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<div class="title">Gaussian1dModels.cpp</div> </div>
</div><!--header-->
<div class="contents">
<p>This example shows the use of Gaussian short rate model for interest rate derivatives.</p>
<div class="fragment"><div class="line"><span class="comment">/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */</span></div>
<div class="line"> </div>
<div class="line"><span class="comment">/*</span></div>
<div class="line"><span class="comment"> Copyright (C) 2014 Peter Caspers</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> This file is part of QuantLib, a free-software/open-source library</span></div>
<div class="line"><span class="comment"> for financial quantitative analysts and developers - http://quantlib.org/</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> QuantLib is free software: you can redistribute it and/or modify it</span></div>
<div class="line"><span class="comment"> under the terms of the QuantLib license. You should have received a</span></div>
<div class="line"><span class="comment"> copy of the license along with this program; if not, please email</span></div>
<div class="line"><span class="comment"> <quantlib-dev@lists.sf.net>. The license is also available online at</span></div>
<div class="line"><span class="comment"> <http://quantlib.org/license.shtml>.</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> This program is distributed in the hope that it will be useful, but WITHOUT</span></div>
<div class="line"><span class="comment"> ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS</span></div>
<div class="line"><span class="comment"> FOR A PARTICULAR PURPOSE. See the license for more details.</span></div>
<div class="line"><span class="comment">*/</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include <ql/qldefines.hpp></span></div>
<div class="line"><span class="preprocessor">#ifdef BOOST_MSVC</span></div>
<div class="line"><span class="preprocessor"># include <ql/auto_link.hpp></span></div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"><span class="preprocessor">#include <ql/instruments/floatfloatswap.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/instruments/floatfloatswaption.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/instruments/nonstandardswaption.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/pricingengines/swap/discountingswapengine.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/pricingengines/swaption/gaussian1dswaptionengine.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/pricingengines/swaption/gaussian1dnonstandardswaptionengine.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/pricingengines/swaption/gaussian1dfloatfloatswaptionengine.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/models/shortrate/onefactormodels/gsr.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/models/shortrate/onefactormodels/markovfunctional.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/models/shortrate/calibrationhelpers/swaptionhelper.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/math/optimization/levenbergmarquardt.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/cashflows/lineartsrpricer.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/indexes/ibor/euribor.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/indexes/swap/euriborswap.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/termstructures/yield/flatforward.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/termstructures/volatility/swaption/swaptionconstantvol.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/rebatedexercise.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/quotes/simplequote.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/time/calendars/target.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/time/daycounters/actual360.hpp></span></div>
<div class="line"><span class="preprocessor">#include <ql/time/daycounters/thirty360.hpp></span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"><span class="preprocessor">#include <iomanip></span></div>
<div class="line"> </div>
<div class="line"><span class="keyword">using namespace </span><a class="code" href="namespace_quant_lib.html">QuantLib</a>;</div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#if defined(QL_ENABLE_SESSIONS)</span></div>
<div class="line"><span class="keyword">namespace </span><a class="code" href="namespace_quant_lib.html">QuantLib</a> {</div>
<div class="line"> </div>
<div class="line"> ThreadKey sessionId() { <span class="keywordflow">return</span> 0; }</div>
<div class="line"> </div>
<div class="line">}</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"> </div>
<div class="line"><span class="comment">// helper function that prints a basket of calibrating swaptions to std::cout</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">void</span> printBasket(</div>
<div class="line"> <span class="keyword">const</span> std::vector<ext::shared_ptr<BlackCalibrationHelper> > &basket) {</div>
<div class="line"> std::cout << <span class="stringliteral">"\n"</span> << std::left << std::setw(20) << <span class="stringliteral">"Expiry"</span> << std::setw(20)</div>
<div class="line"> << <span class="stringliteral">"Maturity"</span> << std::setw(20) << <span class="stringliteral">"Nominal"</span> << std::setw(14)</div>
<div class="line"> << <span class="stringliteral">"Rate"</span> << std::setw(12) << <span class="stringliteral">"Pay/Rec"</span> << std::setw(14)</div>
<div class="line"> << <span class="stringliteral">"Market ivol"</span> << std::fixed << std::setprecision(6)</div>
<div class="line"> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"=================="</span> << std::endl;</div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> j = 0; j < basket.size(); ++j) {</div>
<div class="line"> ext::shared_ptr<SwaptionHelper> helper =</div>
<div class="line"> ext::dynamic_pointer_cast<SwaptionHelper>(basket[j]);</div>
<div class="line"> <a name="_a0"></a><a class="code" href="class_quant_lib_1_1_date.html" title="Concrete date class.">Date</a> endDate = helper->underlyingSwap()->fixedSchedule().dates().back();</div>
<div class="line"> <a name="a1"></a><a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> nominal = helper->underlyingSwap()->nominal();</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> vol = helper->volatility()->value();</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> <a name="a2"></a><a class="code" href="group__manips.html#gac63ea3dad10259db3764c7d15a61cde5" title="output rates and spreads as percentages">rate</a> = helper->underlyingSwap()->fixedRate();</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_date.html" title="Concrete date class.">Date</a> expiry = helper->swaption()->exercise()->date(0);</div>
<div class="line"> VanillaSwap::Type type = helper->swaption()->type();</div>
<div class="line"> std::ostringstream expiryString, endDateString;</div>
<div class="line"> expiryString << expiry;</div>
<div class="line"> endDateString << endDate;</div>
<div class="line"> std::cout << std::setw(20) << expiryString.str() << std::setw(20)</div>
<div class="line"> << endDateString.str() << std::setw(20) << nominal</div>
<div class="line"> << std::setw(14) << <a class="code" href="group__manips.html#gac63ea3dad10259db3764c7d15a61cde5" title="output rates and spreads as percentages">rate</a> << std::setw(12)</div>
<div class="line"> << (type == VanillaSwap::Payer ? <span class="stringliteral">"Payer"</span> : <span class="stringliteral">"Receiver"</span>)</div>
<div class="line"> << std::setw(14) << vol << std::endl;</div>
<div class="line"> }</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"><span class="comment">// helper function that prints the result of a model calibraiton to std::cout</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">void</span> printModelCalibration(</div>
<div class="line"> <span class="keyword">const</span> std::vector<ext::shared_ptr<BlackCalibrationHelper> > &basket,</div>
<div class="line"> <span class="keyword">const</span> <a name="_a3"></a><a class="code" href="class_quant_lib_1_1_array.html" title="1-D array used in linear algebra.">Array</a> &<a name="a4"></a><a class="code" href="group__manips.html#gac402ef7c87f63f7c603ee87210b5750c" title="output volatilities as percentages">volatility</a>) {</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\n"</span> << std::left << std::setw(20) << <span class="stringliteral">"Expiry"</span> << std::setw(14)</div>
<div class="line"> << <span class="stringliteral">"Model sigma"</span> << std::setw(20) << <span class="stringliteral">"Model price"</span></div>
<div class="line"> << std::setw(20) << <span class="stringliteral">"market price"</span> << std::setw(14)</div>
<div class="line"> << <span class="stringliteral">"Model ivol"</span> << std::setw(14) << <span class="stringliteral">"Market ivol"</span> << std::fixed</div>
<div class="line"> << std::setprecision(6) << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span></div>
<div class="line"> <span class="stringliteral">"===================="</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> j = 0; j < basket.size(); ++j) {</div>
<div class="line"> ext::shared_ptr<SwaptionHelper> helper =</div>
<div class="line"> ext::dynamic_pointer_cast<SwaptionHelper>(basket[j]);</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_date.html" title="Concrete date class.">Date</a> expiry = helper->swaption()->exercise()->date(0);</div>
<div class="line"> std::ostringstream expiryString;</div>
<div class="line"> expiryString << expiry;</div>
<div class="line"> std::cout << std::setw(20) << expiryString.str() << std::setw(14)</div>
<div class="line"> << <a class="code" href="group__manips.html#gac402ef7c87f63f7c603ee87210b5750c" title="output volatilities as percentages">volatility</a>[j] << std::setw(20) << basket[j]->modelValue()</div>
<div class="line"> << std::setw(20) << basket[j]->marketValue() << std::setw(14)</div>
<div class="line"> << basket[j]->impliedVolatility(basket[j]->modelValue(), 1E-6,</div>
<div class="line"> 1000, 0.0, 2.0)</div>
<div class="line"> << std::setw(14) << basket[j]->volatility()->value()</div>
<div class="line"> << std::endl;</div>
<div class="line"> }</div>
<div class="line"> <span class="keywordflow">if</span> (<a class="code" href="group__manips.html#gac402ef7c87f63f7c603ee87210b5750c" title="output volatilities as percentages">volatility</a>.size() > basket.size()) <span class="comment">// only for markov model</span></div>
<div class="line"> std::cout << std::setw(20) << <span class="stringliteral">" "</span> << <a class="code" href="group__manips.html#gac402ef7c87f63f7c603ee87210b5750c" title="output volatilities as percentages">volatility</a>.back() << std::endl;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// here the main part of the code starts</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">int</span> main(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> *argv[]) {</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">try</span> {</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nGaussian1dModel Examples"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThis is some example code showing how to use the GSR "</span></div>
<div class="line"> <span class="stringliteral">"\n(Gaussian short rate) and Markov Functional model."</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_date.html" title="Concrete date class.">Date</a> refDate(30, April, 2014);</div>
<div class="line"> <a name="a5"></a><a class="code" href="class_quant_lib_1_1_singleton.html#ab7455b7e1235d292c444095842349291" title="access to the unique instance">Settings::instance</a>().evaluationDate() = refDate;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe evaluation date for this example is set to "</span></div>
<div class="line"> << <a class="code" href="class_quant_lib_1_1_singleton.html#ab7455b7e1235d292c444095842349291" title="access to the unique instance">Settings::instance</a>().evaluationDate() << std::endl;</div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> forward6mLevel = 0.025;</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> oisLevel = 0.02;</div>
<div class="line"> </div>
<div class="line"> <a name="_a6"></a><a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a> forward6mQuote(</div>
<div class="line"> ext::make_shared<SimpleQuote>(forward6mLevel));</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a> oisQuote(ext::make_shared<SimpleQuote>(oisLevel));</div>
<div class="line"> </div>
<div class="line"> <a name="_a7"></a><a class="code" href="class_quant_lib_1_1_handle.html">Handle<YieldTermStructure></a> yts6m(ext::make_shared<FlatForward>(</div>
<div class="line"> 0, <a name="_a8"></a><a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>(), forward6mQuote, <a name="_a9"></a><a class="code" href="class_quant_lib_1_1_actual365_fixed.html" title="Actual/365 (Fixed) day count convention.">Actual365Fixed</a>()));</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_handle.html">Handle<YieldTermStructure></a> ytsOis(ext::make_shared<FlatForward>(</div>
<div class="line"> 0, <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>(), oisQuote, <a class="code" href="class_quant_lib_1_1_actual365_fixed.html" title="Actual/365 (Fixed) day count convention.">Actual365Fixed</a>()));</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<IborIndex> euribor6m =</div>
<div class="line"> ext::make_shared<Euribor>(6 * Months, yts6m);</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nWe assume a multicurve setup, for simplicity with flat yield "</span></div>
<div class="line"> <span class="stringliteral">"\nterm structures. The discounting curve is an Eonia curve at"</span></div>
<div class="line"> <span class="stringliteral">"\na level of "</span> << oisLevel</div>
<div class="line"> << <span class="stringliteral">" and the forwarding curve is an Euribior 6m curve"</span></div>
<div class="line"> << <span class="stringliteral">"\nat a level of "</span> << forward6mLevel << std::endl;</div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> volLevel = 0.20;</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a> volQuote(ext::make_shared<SimpleQuote>(volLevel));</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<SwaptionVolatilityStructure></a> swaptionVol(</div>
<div class="line"> ext::make_shared<ConstantSwaptionVolatility>(</div>
<div class="line"> 0, <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>(), <a name="a10"></a><a class="code" href="group__datetime.html#ggaff46c5ae9385d20709bedade86edd368a013e092c359f6031cc0563fd413ce707">ModifiedFollowing</a>, volQuote, <a class="code" href="class_quant_lib_1_1_actual365_fixed.html" title="Actual/365 (Fixed) day count convention.">Actual365Fixed</a>()));</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nFor the volatility we assume a flat swaption volatility at "</span></div>
<div class="line"> << volLevel << std::endl;</div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> strike = 0.04;</div>
<div class="line"> std::cout << <span class="stringliteral">"\nWe consider a standard 10y bermudan payer swaption "</span></div>
<div class="line"> <span class="stringliteral">"\nwith yearly exercises at a strike of "</span> << strike</div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_date.html" title="Concrete date class.">Date</a> effectiveDate = <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>().<a name="a11"></a><a class="code" href="class_quant_lib_1_1_calendar.html#ab3fc4d2c4ba5243c3f5d51dcb3077ceb">advance</a>(refDate, 2 * Days);</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_date.html" title="Concrete date class.">Date</a> maturityDate = <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>().<a class="code" href="class_quant_lib_1_1_calendar.html#ab3fc4d2c4ba5243c3f5d51dcb3077ceb">advance</a>(effectiveDate, 10 * Years);</div>
<div class="line"> </div>
<div class="line"> <a name="_a12"></a><a class="code" href="class_quant_lib_1_1_schedule.html" title="Payment schedule.">Schedule</a> fixedSchedule(effectiveDate, maturityDate, 1 * Years, <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>(),</div>
<div class="line"> <a class="code" href="group__datetime.html#ggaff46c5ae9385d20709bedade86edd368a013e092c359f6031cc0563fd413ce707">ModifiedFollowing</a>, <a class="code" href="group__datetime.html#ggaff46c5ae9385d20709bedade86edd368a013e092c359f6031cc0563fd413ce707">ModifiedFollowing</a>,</div>
<div class="line"> <a name="a13"></a><a class="code" href="struct_quant_lib_1_1_date_generation.html#a11fcd51ef86118f65e603c1474377a78ae204c9c3e62b1e9a6b60e40cd05256c5">DateGeneration::Forward</a>, <span class="keyword">false</span>);</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_schedule.html" title="Payment schedule.">Schedule</a> floatingSchedule(effectiveDate, maturityDate, 6 * Months,</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>(), <a class="code" href="group__datetime.html#ggaff46c5ae9385d20709bedade86edd368a013e092c359f6031cc0563fd413ce707">ModifiedFollowing</a>,</div>
<div class="line"> <a class="code" href="group__datetime.html#ggaff46c5ae9385d20709bedade86edd368a013e092c359f6031cc0563fd413ce707">ModifiedFollowing</a>, <a class="code" href="struct_quant_lib_1_1_date_generation.html#a11fcd51ef86118f65e603c1474377a78ae204c9c3e62b1e9a6b60e40cd05256c5">DateGeneration::Forward</a>,</div>
<div class="line"> <span class="keyword">false</span>);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<NonstandardSwap> underlying =</div>
<div class="line"> ext::make_shared<NonstandardSwap>(<a name="_a14"></a><a class="code" href="class_quant_lib_1_1_vanilla_swap.html" title="Plain-vanilla swap: fix vs floating leg.">VanillaSwap</a>(</div>
<div class="line"> VanillaSwap::Payer, 1.0, fixedSchedule, strike, <a name="_a15"></a><a class="code" href="class_quant_lib_1_1_thirty360.html" title="30/360 day count convention">Thirty360</a>(),</div>
<div class="line"> floatingSchedule, euribor6m, 0.00, <a name="_a16"></a><a class="code" href="class_quant_lib_1_1_actual360.html" title="Actual/360 day count convention.">Actual360</a>()));</div>
<div class="line"> </div>
<div class="line"> std::vector<Date> exerciseDates;</div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 1; i < 10; ++i)</div>
<div class="line"> exerciseDates.push_back(</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>().advance(fixedSchedule[i], -2 * Days));</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<Exercise> exercise =</div>
<div class="line"> ext::make_shared<BermudanExercise>(exerciseDates, <span class="keyword">false</span>);</div>
<div class="line"> ext::shared_ptr<NonstandardSwaption> swaption =</div>
<div class="line"> ext::make_shared<NonstandardSwaption>(underlying, exercise);</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nThe model is a one factor Hull White model with piecewise "</span></div>
<div class="line"> <span class="stringliteral">"\nvolatility adapted to our exercise dates."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::vector<Date> stepDates(exerciseDates.begin(),</div>
<div class="line"> exerciseDates.end() - 1);</div>
<div class="line"> std::vector<Real> sigmas(stepDates.size() + 1, 0.01);</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> reversion = 0.01;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe reversion is just kept constant at a level of "</span></div>
<div class="line"> << reversion << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nThe model's curve is set to the 6m forward curve. Note that "</span></div>
<div class="line"> <span class="stringliteral">"\nthe model adapts automatically to other curves where "</span></div>
<div class="line"> <span class="stringliteral">"appropriate "</span></div>
<div class="line"> <span class="stringliteral">"\n(e.g. if an index requires a different forwarding curve) or "</span></div>
<div class="line"> <span class="stringliteral">"\nwhere explicitly specified (e.g. in a swaption pricing "</span></div>
<div class="line"> <span class="stringliteral">"engine)."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<Gsr> gsr = ext::make_shared<Gsr>(</div>
<div class="line"> yts6m, stepDates, sigmas, reversion);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<PricingEngine> swaptionEngine =</div>
<div class="line"> ext::make_shared<Gaussian1dSwaptionEngine>(gsr, 64, 7.0, <span class="keyword">true</span>,</div>
<div class="line"> <span class="keyword">false</span>, ytsOis);</div>
<div class="line"> ext::shared_ptr<PricingEngine> nonstandardSwaptionEngine =</div>
<div class="line"> ext::make_shared<Gaussian1dNonstandardSwaptionEngine>(</div>
<div class="line"> gsr, 64, 7.0, <span class="keyword">true</span>, <span class="keyword">false</span>, <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a>(), ytsOis);</div>
<div class="line"> </div>
<div class="line"> swaption->setPricingEngine(nonstandardSwaptionEngine);</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nThe engine can generate a calibration basket in two modes."</span></div>
<div class="line"> <span class="stringliteral">"\nThe first one is called Naive and generates ATM swaptions "</span></div>
<div class="line"> <span class="stringliteral">"adapted to"</span></div>
<div class="line"> <span class="stringliteral">"\nthe exercise dates of the swaption and its maturity date"</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe resulting basket looks as follows:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<SwapIndex> swapBase =</div>
<div class="line"> ext::make_shared<EuriborSwapIsdaFixA>(10 * Years, yts6m, ytsOis);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::vector<ext::shared_ptr<BlackCalibrationHelper> > basket =</div>
<div class="line"> swaption->calibrationBasket(swapBase, *swaptionVol,</div>
<div class="line"> BasketGeneratingEngine::Naive);</div>
<div class="line"> printBasket(basket);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nLet's calibrate our model to this basket. We use a "</span></div>
<div class="line"> <span class="stringliteral">"specialized"</span></div>
<div class="line"> <span class="stringliteral">"\ncalibration method calibrating the sigma function one by one "</span></div>
<div class="line"> <span class="stringliteral">"to"</span></div>
<div class="line"> <span class="stringliteral">"\nthe calibrating vanilla swaptions. The result of this is as "</span></div>
<div class="line"> <span class="stringliteral">"follows:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < basket.size(); ++i)</div>
<div class="line"> basket[i]->setPricingEngine(swaptionEngine);</div>
<div class="line"> </div>
<div class="line"> <a name="_a17"></a><a class="code" href="class_quant_lib_1_1_levenberg_marquardt.html" title="Levenberg-Marquardt optimization method.">LevenbergMarquardt</a> method;</div>
<div class="line"> <a name="_a18"></a><a class="code" href="class_quant_lib_1_1_end_criteria.html" title="Criteria to end optimization process:">EndCriteria</a> ec(1000, 10, 1E-8, 1E-8,</div>
<div class="line"> 1E-8); <span class="comment">// only max iterations use actually used by LM</span></div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> gsr->calibrateVolatilitiesIterative(basket, method, ec);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printModelCalibration(basket, gsr->volatility());</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nFinally we price our bermudan swaption in the "</span></div>
<div class="line"> <span class="stringliteral">"calibrated model:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv = swaption->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nBermudan swaption NPV (ATM calibrated GSR) = "</span></div>
<div class="line"> << std::fixed << std::setprecision(6) << npv << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThere is another mode to generate a calibration basket called"</span></div>
<div class="line"> <span class="stringliteral">"\nMaturityStrikeByDeltaGamma. This means that the maturity,"</span></div>
<div class="line"> <span class="stringliteral">"\nthe strike and the nominal of the calibrating swaptions are"</span></div>
<div class="line"> <span class="stringliteral">"\nobtained matching the NPV, first derivative and second derivative"</span></div>
<div class="line"> <span class="stringliteral">"\nof the swap you will exercise into at at each bermudan call date."</span></div>
<div class="line"> <span class="stringliteral">"\nThe derivatives are taken with respect to the model's state variable."</span></div>
<div class="line"> <span class="stringliteral">"\nLet's try this in our case."</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> basket = swaption->calibrationBasket(</div>
<div class="line"> swapBase, *swaptionVol,</div>
<div class="line"> BasketGeneratingEngine::MaturityStrikeByDeltaGamma);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printBasket(basket);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nThe calibrated nominal is close to the exotics nominal."</span></div>
<div class="line"> <span class="stringliteral">"\nThe expiries and maturity dates of the vanillas are the same"</span></div>
<div class="line"> <span class="stringliteral">"\nas in the case above. The difference is the strike which"</span></div>
<div class="line"> <span class="stringliteral">"\nis now equal to the exotics strike."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nLet's see how this affects the exotics npv. The "</span></div>
<div class="line"> <span class="stringliteral">"\nrecalibrated model is:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < basket.size(); ++i)</div>
<div class="line"> basket[i]->setPricingEngine(swaptionEngine);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> gsr->calibrateVolatilitiesIterative(basket, method, ec);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printModelCalibration(basket, gsr->volatility());</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nAnd the bermudan's price becomes:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> npv = swaption->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nBermudan swaption NPV (deal strike calibrated GSR) = "</span></div>
<div class="line"> << std::setprecision(6) << npv << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nWe can do more complicated things, let's e.g. modify the"</span></div>
<div class="line"> <span class="stringliteral">"\nnominal schedule to be linear amortizing and see what"</span></div>
<div class="line"> <span class="stringliteral">"\nthe effect on the generated calibration basket is:"</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::vector<Real> nominalFixed, nominalFloating;</div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < fixedSchedule.size() - 1; ++i) {</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> tmpNom = 1.0 - (<a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a>)i / (fixedSchedule.size() - 1);</div>
<div class="line"> nominalFixed.push_back(tmpNom);</div>
<div class="line"> nominalFloating.push_back(tmpNom);</div>
<div class="line"> nominalFloating.push_back(</div>
<div class="line"> tmpNom); <span class="comment">// we use that the swap is 6m vs. 1y here</span></div>
<div class="line"> }</div>
<div class="line"> std::vector<Real> strikes(nominalFixed.size(), strike);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<NonstandardSwap> underlying2(<span class="keyword">new</span> <a name="_a19"></a><a class="code" href="class_quant_lib_1_1_nonstandard_swap.html" title="nonstandard swap">NonstandardSwap</a>(</div>
<div class="line"> VanillaSwap::Payer, nominalFixed, nominalFloating, fixedSchedule,</div>
<div class="line"> strikes, <a class="code" href="class_quant_lib_1_1_thirty360.html" title="30/360 day count convention">Thirty360</a>(), floatingSchedule, euribor6m, 1.0, 0.0,</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_actual360.html" title="Actual/360 day count convention.">Actual360</a>()));</div>
<div class="line"> ext::shared_ptr<NonstandardSwaption> swaption2 =</div>
<div class="line"> ext::make_shared<NonstandardSwaption>(underlying2, exercise);</div>
<div class="line"> </div>
<div class="line"> swaption2->setPricingEngine(nonstandardSwaptionEngine);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> basket = swaption2->calibrationBasket(</div>
<div class="line"> swapBase, *swaptionVol,</div>
<div class="line"> BasketGeneratingEngine::MaturityStrikeByDeltaGamma);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printBasket(basket);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe notional is weighted over the underlying exercised "</span></div>
<div class="line"> <span class="stringliteral">"\ninto and the maturity is adjusted downwards. The rate"</span></div>
<div class="line"> <span class="stringliteral">"\non the other hand is not affected."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nYou can also price exotic bond's features. If you have e.g. a"</span></div>
<div class="line"> <span class="stringliteral">"\nbermudan callable fixed bond you can set up the call right "</span></div>
<div class="line"> <span class="stringliteral">"\nas a swaption to enter into a one leg swap with notional"</span></div>
<div class="line"> <span class="stringliteral">"\nreimbursement at maturity."</span></div>
<div class="line"> <span class="stringliteral">"\nThe exercise should then be written as a rebated exercise"</span></div>
<div class="line"> <span class="stringliteral">"\npaying the notional in case of exercise."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe calibration basket looks like this:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::vector<Real> nominalFixed2(nominalFixed.size(), 1.0);</div>
<div class="line"> std::vector<Real> nominalFloating2(nominalFloating.size(),</div>
<div class="line"> 0.0); <span class="comment">// null the second leg</span></div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<NonstandardSwap> underlying3(<span class="keyword">new</span> <a class="code" href="class_quant_lib_1_1_nonstandard_swap.html" title="nonstandard swap">NonstandardSwap</a>(</div>
<div class="line"> VanillaSwap::Receiver, nominalFixed2, nominalFloating2,</div>
<div class="line"> fixedSchedule, strikes, <a class="code" href="class_quant_lib_1_1_thirty360.html" title="30/360 day count convention">Thirty360</a>(), floatingSchedule, euribor6m,</div>
<div class="line"> 1.0, 0.0, <a class="code" href="class_quant_lib_1_1_actual360.html" title="Actual/360 day count convention.">Actual360</a>(), <span class="keyword">false</span>,</div>
<div class="line"> <span class="keyword">true</span>)); <span class="comment">// final capital exchange</span></div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<RebatedExercise> exercise2 =</div>
<div class="line"> ext::make_shared<RebatedExercise>(*exercise, -1.0, 2, <a class="code" href="class_quant_lib_1_1_t_a_r_g_e_t.html" title="TARGET calendar">TARGET</a>());</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<NonstandardSwaption> swaption3 =</div>
<div class="line"> ext::make_shared<NonstandardSwaption>(underlying3, exercise2);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<SimpleQuote> oas0 =</div>
<div class="line"> ext::make_shared<SimpleQuote>(0.0);</div>
<div class="line"> ext::shared_ptr<SimpleQuote> oas100 =</div>
<div class="line"> ext::make_shared<SimpleQuote>(0.01);</div>
<div class="line"> <a name="_a20"></a><a class="code" href="class_quant_lib_1_1_relinkable_handle.html" title="Relinkable handle to an observable.">RelinkableHandle<Quote></a> oas(oas0);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<PricingEngine> nonstandardSwaptionEngine2 =</div>
<div class="line"> ext::make_shared<Gaussian1dNonstandardSwaptionEngine>(</div>
<div class="line"> gsr, 64, 7.0, <span class="keyword">true</span>, <span class="keyword">false</span>, oas); <span class="comment">// change discounting to 6m</span></div>
<div class="line"> </div>
<div class="line"> swaption3->setPricingEngine(nonstandardSwaptionEngine2);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> basket = swaption3->calibrationBasket(</div>
<div class="line"> swapBase, *swaptionVol,</div>
<div class="line"> BasketGeneratingEngine::MaturityStrikeByDeltaGamma);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printBasket(basket);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nNote that nominals are not exactly 1.0 here. This is"</span></div>
<div class="line"> << <span class="stringliteral">"\nbecause we do our bond discounting on 6m level while"</span></div>
<div class="line"> << <span class="stringliteral">"\nthe swaptions are still discounted on OIS level."</span></div>
<div class="line"> << <span class="stringliteral">"\n(You can try this by changing the OIS level to the "</span></div>
<div class="line"> << <span class="stringliteral">"\n6m level, which will produce nominals near 1.0)."</span></div>
<div class="line"> << <span class="stringliteral">"\nThe npv of the call right is (after recalibrating the model)"</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < basket.size(); i++)</div>
<div class="line"> basket[i]->setPricingEngine(swaptionEngine);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> gsr->calibrateVolatilitiesIterative(basket, method, ec);</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv3 = swaption3->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nBond's bermudan call right npv = "</span></div>
<div class="line"> << std::setprecision(6) << npv3 << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nUp to now, no credit spread is included in the pricing."</span></div>
<div class="line"> <span class="stringliteral">"\nWe can do so by specifying an oas in the pricing engine."</span></div>
<div class="line"> <span class="stringliteral">"\nLet's set the spread level to 100bp and regenerate"</span></div>
<div class="line"> <span class="stringliteral">"\nthe calibration basket."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> oas.linkTo(oas100);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> basket = swaption3->calibrationBasket(</div>
<div class="line"> swapBase, *swaptionVol,</div>
<div class="line"> BasketGeneratingEngine::MaturityStrikeByDeltaGamma);</div>
<div class="line"> </div>
<div class="line"> printBasket(basket);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nThe adjusted basket takes the credit spread into account."</span></div>
<div class="line"> <span class="stringliteral">"\nThis is consistent to a hedge where you would have a"</span></div>
<div class="line"> <span class="stringliteral">"\nmargin on the float leg around 100bp,too."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe npv becomes:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < basket.size(); i++)</div>
<div class="line"> basket[i]->setPricingEngine(swaptionEngine);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> gsr->calibrateVolatilitiesIterative(basket, method, ec);</div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv4 = swaption3->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nBond's bermudan call right npv (oas = 100bp) = "</span></div>
<div class="line"> << std::setprecision(6) << npv4 << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nThe next instrument we look at is a CMS 10Y vs Euribor "</span></div>
<div class="line"> <span class="stringliteral">"\n6M swaption. The maturity is again 10 years and the option"</span></div>
<div class="line"> <span class="stringliteral">"\nis exercisable on a yearly basis"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<FloatFloatSwap> underlying4(<span class="keyword">new</span> <a name="_a21"></a><a class="code" href="class_quant_lib_1_1_float_float_swap.html" title="float float swap">FloatFloatSwap</a>(</div>
<div class="line"> VanillaSwap::Payer, 1.0, 1.0, fixedSchedule, swapBase,</div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_thirty360.html" title="30/360 day count convention">Thirty360</a>(), floatingSchedule, euribor6m, <a class="code" href="class_quant_lib_1_1_actual360.html" title="Actual/360 day count convention.">Actual360</a>(), <span class="keyword">false</span>,</div>
<div class="line"> <span class="keyword">false</span>, 1.0, 0.0, <a name="_a22"></a><a class="code" href="class_quant_lib_1_1_null.html" title="template class providing a null value for a given type.">Null<Real></a>(), <a class="code" href="class_quant_lib_1_1_null.html" title="template class providing a null value for a given type.">Null<Real></a>(), 1.0, 0.0010));</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<FloatFloatSwaption> swaption4 =</div>
<div class="line"> ext::make_shared<FloatFloatSwaption>(underlying4, exercise);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<Gaussian1dFloatFloatSwaptionEngine></div>
<div class="line"> floatSwaptionEngine(<span class="keyword">new</span> <a name="_a23"></a><a class="code" href="class_quant_lib_1_1_gaussian1d_float_float_swaption_engine.html" title="One factor model float float swaption engine.">Gaussian1dFloatFloatSwaptionEngine</a>(</div>
<div class="line"> gsr, 64, 7.0, <span class="keyword">true</span>, <span class="keyword">false</span>, <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a>(), ytsOis, <span class="keyword">true</span>));</div>
<div class="line"> </div>
<div class="line"> swaption4->setPricingEngine(floatSwaptionEngine);</div>
<div class="line"> </div>
<div class="line"> std::cout</div>
<div class="line"> << <span class="stringliteral">"\nSince the underlying is quite exotic already, we start with"</span></div>
<div class="line"> <span class="stringliteral">"\npricing this using the LinearTsrPricer for CMS coupon "</span></div>
<div class="line"> <span class="stringliteral">"estimation"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a> reversionQuote(</div>
<div class="line"> ext::make_shared<SimpleQuote>(reversion));</div>
<div class="line"> </div>
<div class="line"> <span class="keyword">const</span> <a class="code" href="namespace_quant_lib.html#afd0d2e08465e4b7e928c75416bd8dc4b" title="Sequence of cash-flows.">Leg</a> &leg0 = underlying4->leg(0);</div>
<div class="line"> <span class="keyword">const</span> <a class="code" href="namespace_quant_lib.html#afd0d2e08465e4b7e928c75416bd8dc4b" title="Sequence of cash-flows.">Leg</a> &leg1 = underlying4->leg(1);</div>
<div class="line"> ext::shared_ptr<CmsCouponPricer> cmsPricer =</div>
<div class="line"> ext::make_shared<LinearTsrPricer>(swaptionVol, reversionQuote);</div>
<div class="line"> ext::shared_ptr<IborCouponPricer> iborPricer(<span class="keyword">new</span> <a name="_a24"></a><a class="code" href="class_quant_lib_1_1_black_ibor_coupon_pricer.html">BlackIborCouponPricer</a>);</div>
<div class="line"> </div>
<div class="line"> setCouponPricer(leg0, cmsPricer);</div>
<div class="line"> setCouponPricer(leg1, iborPricer);</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<PricingEngine> swapPricer =</div>
<div class="line"> ext::make_shared<DiscountingSwapEngine>(ytsOis);</div>
<div class="line"> </div>
<div class="line"> underlying4->setPricingEngine(swapPricer);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv5 = underlying4->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"Underlying CMS Swap NPV = "</span> << std::setprecision(6)</div>
<div class="line"> << npv5 << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" CMS Leg NPV = "</span> << underlying4->legNPV(0)</div>
<div class="line"> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" Euribor Leg NPV = "</span> << underlying4->legNPV(1)</div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nWe generate a naive calibration basket and calibrate "</span></div>
<div class="line"> <span class="stringliteral">"\nthe GSR model to it:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> basket = swaption4->calibrationBasket(swapBase, *swaptionVol,</div>
<div class="line"> BasketGeneratingEngine::Naive);</div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < basket.size(); ++i)</div>
<div class="line"> basket[i]->setPricingEngine(swaptionEngine);</div>
<div class="line"> gsr->calibrateVolatilitiesIterative(basket, method, ec);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printBasket(basket);</div>
<div class="line"> printModelCalibration(basket, gsr->volatility());</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe npv of the bermudan swaption is"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv6 = swaption4->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nFloat swaption NPV (GSR) = "</span> << std::setprecision(6)</div>
<div class="line"> << npv6 << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nIn this case it is also interesting to look at the "</span></div>
<div class="line"> <span class="stringliteral">"\nunderlying swap npv in the GSR model."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nFloat swap NPV (GSR) = "</span> << std::setprecision(6)</div>
<div class="line"> << swaption4->result<<a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a>>(<span class="stringliteral">"underlyingValue"</span>) << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nNot surprisingly, the underlying is priced differently"</span></div>
<div class="line"> <span class="stringliteral">"\ncompared to the LinearTsrPricer, since a different"</span></div>
<div class="line"> <span class="stringliteral">"\nsmile is implied by the GSR model."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThis is exactly where the Markov functional model"</span></div>
<div class="line"> << <span class="stringliteral">"\ncomes into play, because it can calibrate to any"</span></div>
<div class="line"> << <span class="stringliteral">"\ngiven underlying smile (as long as it is arbitrage"</span></div>
<div class="line"> << <span class="stringliteral">"\nfree). We try this now. Of course the usual use case"</span></div>
<div class="line"> << <span class="stringliteral">"\nis not to calibrate to a flat smile as in our simple"</span></div>
<div class="line"> << <span class="stringliteral">"\nexample, still it should be possible, of course..."</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::vector<Date> markovStepDates(exerciseDates.begin(),</div>
<div class="line"> exerciseDates.end());</div>
<div class="line"> <span class="keyword">const</span> std::vector<Date>& cmsFixingDates(markovStepDates);</div>
<div class="line"> std::vector<Real> markovSigmas(markovStepDates.size() + 1, 0.01);</div>
<div class="line"> std::vector<Period> tenors(cmsFixingDates.size(), 10 * Years);</div>
<div class="line"> ext::shared_ptr<MarkovFunctional> markov =</div>
<div class="line"> ext::make_shared<MarkovFunctional>(</div>
<div class="line"> yts6m, reversion, markovStepDates, markovSigmas, swaptionVol,</div>
<div class="line"> cmsFixingDates, tenors, swapBase,</div>
<div class="line"> MarkovFunctional::ModelSettings().withYGridPoints(16));</div>
<div class="line"> </div>
<div class="line"> ext::shared_ptr<Gaussian1dSwaptionEngine> swaptionEngineMarkov =</div>
<div class="line"> ext::make_shared<Gaussian1dSwaptionEngine>(markov, 8, 5.0, <span class="keyword">true</span>,</div>
<div class="line"> <span class="keyword">false</span>, ytsOis);</div>
<div class="line"> ext::shared_ptr<Gaussian1dFloatFloatSwaptionEngine></div>
<div class="line"> floatEngineMarkov =</div>
<div class="line"> ext::make_shared<Gaussian1dFloatFloatSwaptionEngine>(</div>
<div class="line"> markov, 16, 7.0, <span class="keyword">true</span>, <span class="keyword">false</span>, <a class="code" href="class_quant_lib_1_1_handle.html" title="Shared handle to an observable.">Handle<Quote></a>(), ytsOis,</div>
<div class="line"> <span class="keyword">true</span>);</div>
<div class="line"> </div>
<div class="line"> swaption4->setPricingEngine(floatEngineMarkov);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv7 = swaption4->NPV();</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe option npv is the markov model is:"</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nFloat swaption NPV (Markov) = "</span> << std::setprecision(6)</div>
<div class="line"> << npv7 << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThis is not too far from the GSR price."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nMore interesting is the question how well the Markov"</span></div>
<div class="line"> << <span class="stringliteral">"\nmodel did its job to match our input smile. For this"</span></div>
<div class="line"> << <span class="stringliteral">"\nwe look at the underlying npv under the Markov model"</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nFloat swap NPV (Markov) = "</span> << std::setprecision(6)</div>
<div class="line"> << swaption4->result<<a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a>>(<span class="stringliteral">"underlyingValue"</span>) << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThis is closer to our terminal swap rate model price."</span></div>
<div class="line"> <span class="stringliteral">"\nA perfect match is not expected anyway, because the"</span></div>
<div class="line"> <span class="stringliteral">"\ndynamics of the underlying rate in the linear"</span></div>
<div class="line"> <span class="stringliteral">"\nmodel is different from the Markov model, of"</span></div>
<div class="line"> <span class="stringliteral">"\ncourse."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThe Markov model can not only calibrate to the"</span></div>
<div class="line"> <span class="stringliteral">"\nunderlying smile, but has at the same time a"</span></div>
<div class="line"> <span class="stringliteral">"\nsigma function (similar to the GSR model) which"</span></div>
<div class="line"> <span class="stringliteral">"\ncan be used to calibrate to a second instrument"</span></div>
<div class="line"> <span class="stringliteral">"\nset. We do this here to calibrate to our coterminal"</span></div>
<div class="line"> <span class="stringliteral">"\nATM swaptions from above."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThis is a computationally demanding task, so"</span></div>
<div class="line"> <span class="stringliteral">"\ndepending on your machine, this may take a"</span></div>
<div class="line"> <span class="stringliteral">"\nwhile now..."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span> (<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> i = 0; i < basket.size(); ++i)</div>
<div class="line"> basket[i]->setPricingEngine(swaptionEngineMarkov);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> markov->calibrate(basket, method, ec);</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> printModelCalibration(basket, markov->volatility());</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nNow let's have a look again at the underlying pricing."</span></div>
<div class="line"> <span class="stringliteral">"\nIt shouldn't have changed much, because the underlying"</span></div>
<div class="line"> <span class="stringliteral">"\nsmile is still matched."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> npv8 = swaption4->result<<a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a>>(<span class="stringliteral">"underlyingValue"</span>);</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nFloat swap NPV (Markov) = "</span> << std::setprecision(6)</div>
<div class="line"> << npv8 << std::endl;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThis is close to the previous value as expected."</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nAs a final remark we note that the calibration to"</span></div>
<div class="line"> << <span class="stringliteral">"\ncoterminal swaptions is not particularly reasonable"</span></div>
<div class="line"> << <span class="stringliteral">"\nhere, because the european call rights are not"</span></div>
<div class="line"> << <span class="stringliteral">"\nwell represented by these swaptions."</span></div>
<div class="line"> << <span class="stringliteral">"\nSecondly, our CMS swaption is sensitive to the"</span></div>
<div class="line"> << <span class="stringliteral">"\ncorrelation between the 10y swap rate and the"</span></div>
<div class="line"> << <span class="stringliteral">"\nEuribor 6M rate. Since the Markov model is one factor"</span></div>
<div class="line"> << <span class="stringliteral">"\nit will most probably underestimate the market value"</span></div>
<div class="line"> << <span class="stringliteral">"\nby construction."</span> << std::endl;</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"\nThat was it. Thank you for running this demo. Bye."</span></div>
<div class="line"> << std::endl;</div>
<div class="line"> </div>
<div class="line"> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> <a name="_a25"></a><a class="code" href="class_quant_lib_1_1_error.html" title="Base error class.">QuantLib::Error</a>& e) {</div>
<div class="line"> std::cout << <span class="stringliteral">"terminated with a ql exception: "</span> << e.<a name="a26"></a><a class="code" href="class_quant_lib_1_1_error.html#a79009ed133fa02b942ddce8f0b987f3e" title="returns the error message.">what</a>()</div>
<div class="line"> << std::endl;</div>
<div class="line"> <span class="keywordflow">return</span> 1;</div>
<div class="line"> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> std::exception& e) {</div>
<div class="line"> std::cout << <span class="stringliteral">"terminated with a general exception: "</span> << e.what()</div>
<div class="line"> << std::endl;</div>
<div class="line"> <span class="keywordflow">return</span> 1;</div>
<div class="line"> }</div>
<div class="line">}</div>
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