/src/quantlib/ql/pricingengines/barrier/analytictwoassetbarrierengine.cpp

Source (jump to first uncovered line)
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2012 Master IMAFA - Polytech'Nice Sophia - Université de Nice Sophia Antipolis

 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/exercise.hpp>
#include <ql/pricingengines/barrier/analytictwoassetbarrierengine.hpp>
#include <ql/math/distributions/bivariatenormaldistribution.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <utility>

namespace QuantLib {

    AnalyticTwoAssetBarrierEngine::AnalyticTwoAssetBarrierEngine(
        ext::shared_ptr<GeneralizedBlackScholesProcess> process1,
        ext::shared_ptr<GeneralizedBlackScholesProcess> process2,
        Handle<Quote> rho)
    : process1_(std::move(process1)), process2_(std::move(process2)), rho_(std::move(rho)) {
        registerWith(process1_);
        registerWith(process2_);
        registerWith(rho_);
    }

    void AnalyticTwoAssetBarrierEngine::calculate() const {
        ext::shared_ptr<PlainVanillaPayoff> payoff =
            ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
        QL_REQUIRE(payoff, "non-plain payoff given");
        QL_REQUIRE(payoff->strike()>0.0,"strike must be positive");

        Real spot2 = process2_->x0();
        // option is triggered by S2
        QL_REQUIRE(spot2 > 0.0, "negative or null underlying given");
        QL_REQUIRE(!triggered(spot2), "barrier touched");

        Barrier::Type barrierType = arguments_.barrierType;

        switch (payoff->optionType()) {
          case Option::Call:
            switch (barrierType) {
              case Barrier::DownOut:
                results_.value = A(1,-1) +B(1,-1) ;
                break;
              case Barrier::UpOut:
                results_.value = A(1,1) + B(1,1) ;
                break;
              case Barrier::DownIn:
                results_.value = call()-(A(1,-1) +B(1,-1) );
                break;
              case Barrier::UpIn:
                results_.value = call()-(A(1,1) +B(1,1));
                break;
            }
            break;
          case Option::Put:
            switch (barrierType) {
              case Barrier::DownOut:
                results_.value = A(-1,-1)+B(-1,-1) ;
                break;
              case Barrier::UpOut:
                results_.value = A(-1,1)+B(-1,1) ;
                break;
              case Barrier::DownIn:
                results_.value = put()-(A(-1,-1) +B(-1,-1) );
                break;
              case Barrier::UpIn:
                results_.value = put()-(A(-1,1) +B(-1,1) );
                break;
            }
            break;
          default:
            QL_FAIL("unknown type");
        }
    }

    Real AnalyticTwoAssetBarrierEngine::underlying1() const {
        return process1_->x0();
    }

    Real AnalyticTwoAssetBarrierEngine::underlying2() const {
        return process2_->x0();
    }

    Real AnalyticTwoAssetBarrierEngine::strike() const {
        ext::shared_ptr<PlainVanillaPayoff> payoff =
            ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
        QL_REQUIRE(payoff, "non-plain payoff given");
        return payoff->strike();
    }

    Time AnalyticTwoAssetBarrierEngine::residualTime() const {
        return process1_->time(arguments_.exercise->lastDate());
    }

    Volatility AnalyticTwoAssetBarrierEngine::volatility1() const {
        return process1_->blackVolatility()->blackVol(residualTime(), strike());
    }

    Volatility AnalyticTwoAssetBarrierEngine::volatility2() const {
        return process2_->blackVolatility()->blackVol(residualTime(), strike());
    }

    Real AnalyticTwoAssetBarrierEngine::barrier() const {
        return arguments_.barrier;
    }

    Real AnalyticTwoAssetBarrierEngine::rho() const {
        return rho_->value();
    }

    Rate AnalyticTwoAssetBarrierEngine::riskFreeRate() const {
        return process1_->riskFreeRate()->zeroRate(residualTime(),
                                                   Continuous, NoFrequency);
    }


    Rate AnalyticTwoAssetBarrierEngine::dividendYield1() const {
        return process1_->dividendYield()->zeroRate(residualTime(),
                                                    Continuous, NoFrequency);
    }

    Rate AnalyticTwoAssetBarrierEngine::dividendYield2() const {
        return process2_->dividendYield()->zeroRate(residualTime(),
                                                    Continuous, NoFrequency);
    }

    Rate AnalyticTwoAssetBarrierEngine::costOfCarry1() const {
        return riskFreeRate() - dividendYield1();
    }

    Rate AnalyticTwoAssetBarrierEngine::costOfCarry2() const {
        return riskFreeRate() - dividendYield2();
    }

    Real AnalyticTwoAssetBarrierEngine::d1() const {
        return (std::log(underlying1()/strike())+(mu(costOfCarry1(),volatility1())+volatility1()*volatility1())*residualTime())/
            (volatility1()*std::sqrt(residualTime()));
    }

    Real AnalyticTwoAssetBarrierEngine::d2() const {
        return d1() - volatility1()*std::sqrt(residualTime());
    }

    Real AnalyticTwoAssetBarrierEngine::d3() const {
        return d1()+ (2*rho()*std::log(barrier()/underlying2()))/(volatility2()*std::sqrt(residualTime()));
    }

    Real AnalyticTwoAssetBarrierEngine::d4() const {
        return d2()+ (2*rho()*std::log(barrier()/underlying2()))/(volatility2()*std::sqrt(residualTime()));
    }

    Real AnalyticTwoAssetBarrierEngine::e1() const {
        return (std::log(barrier()/underlying2())-(mu(costOfCarry2(),volatility2())+rho()*volatility1()*volatility2())*residualTime())/
        (volatility2()*std::sqrt(residualTime()));
    }

    Real AnalyticTwoAssetBarrierEngine::e2() const {
         return e1()+rho()*volatility1()*std::sqrt(residualTime());
    }

    Real AnalyticTwoAssetBarrierEngine::e3() const {
            return e1()-(2*std::log(barrier()/underlying2()))/(volatility2()*std::sqrt(residualTime()));
    }

    Real AnalyticTwoAssetBarrierEngine::e4() const {
        return e2()-(2*std::log(barrier()/underlying2()))/(volatility2()*std::sqrt(residualTime()));
    }

    Real AnalyticTwoAssetBarrierEngine::mu(Real b, Real vol) const {
        return b-(vol*vol)/2;
    }

    Real AnalyticTwoAssetBarrierEngine::call() const {
        CumulativeNormalDistribution nd;
        return underlying1()*nd(d1())-strike()*std::exp(-riskFreeRate()*residualTime())*nd(d2());
    }

    Real AnalyticTwoAssetBarrierEngine::put() const {
        CumulativeNormalDistribution nd;
        return strike()*std::exp(-riskFreeRate()*residualTime())*nd(-d2())-underlying1()*nd(-d1());
    }

    Real AnalyticTwoAssetBarrierEngine::A(Real eta, Real phi) const {
        Real S1 = underlying1(), S2 = underlying2();
        Rate b1 = costOfCarry1(), b2 = costOfCarry2();
        Rate r = riskFreeRate();
        Time T = residualTime();
        Real H = barrier(), X = strike();
        Volatility sigma1 = volatility1(), sigma2 = volatility2();
        Real rho = rho_->value();

        Rate mu1 = b1 - sigma1*sigma1/2.0;
        Rate mu2 = b2 - sigma2*sigma2/2.0;

        Real d1 = (std::log(S1/X)+(mu1+sigma1*sigma1)*T)/
            (sigma1*std::sqrt(T));
        Real d2 = d1 - sigma1*std::sqrt(T);
        Real d3 = d1 + (2*rho*std::log(H/S2))/(sigma2*std::sqrt(T));
        Real d4 = d2 + (2*rho*std::log(H/S2))/(sigma2*std::sqrt(T));

        Real e1 = (std::log(H/S2)-(mu2+rho*sigma1*sigma2)*T)/
            (sigma2*std::sqrt(T));
        Real e2 = e1 + rho*sigma1*std::sqrt(T);
        Real e3 = e1 - (2*std::log(H/S2))/(sigma2*std::sqrt(T));
        Real e4 = e2 - (2*std::log(H/S2))/(sigma2*std::sqrt(T));

        Real w =
            eta*S1*std::exp((b1-r)*T) *
            (M(eta*d1, phi*e1,-eta*phi*rho)
             -std::exp((2*(mu2+rho*sigma1*sigma2)*std::log(H/S2))/(sigma2*sigma2))
             *M(eta*d3, phi*e3, -eta*phi*rho))

            - eta*X*std::exp(-r*T) *
            (M(eta*d2, phi*e2, -eta*phi*rho)
             -std::exp((2*mu2*std::log(H/S2))/(sigma2*sigma2))*
             M(eta*d4, phi*e4, -eta*phi*rho) ) ;

        return w;
    }

    Real AnalyticTwoAssetBarrierEngine::B(Real, Real) const {
        return 0.0;
    }

    Real AnalyticTwoAssetBarrierEngine::M(Real m_a, Real m_b, Real rho) const {
        BivariateCumulativeNormalDistributionDr78 f(rho);
        return f(m_a, m_b);
    }

}


Coverage Report

Created: 2025-08-11 06:28

Line	Count	Source (jump to first uncovered line)
1		/* -- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -- */
2
3		/*
4		Copyright (C) 2012 Master IMAFA - Polytech'Nice Sophia - Université de Nice Sophia Antipolis
5
6		This file is part of QuantLib, a free-software/open-source library
7		for financial quantitative analysts and developers - http://quantlib.org/
8
9		QuantLib is free software: you can redistribute it and/or modify it
10		under the terms of the QuantLib license. You should have received a
11		copy of the license along with this program; if not, please email
12		<quantlib-dev@lists.sf.net>. The license is also available online at
13		<http://quantlib.org/license.shtml>.
14
15		This program is distributed in the hope that it will be useful, but WITHOUT
16		ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17		FOR A PARTICULAR PURPOSE. See the license for more details.
18		*/
19
20		#include <ql/exercise.hpp>
21		#include <ql/pricingengines/barrier/analytictwoassetbarrierengine.hpp>
22		#include <ql/math/distributions/bivariatenormaldistribution.hpp>
23		#include <ql/math/distributions/normaldistribution.hpp>
24		#include <utility>
25
26		namespace QuantLib {
27
28		AnalyticTwoAssetBarrierEngine::AnalyticTwoAssetBarrierEngine(
29		ext::shared_ptr<GeneralizedBlackScholesProcess> process1,
30		ext::shared_ptr<GeneralizedBlackScholesProcess> process2,
31		Handle<Quote> rho)
32	0	: process1_(std::move(process1)), process2_(std::move(process2)), rho_(std::move(rho)) {
33	0	registerWith(process1_);
34	0	registerWith(process2_);
35	0	registerWith(rho_);
36	0	}
37
38	0	void AnalyticTwoAssetBarrierEngine::calculate() const {
39	0	ext::shared_ptr<PlainVanillaPayoff> payoff =
40	0	ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
41	0	QL_REQUIRE(payoff, "non-plain payoff given");
42	0	QL_REQUIRE(payoff->strike()>0.0,"strike must be positive");
43
44	0	Real spot2 = process2_->x0();
45		// option is triggered by S2
46	0	QL_REQUIRE(spot2 > 0.0, "negative or null underlying given");
47	0	QL_REQUIRE(!triggered(spot2), "barrier touched");
48
49	0	Barrier::Type barrierType = arguments_.barrierType;
50
51	0	switch (payoff->optionType()) {
52	0	case Option::Call:
53	0	switch (barrierType) {
54	0	case Barrier::DownOut:
55	0	results_.value = A(1,-1) +B(1,-1) ;
56	0	break;
57	0	case Barrier::UpOut:
58	0	results_.value = A(1,1) + B(1,1) ;
59	0	break;
60	0	case Barrier::DownIn:
61	0	results_.value = call()-(A(1,-1) +B(1,-1) );
62	0	break;
63	0	case Barrier::UpIn:
64	0	results_.value = call()-(A(1,1) +B(1,1));
65	0	break;
66	0	}
67	0	break;
68	0	case Option::Put:
69	0	switch (barrierType) {
70	0	case Barrier::DownOut:
71	0	results_.value = A(-1,-1)+B(-1,-1) ;
72	0	break;
73	0	case Barrier::UpOut:
74	0	results_.value = A(-1,1)+B(-1,1) ;
75	0	break;
76	0	case Barrier::DownIn:
77	0	results_.value = put()-(A(-1,-1) +B(-1,-1) );
78	0	break;
79	0	case Barrier::UpIn:
80	0	results_.value = put()-(A(-1,1) +B(-1,1) );
81	0	break;
82	0	}
83	0	break;
84	0	default:
85	0	QL_FAIL("unknown type");
86	0	}
87	0	}
88
89	0	Real AnalyticTwoAssetBarrierEngine::underlying1() const {
90	0	return process1_->x0();
91	0	}
92
93	0	Real AnalyticTwoAssetBarrierEngine::underlying2() const {
94	0	return process2_->x0();
95	0	}
96
97	0	Real AnalyticTwoAssetBarrierEngine::strike() const {
98	0	ext::shared_ptr<PlainVanillaPayoff> payoff =
99	0	ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
100	0	QL_REQUIRE(payoff, "non-plain payoff given");
101	0	return payoff->strike();
102	0	}
103
104	0	Time AnalyticTwoAssetBarrierEngine::residualTime() const {
105	0	return process1_->time(arguments_.exercise->lastDate());
106	0	}
107
108	0	Volatility AnalyticTwoAssetBarrierEngine::volatility1() const {
109	0	return process1_->blackVolatility()->blackVol(residualTime(), strike());
110	0	}
111
112	0	Volatility AnalyticTwoAssetBarrierEngine::volatility2() const {
113	0	return process2_->blackVolatility()->blackVol(residualTime(), strike());
114	0	}
115
116	0	Real AnalyticTwoAssetBarrierEngine::barrier() const {
117	0	return arguments_.barrier;
118	0	}
119
120	0	Real AnalyticTwoAssetBarrierEngine::rho() const {
121	0	return rho_->value();
122	0	}
123
124	0	Rate AnalyticTwoAssetBarrierEngine::riskFreeRate() const {
125	0	return process1_->riskFreeRate()->zeroRate(residualTime(),
126	0	Continuous, NoFrequency);
127	0	}
128
129
130	0	Rate AnalyticTwoAssetBarrierEngine::dividendYield1() const {
131	0	return process1_->dividendYield()->zeroRate(residualTime(),
132	0	Continuous, NoFrequency);
133	0	}
134
135	0	Rate AnalyticTwoAssetBarrierEngine::dividendYield2() const {
136	0	return process2_->dividendYield()->zeroRate(residualTime(),
137	0	Continuous, NoFrequency);
138	0	}
139
140	0	Rate AnalyticTwoAssetBarrierEngine::costOfCarry1() const {
141	0	return riskFreeRate() - dividendYield1();
142	0	}
143
144	0	Rate AnalyticTwoAssetBarrierEngine::costOfCarry2() const {
145	0	return riskFreeRate() - dividendYield2();
146	0	}
147
148	0	Real AnalyticTwoAssetBarrierEngine::d1() const {
149	0	return (std::log(underlying1()/strike())+(mu(costOfCarry1(),volatility1())+volatility1()volatility1())residualTime())/
150	0	(volatility1()*std::sqrt(residualTime()));
151	0	}
152
153	0	Real AnalyticTwoAssetBarrierEngine::d2() const {
154	0	return d1() - volatility1()*std::sqrt(residualTime());
155	0	}
156
157	0	Real AnalyticTwoAssetBarrierEngine::d3() const {
158	0	return d1()+ (2rho()std::log(barrier()/underlying2()))/(volatility2()*std::sqrt(residualTime()));
159	0	}
160
161	0	Real AnalyticTwoAssetBarrierEngine::d4() const {
162	0	return d2()+ (2rho()std::log(barrier()/underlying2()))/(volatility2()*std::sqrt(residualTime()));
163	0	}
164
165	0	Real AnalyticTwoAssetBarrierEngine::e1() const {
166	0	return (std::log(barrier()/underlying2())-(mu(costOfCarry2(),volatility2())+rho()volatility1()volatility2())*residualTime())/
167	0	(volatility2()*std::sqrt(residualTime()));
168	0	}
169
170	0	Real AnalyticTwoAssetBarrierEngine::e2() const {
171	0	return e1()+rho()volatility1()std::sqrt(residualTime());
172	0	}
173
174	0	Real AnalyticTwoAssetBarrierEngine::e3() const {
175	0	return e1()-(2std::log(barrier()/underlying2()))/(volatility2()std::sqrt(residualTime()));
176	0	}
177
178	0	Real AnalyticTwoAssetBarrierEngine::e4() const {
179	0	return e2()-(2std::log(barrier()/underlying2()))/(volatility2()std::sqrt(residualTime()));
180	0	}
181
182	0	Real AnalyticTwoAssetBarrierEngine::mu(Real b, Real vol) const {
183	0	return b-(vol*vol)/2;
184	0	}
185
186	0	Real AnalyticTwoAssetBarrierEngine::call() const {
187	0	CumulativeNormalDistribution nd;
188	0	return underlying1()nd(d1())-strike()std::exp(-riskFreeRate()residualTime())nd(d2());
189	0	}
190
191	0	Real AnalyticTwoAssetBarrierEngine::put() const {
192	0	CumulativeNormalDistribution nd;
193	0	return strike()std::exp(-riskFreeRate()residualTime())nd(-d2())-underlying1()nd(-d1());
194	0	}
195
196	0	Real AnalyticTwoAssetBarrierEngine::A(Real eta, Real phi) const {
197	0	Real S1 = underlying1(), S2 = underlying2();
198	0	Rate b1 = costOfCarry1(), b2 = costOfCarry2();
199	0	Rate r = riskFreeRate();
200	0	Time T = residualTime();
201	0	Real H = barrier(), X = strike();
202	0	Volatility sigma1 = volatility1(), sigma2 = volatility2();
203	0	Real rho = rho_->value();
204
205	0	Rate mu1 = b1 - sigma1*sigma1/2.0;
206	0	Rate mu2 = b2 - sigma2*sigma2/2.0;
207
208	0	Real d1 = (std::log(S1/X)+(mu1+sigma1sigma1)T)/
209	0	(sigma1*std::sqrt(T));
210	0	Real d2 = d1 - sigma1*std::sqrt(T);
211	0	Real d3 = d1 + (2rhostd::log(H/S2))/(sigma2*std::sqrt(T));
212	0	Real d4 = d2 + (2rhostd::log(H/S2))/(sigma2*std::sqrt(T));
213
214	0	Real e1 = (std::log(H/S2)-(mu2+rhosigma1sigma2)*T)/
215	0	(sigma2*std::sqrt(T));
216	0	Real e2 = e1 + rhosigma1std::sqrt(T);
217	0	Real e3 = e1 - (2std::log(H/S2))/(sigma2std::sqrt(T));
218	0	Real e4 = e2 - (2std::log(H/S2))/(sigma2std::sqrt(T));
219
220	0	Real w =
221	0	etaS1std::exp((b1-r)T)
222	0	(M(etad1, phie1,-etaphirho)
223	0	-std::exp((2(mu2+rhosigma1sigma2)std::log(H/S2))/(sigma2*sigma2))
224	0	M(etad3, phie3, -etaphi*rho))
225
226	0	- etaXstd::exp(-rT)
227	0	(M(etad2, phie2, -etaphirho)
228	0	-std::exp((2mu2std::log(H/S2))/(sigma2sigma2))
229	0	M(etad4, phie4, -etaphirho) ) ;
230
231	0	return w;
232	0	}
233
234	0	Real AnalyticTwoAssetBarrierEngine::B(Real, Real) const {
235	0	return 0.0;
236	0	}
237
238	0	Real AnalyticTwoAssetBarrierEngine::M(Real m_a, Real m_b, Real rho) const {
239	0	BivariateCumulativeNormalDistributionDr78 f(rho);
240	0	return f(m_a, m_b);
241	0	}
242
243		}
244