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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Thema Consulting SA
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 <ql/exercise.hpp>
#include <ql/pricingengines/barrier/analyticdoublebarrierbinaryengine.hpp>
#include <utility>
using std::fabs;
namespace QuantLib {
// number of iterations ...
static Real PI= 3.14159265358979323846264338327950;
// calc helper object
class AnalyticDoubleBarrierBinaryEngine_helper
{
public:
AnalyticDoubleBarrierBinaryEngine_helper(
const ext::shared_ptr<GeneralizedBlackScholesProcess>& process,
const ext::shared_ptr<CashOrNothingPayoff> &payoff,
const DoubleBarrierOption::arguments &arguments):
process_(process),
payoff_(payoff),
arguments_(arguments)
{
}
Real payoffAtExpiry(Real spot, Real variance,
DoubleBarrier::Type barrierType,
Size maxIteration = 100,
Real requiredConvergence = 1e-8);
Real payoffKIKO(Real spot, Real variance,
DoubleBarrier::Type barrierType,
Size maxIteration = 1000,
Real requiredConvergence = 1e-8);
private:
const ext::shared_ptr<GeneralizedBlackScholesProcess>& process_;
const ext::shared_ptr<CashOrNothingPayoff> &payoff_;
const DoubleBarrierOption::arguments &arguments_;
};
// helper object methods
Real AnalyticDoubleBarrierBinaryEngine_helper::payoffAtExpiry(
Real spot, Real variance, DoubleBarrier::Type barrierType,
Size maxIteration, Real requiredConvergence)
{
QL_REQUIRE(spot>0.0,
"positive spot value required");
QL_REQUIRE(variance>=0.0,
"negative variance not allowed");
Time residualTime = process_->time(arguments_.exercise->lastDate());
QL_REQUIRE(residualTime>0.0,
"expiration time must be > 0");
// Option::Type type = payoff_->optionType(); // this is not used ?
Real cash = payoff_->cashPayoff();
Real barrier_lo = arguments_.barrier_lo;
Real barrier_hi = arguments_.barrier_hi;
Real sigmaq = variance/residualTime;
Real r = process_->riskFreeRate()->zeroRate(residualTime, Continuous,
NoFrequency);
Real q = process_->dividendYield()->zeroRate(residualTime,
Continuous, NoFrequency);
Real b = r - q;
Real alpha = -0.5 * ( 2*b/sigmaq - 1);
Real beta = -0.25 * std::pow(( 2*b/sigmaq - 1), 2) - 2 * r/sigmaq;
Real Z = std::log(barrier_hi / barrier_lo);
Real factor = ((2*PI*cash)/std::pow(Z,2)); // common factor
Real lo_alpha = std::pow(spot/barrier_lo, alpha);
Real hi_alpha = std::pow(spot/barrier_hi, alpha);
Real tot = 0, term = 0;
for (Size i = 1 ; i < maxIteration ; ++i)
{
Real term1 = (lo_alpha-std::pow(-1.0, (int)i)*hi_alpha) /
(std::pow(alpha,2)+std::pow(i*PI/Z, 2));
Real term2 = std::sin(i*PI/Z * std::log(spot/barrier_lo));
Real term3 = std::exp(-0.5*(std::pow(i*PI/Z,2)-beta)*variance);
term = factor * i * term1 * term2 * term3;
tot += term;
}
// Check if convergence is sufficiently fast (for extreme parameters with big alpha the convergence can be very
// poor, see for example Hui "One-touch double barrier binary option value")
QL_REQUIRE(std::fabs(term) < requiredConvergence, "serie did not converge sufficiently fast");
if (barrierType == DoubleBarrier::KnockOut)
return std::max(tot, 0.0); // KO
else {
Rate discount = process_->riskFreeRate()->discount(
arguments_.exercise->lastDate());
QL_REQUIRE(discount>0.0,
"positive discount required");
return std::max(cash * discount - tot, 0.0); // KI
}
}
// helper object methods
Real AnalyticDoubleBarrierBinaryEngine_helper::payoffKIKO(
Real spot, Real variance, DoubleBarrier::Type barrierType,
Size maxIteration, Real requiredConvergence)
{
QL_REQUIRE(spot>0.0,
"positive spot value required");
QL_REQUIRE(variance>=0.0,
"negative variance not allowed");
Time residualTime = process_->time(arguments_.exercise->lastDate());
QL_REQUIRE(residualTime>0.0,
"expiration time must be > 0");
Real cash = payoff_->cashPayoff();
Real barrier_lo = arguments_.barrier_lo;
Real barrier_hi = arguments_.barrier_hi;
if (barrierType == DoubleBarrier::KOKI)
std::swap(barrier_lo, barrier_hi);
Real sigmaq = variance/residualTime;
Real r = process_->riskFreeRate()->zeroRate(residualTime, Continuous,
NoFrequency);
Real q = process_->dividendYield()->zeroRate(residualTime,
Continuous, NoFrequency);
Real b = r - q;
Real alpha = -0.5 * ( 2*b/sigmaq - 1);
Real beta = -0.25 * std::pow(( 2*b/sigmaq - 1), 2) - 2 * r/sigmaq;
Real Z = std::log(barrier_hi / barrier_lo);
Real log_S_L = std::log(spot / barrier_lo);
Real tot = 0, term = 0;
for (Size i = 1 ; i < maxIteration ; ++i)
{
Real factor = std::pow(i*PI/Z,2)-beta;
Real term1 = (beta - std::pow(i*PI/Z,2) * std::exp(-0.5*factor*variance)) / factor;
Real term2 = std::sin(i * PI/Z * log_S_L);
term = (2.0/(i*PI)) * term1 * term2;
tot += term;
}
tot += 1 - log_S_L / Z;
tot *= cash*std::pow(spot/barrier_lo, alpha);
// Check if convergence is sufficiently fast
QL_REQUIRE(fabs(term) < requiredConvergence, "serie did not converge sufficiently fast");
return std::max(tot, 0.0);
}
AnalyticDoubleBarrierBinaryEngine::AnalyticDoubleBarrierBinaryEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process)
: process_(std::move(process)) {
registerWith(process_);
}
void AnalyticDoubleBarrierBinaryEngine::calculate() const {
if (arguments_.barrierType == DoubleBarrier::KIKO ||
arguments_.barrierType == DoubleBarrier::KOKI) {
ext::shared_ptr<AmericanExercise> ex =
ext::dynamic_pointer_cast<AmericanExercise>(
arguments_.exercise);
QL_REQUIRE(ex, "KIKO/KOKI options must have American exercise");
QL_REQUIRE(ex->dates()[0] <=
process_->blackVolatility()->referenceDate(),
"American option with window exercise not handled yet");
} else {
ext::shared_ptr<EuropeanExercise> ex =
ext::dynamic_pointer_cast<EuropeanExercise>(
arguments_.exercise);
QL_REQUIRE(ex, "non-European exercise given");
}
ext::shared_ptr<CashOrNothingPayoff> payoff =
ext::dynamic_pointer_cast<CashOrNothingPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "a cash-or-nothing payoff must be given");
Real spot = process_->stateVariable()->value();
QL_REQUIRE(spot > 0.0, "negative or null underlying given");
Real variance =
process_->blackVolatility()->blackVariance(
arguments_.exercise->lastDate(),
payoff->strike());
Real barrier_lo = arguments_.barrier_lo;
Real barrier_hi = arguments_.barrier_hi;
DoubleBarrier::Type barrierType = arguments_.barrierType;
QL_REQUIRE(barrier_lo>0.0,
"positive low barrier value required");
QL_REQUIRE(barrier_hi>0.0,
"positive high barrier value required");
QL_REQUIRE(barrier_lo < barrier_hi,
"barrier_lo must be < barrier_hi");
QL_REQUIRE(barrierType == DoubleBarrier::KnockIn ||
barrierType == DoubleBarrier::KnockOut ||
barrierType == DoubleBarrier::KIKO ||
barrierType == DoubleBarrier::KOKI,
"Unsupported barrier type");
// degenerate cases
switch (barrierType) {
case DoubleBarrier::KnockOut:
if (spot <= barrier_lo || spot >= barrier_hi) {
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
case DoubleBarrier::KnockIn:
if (spot <= barrier_lo || spot >= barrier_hi) {
// knocked in - pays
results_.value = payoff->cashPayoff();
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
case DoubleBarrier::KIKO:
if (spot >= barrier_hi) {
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
} else if (spot <= barrier_lo) {
// knocked in, pays
results_.value = payoff->cashPayoff();
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
case DoubleBarrier::KOKI:
if (spot <= barrier_lo) {
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
} else if (spot >= barrier_hi) {
// knocked in, pays
results_.value = payoff->cashPayoff();
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
}
AnalyticDoubleBarrierBinaryEngine_helper helper(process_,
payoff, arguments_);
switch (barrierType)
{
case DoubleBarrier::KnockOut:
case DoubleBarrier::KnockIn:
results_.value = helper.payoffAtExpiry(spot, variance, barrierType);
break;
case DoubleBarrier::KIKO:
case DoubleBarrier::KOKI:
results_.value = helper.payoffKIKO(spot, variance, barrierType);
break;
}
}
}
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