/usr/include/ql/experimental/barrieroption/vannavolgadoublebarrierengine.hpp is in libquantlib0-dev 1.7.1-1.
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/*
Copyright (C) 2013 Yue Tian
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.
*/
/*! \file vannavolgadoublebarrierengine.hpp
\brief Vanna/Volga double-barrier option engine
*/
#ifndef quantlib_vanna_volga_double_barrier_engine_hpp
#define quantlib_vanna_volga_double_barrier_engine_hpp
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/experimental/barrieroption/doublebarrieroption.hpp>
#include <ql/experimental/barrieroption/vannavolgainterpolation.hpp>
#include <ql/experimental/fx/deltavolquote.hpp>
#include <ql/experimental/fx/blackdeltacalculator.hpp>
#include <ql/pricingengines/barrier/analyticbarrierengine.hpp>
#include <ql/math/matrix.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/time/calendars/all.hpp>
namespace QuantLib {
//! Vanna Volga double-barrier option engine
/*!
\ingroup barrierengines
*/
template <class DoubleBarrierEngine>
class VannaVolgaDoubleBarrierEngine
: public GenericEngine<DoubleBarrierOption::arguments,
DoubleBarrierOption::results> {
public:
// Constructor
VannaVolgaDoubleBarrierEngine(
const Handle<DeltaVolQuote> atmVol,
const Handle<DeltaVolQuote> vol25Put,
const Handle<DeltaVolQuote> vol25Call,
const Handle<Quote> spotFX,
const Handle<YieldTermStructure> domesticTS,
const Handle<YieldTermStructure> foreignTS,
const bool adaptVanDelta = false,
const Real bsPriceWithSmile = 0.0,
int series = 5
)
: GenericEngine<DoubleBarrierOption::arguments,
DoubleBarrierOption::results>(),
atmVol_(atmVol), vol25Put_(vol25Put), vol25Call_(vol25Call), T_(atmVol_->maturity()),
spotFX_(spotFX), domesticTS_(domesticTS), foreignTS_(foreignTS),
adaptVanDelta_(adaptVanDelta), bsPriceWithSmile_(bsPriceWithSmile),
series_(series){
QL_REQUIRE(vol25Put_->delta() == -0.25, "25 delta put is required by vanna volga method");
QL_REQUIRE(vol25Call_->delta() == 0.25, "25 delta call is required by vanna volga method");
QL_REQUIRE(vol25Put_->maturity() == vol25Call_->maturity() && vol25Put_->maturity() == atmVol_->maturity(),
"Maturity of 3 vols are not the same");
QL_REQUIRE(!domesticTS_.empty(), "domestic yield curve is not defined");
QL_REQUIRE(!foreignTS_.empty(), "foreign yield curve is not defined");
registerWith(atmVol_);
registerWith(vol25Put_);
registerWith(vol25Call_);
registerWith(spotFX_);
registerWith(domesticTS_);
registerWith(foreignTS_);
}
virtual void calculate() const {
using std::sqrt;
const Real sigmaShift_vega = 0.001;
const Real sigmaShift_volga = 0.0001;
const Real spotShift_delta = 0.0001 * spotFX_->value();
const Real sigmaShift_vanna = 0.0001;
QL_REQUIRE(arguments_.barrierType==DoubleBarrier::KnockIn ||
arguments_.barrierType==DoubleBarrier::KnockOut,
"Only same type barrier supported");
Handle<Quote> x0Quote( //used for shift
boost::make_shared<SimpleQuote>(spotFX_->value()));
Handle<Quote> atmVolQuote( //used for shift
boost::make_shared<SimpleQuote>(atmVol_->value()));
boost::shared_ptr<BlackVolTermStructure> blackVolTS =
boost::make_shared<BlackConstantVol>(
Settings::instance().evaluationDate(),
NullCalendar(), atmVolQuote, Actual365Fixed());
boost::shared_ptr<BlackScholesMertonProcess> stochProcess =
boost::make_shared<BlackScholesMertonProcess>(
x0Quote,
foreignTS_,
domesticTS_,
Handle<BlackVolTermStructure>(blackVolTS));
boost::shared_ptr<PricingEngine> engineBS =
boost::make_shared<DoubleBarrierEngine>(stochProcess,
series_);
BlackDeltaCalculator blackDeltaCalculatorAtm(
Option::Call, atmVol_->deltaType(), x0Quote->value(),
domesticTS_->discount(T_), foreignTS_->discount(T_),
atmVol_->value() * sqrt(T_));
Real atmStrike = blackDeltaCalculatorAtm.atmStrike(atmVol_->atmType());
Real call25Vol = vol25Call_->value();
Real put25Vol = vol25Put_->value();
BlackDeltaCalculator blackDeltaCalculatorPut25(
Option::Put, vol25Put_->deltaType(), x0Quote->value(),
domesticTS_->discount(T_), foreignTS_->discount(T_),
put25Vol * sqrt(T_));
Real put25Strike = blackDeltaCalculatorPut25.strikeFromDelta(-0.25);
BlackDeltaCalculator blackDeltaCalculatorCall25(
Option::Call, vol25Call_->deltaType(), x0Quote->value(),
domesticTS_->discount(T_), foreignTS_->discount(T_),
call25Vol * sqrt(T_));
Real call25Strike = blackDeltaCalculatorCall25.strikeFromDelta(0.25);
//here use vanna volga interpolated smile to price vanilla
std::vector<Real> strikes;
std::vector<Real> vols;
strikes.push_back(put25Strike);
vols.push_back(put25Vol);
strikes.push_back(atmStrike);
vols.push_back(atmVol_->value());
strikes.push_back(call25Strike);
vols.push_back(call25Vol);
VannaVolga vannaVolga(x0Quote->value(), foreignTS_->discount(T_), foreignTS_->discount(T_), T_);
Interpolation interpolation = vannaVolga.interpolate(strikes.begin(), strikes.end(), vols.begin());
interpolation.enableExtrapolation();
const boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
Real strikeVol = interpolation(payoff->strike());
//vannila option price
Real vanillaOption = blackFormula(payoff->optionType(), payoff->strike(),
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
strikeVol * sqrt(T_),
domesticTS_->discount(T_));
//already out
if((x0Quote->value() > arguments_.barrier_hi || x0Quote->value() < arguments_.barrier_lo)
&& arguments_.barrierType == DoubleBarrier::KnockOut){
results_.value = 0.0;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
//already in
else if((x0Quote->value() > arguments_.barrier_hi || x0Quote->value() < arguments_.barrier_lo)
&& arguments_.barrierType == DoubleBarrier::KnockIn){
results_.value = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
else{
//set up BS barrier option pricing
//only calculate out barrier option price
// in barrier price = vanilla - out barrier
boost::shared_ptr<StrikedTypePayoff> payoff
= boost::static_pointer_cast<StrikedTypePayoff> (arguments_.payoff);
DoubleBarrierOption doubleBarrierOption(arguments_.barrierType,
arguments_.barrier_lo,
arguments_.barrier_hi,
arguments_.rebate,
payoff,
arguments_.exercise);
doubleBarrierOption.setPricingEngine(engineBS);
//BS price
Real priceBS = doubleBarrierOption.NPV();
Real priceAtmCallBS = blackFormula(Option::Call,atmStrike,
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
atmVol_->value() * sqrt(T_),
domesticTS_->discount(T_));
Real price25CallBS = blackFormula(Option::Call,call25Strike,
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
atmVol_->value() * sqrt(T_),
domesticTS_->discount(T_));
Real price25PutBS = blackFormula(Option::Put,put25Strike,
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
atmVol_->value() * sqrt(T_),
domesticTS_->discount(T_));
//market price
Real priceAtmCallMkt = blackFormula(Option::Call,atmStrike,
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
atmVol_->value() * sqrt(T_),
domesticTS_->discount(T_));
Real price25CallMkt = blackFormula(Option::Call,call25Strike,
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
call25Vol * sqrt(T_),
domesticTS_->discount(T_));
Real price25PutMkt = blackFormula(Option::Put,put25Strike,
x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_),
put25Vol * sqrt(T_),
domesticTS_->discount(T_));
//Analytical Black Scholes formula
NormalDistribution norm;
Real d1atm = (std::log(x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_)/atmStrike)
+ 0.5*std::pow(atmVolQuote->value(),2.0) * T_)/(atmVolQuote->value() * sqrt(T_));
Real vegaAtm_Analytical = x0Quote->value() * norm(d1atm) * sqrt(T_) * foreignTS_->discount(T_);
Real vannaAtm_Analytical = vegaAtm_Analytical/x0Quote->value() *(1.0 - d1atm/(atmVolQuote->value()*sqrt(T_)));
Real volgaAtm_Analytical = vegaAtm_Analytical * d1atm * (d1atm - atmVolQuote->value() * sqrt(T_))/atmVolQuote->value();
Real d125call = (std::log(x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_)/call25Strike)
+ 0.5*std::pow(atmVolQuote->value(),2.0) * T_)/(atmVolQuote->value() * sqrt(T_));
Real vega25Call_Analytical = x0Quote->value() * norm(d125call) * sqrt(T_) * foreignTS_->discount(T_);
Real vanna25Call_Analytical = vega25Call_Analytical/x0Quote->value() *(1.0 - d125call/(atmVolQuote->value()*sqrt(T_)));
Real volga25Call_Analytical = vega25Call_Analytical * d125call * (d125call - atmVolQuote->value() * sqrt(T_))/atmVolQuote->value();
Real d125Put = (std::log(x0Quote->value()* foreignTS_->discount(T_)/ domesticTS_->discount(T_)/put25Strike)
+ 0.5*std::pow(atmVolQuote->value(),2.0) * T_)/(atmVolQuote->value() * sqrt(T_));
Real vega25Put_Analytical = x0Quote->value() * norm(d125Put) * sqrt(T_) * foreignTS_->discount(T_);
Real vanna25Put_Analytical = vega25Put_Analytical/x0Quote->value() *(1.0 - d125Put/(atmVolQuote->value()*sqrt(T_)));
Real volga25Put_Analytical = vega25Put_Analytical * d125Put * (d125Put - atmVolQuote->value() * sqrt(T_))/atmVolQuote->value();
//BS vega
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_vega);
doubleBarrierOption.recalculate();
Real vegaBarBS = (doubleBarrierOption.NPV() - priceBS)/sigmaShift_vega;
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() - sigmaShift_vega);//setback
//BS volga
//vegaBar2
//base NPV
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_volga);
doubleBarrierOption.recalculate();
Real priceBS2 = doubleBarrierOption.NPV();
//shifted npv
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_vega);
doubleBarrierOption.recalculate();
Real vegaBarBS2 = (doubleBarrierOption.NPV() - priceBS2)/sigmaShift_vega;
Real volgaBarBS = (vegaBarBS2 - vegaBarBS)/sigmaShift_volga;
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value()
- sigmaShift_volga
- sigmaShift_vega);//setback
//BS Delta
//base delta
boost::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() + spotShift_delta);//shift forth
doubleBarrierOption.recalculate();
Real priceBS_delta1 = doubleBarrierOption.NPV();
boost::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() - 2 * spotShift_delta);//shift back
doubleBarrierOption.recalculate();
Real priceBS_delta2 = doubleBarrierOption.NPV();
boost::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() + spotShift_delta);//set back
Real deltaBar1 = (priceBS_delta1 - priceBS_delta2)/(2.0*spotShift_delta);
//shifted vanna
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_vanna);//shift sigma
//shifted delta
boost::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() + spotShift_delta);//shift forth
doubleBarrierOption.recalculate();
priceBS_delta1 = doubleBarrierOption.NPV();
boost::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() - 2 * spotShift_delta);//shift back
doubleBarrierOption.recalculate();
priceBS_delta2 = doubleBarrierOption.NPV();
boost::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() + spotShift_delta);//set back
Real deltaBar2 = (priceBS_delta1 - priceBS_delta2)/(2.0*spotShift_delta);
Real vannaBarBS = (deltaBar2 - deltaBar1)/sigmaShift_vanna;
boost::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() - sigmaShift_vanna);//set back
//Matrix
Matrix A(3,3,0.0);
//analytical
A[0][0] = vegaAtm_Analytical;
A[0][1] = vega25Call_Analytical;
A[0][2] = vega25Put_Analytical;
A[1][0] = vannaAtm_Analytical;
A[1][1] = vanna25Call_Analytical;
A[1][2] = vanna25Put_Analytical;
A[2][0] = volgaAtm_Analytical;
A[2][1] = volga25Call_Analytical;
A[2][2] = volga25Put_Analytical;
Array b(3,0.0);
b[0] = vegaBarBS;
b[1] = vannaBarBS;
b[2] = volgaBarBS;
Array q = inverse(A) * b;
Real H = arguments_.barrier_hi;
Real L = arguments_.barrier_lo;
Real theta_tilt_minus = ((domesticTS_->zeroRate(T_, Continuous) - foreignTS_->zeroRate(T_, Continuous))/atmVol_->value() - atmVol_->value()/2.0)*std::sqrt(T_);
Real h = 1.0/atmVol_->value() * std::log(H/x0Quote->value())/std::sqrt(T_);
Real l = 1.0/atmVol_->value() * std::log(L/x0Quote->value())/std::sqrt(T_);
CumulativeNormalDistribution cnd;
Real doubleNoTouch = 0.0;
for(int j = -series_; j< series_;j++ ){
Real e_minus = 2*j*(h-l) - theta_tilt_minus;
doubleNoTouch += std::exp(-2.0*j*theta_tilt_minus*(h-l))*(cnd(h+e_minus) - cnd(l+e_minus))
- std::exp(-2.0*j*theta_tilt_minus*(h-l)+2.0*theta_tilt_minus*h)*(cnd(h-2.0*h+e_minus) - cnd(l-2.0*h+e_minus));
}
Real p_survival = doubleNoTouch;
Real lambda = p_survival ;
Real adjust = q[0]*(priceAtmCallMkt - priceAtmCallBS)
+ q[1]*(price25CallMkt - price25CallBS)
+ q[2]*(price25PutMkt - price25PutBS);
Real outPrice = priceBS + lambda*adjust;//
Real inPrice;
//adapt Vanilla delta
if(adaptVanDelta_ == true){
outPrice += lambda*(bsPriceWithSmile_ - vanillaOption);
//capfloored by (0, vanilla)
outPrice = std::max(0.0, std::min(bsPriceWithSmile_, outPrice));
inPrice = bsPriceWithSmile_ - outPrice;
}
else{
//capfloored by (0, vanilla)
outPrice = std::max(0.0, std::min(vanillaOption , outPrice));
inPrice = vanillaOption - outPrice;
}
if(arguments_.barrierType == DoubleBarrier::KnockOut)
results_.value = outPrice;
else
results_.value = inPrice;
results_.additionalResults["VanillaPrice"] = vanillaOption;
results_.additionalResults["BarrierInPrice"] = inPrice;
results_.additionalResults["BarrierOutPrice"] = outPrice;
results_.additionalResults["lambda"] = lambda;
}
}
private:
const Handle<DeltaVolQuote> atmVol_;
const Handle<DeltaVolQuote> vol25Put_;
const Handle<DeltaVolQuote> vol25Call_;
const Time T_;
const Handle<Quote> spotFX_;
const Handle<YieldTermStructure> domesticTS_;
const Handle<YieldTermStructure> foreignTS_;
const bool adaptVanDelta_;
const Real bsPriceWithSmile_;
const int series_;
};
}
#endif
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