1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
5 Copyright (C) 2007 StatPro Italia srl
6
7 This file is part of QuantLib, a free-software/open-source library
8 for financial quantitative analysts and developers - http://quantlib.org/
9
10 QuantLib is free software: you can redistribute it and/or modify it
11 under the terms of the QuantLib license. You should have received a
12 copy of the license along with this program; if not, please email
13 <quantlib-dev@lists.sf.net>. The license is also available online at
14 <http://quantlib.org/license.shtml>.
15
16 This program is distributed in the hope that it will be useful, but WITHOUT
17 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
18 FOR A PARTICULAR PURPOSE. See the license for more details.
19*/
20
21#include <ql/models/shortrate/onefactormodels/vasicek.hpp>
22#include <ql/pricingengines/blackformula.hpp>
23
24namespace QuantLib {
25
26 Vasicek::Vasicek(Rate r0, Real a, Real b, Real sigma, Real lambda)
27 : OneFactorAffineModel(4), r0_(r0),
28 a_(arguments_[0]), b_(arguments_[1]), sigma_(arguments_[2]),
29 lambda_(arguments_[3]) {
30 a_ = ConstantParameter(a, PositiveConstraint());
31 b_ = ConstantParameter(b, NoConstraint());
32 sigma_ = ConstantParameter(sigma, PositiveConstraint());
33 lambda_ = ConstantParameter(lambda, NoConstraint());
34 }
35
36 Real Vasicek::A(Time t, Time T) const {
37 Real _a = a();
38 if (_a < std::sqrt(QL_EPSILON)) {
39 return 0.0;
40 } else {
41 Real sigma2 = sigma()*sigma();
42 Real bt = B(t, T);
43 return std::exp(x: (b() + lambda()*sigma()/_a
44 - 0.5*sigma2/(_a*_a))*(bt - (T - t))
45 - 0.25*sigma2*bt*bt/_a);
46 }
47 }
48
49 Real Vasicek::B(Time t, Time T) const {
50 Real _a = a();
51 if (_a < std::sqrt(QL_EPSILON))
52 return (T - t);
53 else
54 return (1.0 - std::exp(x: -_a*(T - t)))/_a;
55 }
56
57 Real Vasicek::discountBondOption(Option::Type type,
58 Real strike, Time maturity,
59 Time bondMaturity) const {
60
61 Real v;
62 Real _a = a();
63 if (std::fabs(x: maturity) < QL_EPSILON) {
64 v = 0.0;
65 } else if (_a < std::sqrt(QL_EPSILON)) {
66 v = sigma()*B(t: maturity, T: bondMaturity)* std::sqrt(x: maturity);
67 } else {
68 v = sigma()*B(t: maturity, T: bondMaturity)*
69 std::sqrt(x: 0.5*(1.0 - std::exp(x: -2.0*_a*maturity))/_a);
70 }
71 Real f = discountBond(now: 0.0, maturity: bondMaturity, rate: r0_);
72 Real k = discountBond(now: 0.0, maturity, rate: r0_)*strike;
73
74 return blackFormula(optionType: type, strike: k, forward: f, stdDev: v);
75 }
76
77}
78
79

source code of quantlib/ql/models/shortrate/onefactormodels/vasicek.cpp