res=phi_*fDiscount_*cumD1(strike);
break;
case DeltaVolQuote::Fwd:
res=phi_*cumD1(strike);
break;
case DeltaVolQuote::PaSpot:
res=phi_*fDiscount_*cumD2(strike)*strike/forward_;
break;
case DeltaVolQuote::PaFwd:
res=phi_*cumD2(strike)*strike/forward_;
break;
default:
QL_FAIL("invalid delta type");
}
return res;
}
Real BlackDeltaCalculator::strikeFromDelta(Real delta) const {
return(strikeFromDelta(delta, dt_));
}
Real BlackDeltaCalculator::strikeFromDelta(Real delta,
DeltaVolQuote::DeltaType dt)
const{
Real res=0.0;
Real arg=0.0;
InverseCumulativeNormal f;
QL_REQUIRE(delta*phi_>=0.0, "Option type and delta are incoherent.");
switch (dt) {
case DeltaVolQuote::Spot:
QL_REQUIRE(std::fabs(delta)<=fDiscount_,
"Spot delta out of range.");
arg=-phi_*f(phi_*delta/fDiscount_)*stdDev_+0.5*stdDev_*stdDev_;
res=forward_*exp(arg);
break;
case DeltaVolQuote::Fwd:
QL_REQUIRE(std::fabs(delta)<=1.0,
"Forward delta out of range.");
arg=-phi_*f(phi_*delta)*stdDev_+0.5*stdDev_*stdDev_;
res=forward_*exp(arg);
break;
case DeltaVolQuote::PaSpot:
case DeltaVolQuote::PaFwd: {
// This has to be solved numerically. One of the
// problems is that the premium adjusted call delta is
// not monotonic in strike, such that two solutions
// might occur. The one right to the max of the delta is
// considered to be the correct strike. Some proper
// interval bounds for the strike need to be chosen, the
// numerics can otherwise be very unreliable and
// unstable. I've chosen Brent over Newton, since the
// interval can be specified explicitly and we can not
// run into the area on the left of the maximum. The
// put delta doesn't have this property and can be
// solved without any problems, but also numerically.
BlackDeltaPremiumAdjustedSolverClass f(
ot_, dt , spot_,dDiscount_, fDiscount_, stdDev_,delta);
Brent solver;
solver.setMaxEvaluations(1000);
Real accuracy = 1.0e-10;
Real rightLimit=0.0;
Real leftLimit=0.0;
// Strike of not premium adjusted is always to the right of premium adjusted
if (dt==DeltaVolQuote::PaSpot) {
rightLimit=strikeFromDelta(delta, DeltaVolQuote::Spot);
} else {
rightLimit=strikeFromDelta(delta, DeltaVolQuote::Fwd);
}
if (phi_<0) { // if put
res=solver.solve(f, accuracy, rightLimit, 0.0, spot_*100.0);
break;
} else {
// find out the left limit which is the strike
// corresponding to the value where premium adjusted
// deltas have their maximum.
BlackDeltaPremiumAdjustedMaxStrikeClass g(
ot_,dt, spot_,dDiscount_, fDiscount_, stdDev_);
leftLimit=solver.solve(g, accuracy, rightLimit*0.5,
0.0, rightLimit);
Real guess=leftLimit+(rightLimit-leftLimit)*0.5;
res=solver.solve(f, accuracy, guess, leftLimit, rightLimit);
} // end if phi<0 else
break;
}
default:
QL_FAIL("invalid delta type");
}
return res;
}
Real BlackDeltaCalculator::atmStrike(DeltaVolQuote::AtmType atmT) const {
Real res=0.0;
switch(atmT) {
case DeltaVolQuote::AtmDeltaNeutral:
if(dt_==DeltaVolQuote::Spot || dt_==DeltaVolQuote::Fwd){
res=fExpPos_;
} else {
res=fExpNeg_;
}
break;
case DeltaVolQuote::AtmFwd:
res=forward_;
break;
case DeltaVolQuote::AtmGammaMax: case DeltaVolQuote::AtmVegaMax:
res=fExpPos_;
break;
case DeltaVolQuote::AtmPutCall50:
QL_REQUIRE(dt_==DeltaVolQuote::Fwd,
"|PutDelta|=CallDelta=0.50 only possible for forward delta.");
res=fExpPos_;
break;
default:
QL_FAIL("invalid atm type");
}
return res;
}
Real BlackDeltaCalculator::cumD1(Real strike) const {
Real d1_=0.0;
Real cum_d1_pos_ = 1.0; // N(d1)
Real cum_d1_neg_ = 0.0; // N(-d1)
CumulativeNormalDistribution f;
if (stdDev_>=QL_EPSILON) {
if(strike>0) {
d1_ = std::log(forward_/strike)/stdDev_ + 0.5*stdDev_;
return f(phi_*d1_);
}
} else {
if (forward_<strike) {
cum_d1_pos_ = 0.0;
cum_d1_neg_ = 1.0;
} else if(forward_==strike){
d1_ = 0.5*stdDev_;
return f(phi_*d1_);
}
}
if (phi_>0) { // if Call
return cum_d1_pos_;
} else {
return cum_d1_neg_;
}
}
Real BlackDeltaCalculator::nD1(Real strike) const {
Real d1_=0.0;
Real n_d1_ = 0.0; // n(d1)
if (stdDev_>=QL_EPSILON){
if(strike>0){
d1_ = std::log(forward_/strike)/stdDev_ + 0.5*stdDev_;
CumulativeNormalDistribution f;
n_d1_ = f.derivative(d1_);
}
}
return n_d1_;
}
Real BlackDeltaCalculator::cumD2(Real strike) const {
Real d2_=0.0;
Real cum_d2_pos_= 1.0; // N(d2)
Real cum_d2_neg_= 0.0; // N(-d2)
CumulativeNormalDistribution f;
if (stdDev_>=QL_EPSILON){
if(strike>0){
d2_ = std::log(forward_/strike)/stdDev_ - 0.5*stdDev_;
return f(phi_*d2_);
}
} else {
if (forward_<strike) {
cum_d2_pos_= 0.0;
cum_d2_neg_= 1.0;
} else if (forward_==strike) {
d2_ = -0.5*stdDev_;
return(f(phi_*d2_));
}
}
if (phi_>0) { // if Call
return cum_d2_pos_;
} else {
return cum_d2_neg_;
}
}
Real BlackDeltaCalculator::nD2(Real strike) const {
Real d2_=0.0;
Real n_d2_= 0.0; // n(d2)
if (stdDev_>=QL_EPSILON){
if(strike>0){
d2_ = std::log(forward_/strike)/stdDev_ - 0.5*stdDev_;
CumulativeNormalDistribution f;
n_d2_ = f.derivative(d2_);
}
}
return n_d2_;
}
void BlackDeltaCalculator::setDeltaType(DeltaVolQuote::DeltaType dt){
dt_=dt;
}
void BlackDeltaCalculator::setOptionType(Option::Type ot){
ot_=ot;
phi_=Integer(ot_);
}
// helper classes
BlackDeltaPremiumAdjustedSolverClass::BlackDeltaPremiumAdjustedSolverClass(
Option::Type ot,
DeltaVolQuote::DeltaType dt,
Real spot,
DiscountFactor dDiscount, // domestic discount
DiscountFactor fDiscount, // foreign discount
Real stdDev,
Real delta):
bdc_(ot,dt,spot,dDiscount,fDiscount,stdDev), delta_(delta) {}
Real BlackDeltaPremiumAdjustedSolverClass::operator()(Real strike) const {
return bdc_.deltaFromStrike(strike)-delta_;
}
BlackDeltaPremiumAdjustedMaxStrikeClass::BlackDeltaPremiumAdjustedMaxStrikeClass(
Option::Type ot,
DeltaVolQuote::DeltaType dt,
Real spot,
DiscountFactor dDiscount, // domestic discount
DiscountFactor fDiscount, // foreign discount
Real stdDev):
bdc_(ot,dt,spot,dDiscount,fDiscount,stdDev), stdDev_(stdDev) {}
Real BlackDeltaPremiumAdjustedMaxStrikeClass::operator()(Real strike) const {
return bdc_.cumD2(strike)*stdDev_ - bdc_.nD2(strike);
}
}
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