| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2013 Peter Caspers |
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| 5 | |
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| 6 | This file is part of QuantLib, a free-software/open-source library |
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| 7 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 8 | |
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| 9 | QuantLib is free software: you can redistribute it and/or modify it |
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| 10 | under the terms of the QuantLib license. You should have received a |
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| 11 | copy of the license along with this program; if not, please email |
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| 12 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 13 | <http://quantlib.org/license.shtml>. |
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| 14 | |
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| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 17 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 18 | */ |
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| 19 | |
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| 20 | #include <ql/processes/mfstateprocess.hpp> |
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| 21 | |
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| 22 | namespace QuantLib { |
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| 23 | |
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| 24 | MfStateProcess::MfStateProcess(Real reversion, const Array& times, const Array& vols) |
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| 25 | : reversion_(reversion), times_(times), vols_(vols) { |
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| 26 | if (reversion_ < QL_EPSILON && -reversion_ < QL_EPSILON) |
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| 27 | reversionZero_ = true; |
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| 28 | QL_REQUIRE(times.size() == vols.size() - 1, |
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| 29 | "number of volatilities (" |
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| 30 | << vols.size() << ") compared to number of times (" |
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| 31 | << times_.size() << " must be bigger by one" ); |
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| 32 | for (int i = 0; i < ((int)times.size()) - 1; i++) |
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| 33 | QL_REQUIRE(times[i] < times[i + 1], "times must be increasing (" |
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| 34 | << times[i] << "@" << i |
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| 35 | << " , " << times[i + 1] |
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| 36 | << "@" << i + 1 << ")" ); |
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| 37 | for (Size i = 0; i < vols.size(); i++) |
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| 38 | QL_REQUIRE(vols[i] >= 0.0, "volatilities must be non negative (" |
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| 39 | << vols[i] << "@" << i << ")" ); |
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| 40 | } |
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| 41 | |
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| 42 | Real MfStateProcess::x0() const { return 0.0; } |
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| 43 | |
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| 44 | Real MfStateProcess::drift(Time, Real) const { return 0.0; } |
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| 45 | |
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| 46 | Real MfStateProcess::diffusion(Time t, Real) const { |
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| 47 | Size i = |
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| 48 | std::upper_bound(first: times_.begin(), last: times_.end(), val: t) - times_.begin(); |
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| 49 | return vols_[i]; |
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| 50 | } |
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| 51 | |
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| 52 | Real MfStateProcess::expectation(Time, Real x0, Time dt) const { |
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| 53 | return x0; |
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| 54 | } |
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| 55 | |
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| 56 | Real MfStateProcess::stdDeviation(Time t, Real x0, Time dt) const { |
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| 57 | return std::sqrt(x: variance(t0: t, x0, dt)); |
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| 58 | } |
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| 59 | |
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| 60 | Real MfStateProcess::variance(Time t, Real, Time dt) const { |
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| 61 | |
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| 62 | if (dt < QL_EPSILON) |
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| 63 | return 0.0; |
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| 64 | if (times_.empty()) |
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| 65 | return reversionZero_ ? dt |
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| 66 | : 1.0 / (2.0 * reversion_) * |
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| 67 | (std::exp(x: 2.0 * reversion_ * (t + dt)) - |
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| 68 | std::exp(x: 2.0 * reversion_ * t)); |
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| 69 | |
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| 70 | Size i = |
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| 71 | std::upper_bound(first: times_.begin(), last: times_.end(), val: t) - times_.begin(); |
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| 72 | Size j = std::upper_bound(first: times_.begin(), last: times_.end(), val: t + dt) - |
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| 73 | times_.begin(); |
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| 74 | |
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| 75 | Real v = 0.0; |
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| 76 | |
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| 77 | for (Size k = i; k < j; k++) { |
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| 78 | if (reversionZero_) |
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| 79 | v += vols_[k] * vols_[k] * |
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| 80 | (times_[k] - std::max(a: k > 0 ? times_[k - 1] : 0.0, b: t)); |
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| 81 | else |
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| 82 | v += 1.0 / (2.0 * reversion_) * vols_[k] * vols_[k] * |
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| 83 | (std::exp(x: 2.0 * reversion_ * times_[k]) - |
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| 84 | std::exp(x: 2.0 * reversion_ * |
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| 85 | std::max(a: k > 0 ? times_[k - 1] : 0.0, b: t))); |
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| 86 | } |
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| 87 | |
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| 88 | if (reversionZero_) |
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| 89 | v += vols_[j] * vols_[j] * |
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| 90 | (t + dt - std::max(a: j > 0 ? times_[j - 1] : 0.0, b: t)); |
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| 91 | else |
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| 92 | v += 1.0 / (2.0 * reversion_) * vols_[j] * vols_[j] * |
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| 93 | (std::exp(x: 2.0 * reversion_ * (t + dt)) - |
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| 94 | std::exp(x: 2.0 * reversion_ * |
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| 95 | (std::max(a: j > 0 ? times_[j - 1] : 0.0, b: t)))); |
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| 96 | |
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| 97 | return v; |
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| 98 | } |
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| 99 | } |
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| 100 | |
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