1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Warren Chou
Copyright (C) 2007 StatPro Italia srl
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/pricingengines/lookback/analyticcontinuousfloatinglookback.hpp>
#include <ql/exercise.hpp>
namespace QuantLib {
AnalyticContinuousFloatingLookbackEngine::
AnalyticContinuousFloatingLookbackEngine(
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process)
: process_(process) {
registerWith(process_);
}
void AnalyticContinuousFloatingLookbackEngine::calculate() const {
boost::shared_ptr<FloatingTypePayoff> payoff =
boost::dynamic_pointer_cast<FloatingTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "Non-floating payoff given");
QL_REQUIRE(process_->x0() > 0.0, "negative or null underlying");
switch (payoff->optionType()) {
case Option::Call:
results_.value = A(1);
break;
case Option::Put:
results_.value = A(-1);
break;
default:
QL_FAIL("Unknown type");
}
}
Real AnalyticContinuousFloatingLookbackEngine::underlying() const {
return process_->x0();
}
Time AnalyticContinuousFloatingLookbackEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Volatility AnalyticContinuousFloatingLookbackEngine::volatility() const {
return process_->blackVolatility()->blackVol(residualTime(), minmax());
}
Real AnalyticContinuousFloatingLookbackEngine::stdDeviation() const {
return volatility() * std::sqrt(residualTime());
}
Rate AnalyticContinuousFloatingLookbackEngine::riskFreeRate() const {
return process_->riskFreeRate()->zeroRate(residualTime(), Continuous,
NoFrequency);
}
DiscountFactor AnalyticContinuousFloatingLookbackEngine::riskFreeDiscount()
const {
return process_->riskFreeRate()->discount(residualTime());
}
Rate AnalyticContinuousFloatingLookbackEngine::dividendYield() const {
return process_->dividendYield()->zeroRate(residualTime(),
Continuous, NoFrequency);
}
DiscountFactor AnalyticContinuousFloatingLookbackEngine::dividendDiscount()
const {
return process_->dividendYield()->discount(residualTime());
}
Real AnalyticContinuousFloatingLookbackEngine::minmax() const {
return arguments_.minmax;
}
Real AnalyticContinuousFloatingLookbackEngine::A(Real eta) const {
Volatility vol = volatility();
Real lambda = 2.0*(riskFreeRate() - dividendYield())/(vol*vol);
Real s = underlying()/minmax();
Real d1 = std::log(s)/stdDeviation() + 0.5*(lambda+1.0)*stdDeviation();
Real n1 = f_(eta*d1);
Real n2 = f_(eta*(d1-stdDeviation()));
Real n3 = f_(eta*(-d1+lambda*stdDeviation()));
Real n4 = f_(eta*-d1);
Real pow_s = std::pow(s, -lambda);
return eta*((underlying() * dividendDiscount() * n1 -
minmax() * riskFreeDiscount() * n2) +
(underlying() * riskFreeDiscount() *
(pow_s * n3 - dividendDiscount()* n4/riskFreeDiscount())/
lambda));
}
}
|
