fxvolsmile.cpp

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/*
 Copyright (C) 2017 Quaternion Risk Management Ltd
 All rights reserved.
 
 This file is part of ORE, a free-software/open-source library
 for transparent pricing and risk analysis - http://opensourcerisk.org
 
 ORE is free software: you can redistribute it and/or modify it
 under the terms of the Modified BSD License.  You should have received a
 copy of the license along with this program.
 The license is also available online at <http://opensourcerisk.org>
 
 This program is distributed on the basis that it will form a useful
 contribution to risk analytics and model standardisation, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.
*/
 
/*! \file fxvolsmile.cpp
    \brief fx vol smile
*/
 
#include "toplevelfixture.hpp"
#include <boost/make_shared.hpp>
#include <boost/test/unit_test.hpp>
#include <ql/math/matrix.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/equityfx/blackvariancesurface.hpp>
#include <ql/termstructures/yield/discountcurve.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/utilities/dataparsers.hpp>
#include <qle/termstructures/blackinvertedvoltermstructure.hpp>
#include <qle/termstructures/fxblackvolsurface.hpp>
#include <qle/termstructures/fxvannavolgasmilesection.hpp>
 
using namespace QuantLib;
using namespace QuantExt;
using namespace boost::unit_test_framework;
using namespace std;
 
namespace {
 
struct CommonVars {
 
    /* ------ GLOBAL VARIABLES ------ */
    Date today;
    DayCounter dc;
    vector<Date> dates;
    vector<Real> strikes;
    Matrix vols;
    vector<Real> atmVols;
 
    vector<Volatility> rrs;
    vector<Volatility> bfs;
 
    Handle<Quote> baseSpot;
    Handle<YieldTermStructure> baseDomesticYield;
    Handle<YieldTermStructure> baseForeignYield;
 
    CommonVars() {
 
        today = Date(1, Jan, 2014);
        dc = ActualActual(ActualActual::ISDA);
 
        Settings::instance().evaluationDate() = today;
 
        dates.push_back(Date(1, Feb, 2014));
        dates.push_back(Date(1, Mar, 2014));
        dates.push_back(Date(1, Apr, 2014));
        dates.push_back(Date(1, Jan, 2015));
 
        strikes.push_back(90);
        strikes.push_back(100);
        strikes.push_back(110);
 
        vols = Matrix(3, 4);
        vols[0][0] = 0.12;
        vols[1][0] = 0.10;
        vols[2][0] = 0.13;
        vols[0][1] = 0.22;
        vols[1][1] = 0.20;
        vols[2][1] = 0.23;
        vols[0][2] = 0.32;
        vols[1][2] = 0.30;
        vols[2][2] = 0.33;
        vols[0][3] = 0.42;
        vols[1][3] = 0.40;
        vols[2][3] = 0.43;
 
        atmVols.push_back(0.1);
        atmVols.push_back(0.2);
        atmVols.push_back(0.3);
        atmVols.push_back(0.4);
 
        rrs = vector<Volatility>(atmVols.size(), 0.01);
        bfs = vector<Volatility>(atmVols.size(), 0.001);
 
        baseSpot = Handle<Quote>(QuantLib::ext::shared_ptr<Quote>(new SimpleQuote(100)));
 
        baseDomesticYield = Handle<YieldTermStructure>(
            QuantLib::ext::make_shared<FlatForward>(today, Handle<Quote>(QuantLib::ext::make_shared<SimpleQuote>(0.03)), dc));
        baseForeignYield = Handle<YieldTermStructure>(
            QuantLib::ext::make_shared<FlatForward>(today, Handle<Quote>(QuantLib::ext::make_shared<SimpleQuote>(0.01)), dc));
    }
};
 
struct VolData {
    const char* tenor;
    Volatility atm;
    Volatility rr;
    Volatility bf;
    Time time;
    Real df_d;
    Real df_f;
};
 
} // namespace
 
BOOST_FIXTURE_TEST_SUITE(QuantExtTestSuite, qle::test::TopLevelFixture)
 
BOOST_AUTO_TEST_SUITE(FxVolSmileTest)
 
BOOST_AUTO_TEST_CASE(testVannaVolgaFxSmileSection) {
 
    BOOST_TEST_MESSAGE("Testing fx vanna volga smile");
 
    SavedSettings backup;
 
    // test numbers from Castagna & Mercurio (2006)
    // http://papers.ssrn.com/sol3/papers.cfm?abstract_id=873788
    // page 5
    Settings::instance().evaluationDate() = Date(1, July, 2005);
    Time t = 94 / (double)365;
    Real S0 = 1.205;
    Volatility sig_atm = 0.0905;
    Volatility sig_rr = -0.005;
    Volatility sig_bf = 0.0013;
    // page 11
    DiscountFactor df_usd = 0.9902752;
    DiscountFactor df_eur = 0.9945049;
 
    // Rates
    Real rd = -::log(df_usd) / t;
    Real rf = -::log(df_eur) / t;
 
    VannaVolgaSmileSection vvss(S0, rd, rf, t, sig_atm, sig_rr, sig_bf);
 
    // Check the Strike and Vol values from the paper
    Real tolerance = 0.0001; // 4 decimal places
    if (fabs(vvss.k_atm() - 1.2114) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to calculte ATM strike, got " << vvss.k_atm());
    if (fabs(vvss.k_p() - 1.1733) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to calculate 25P strike, got " << vvss.k_p());
    if (fabs(vvss.k_c() - 1.2487) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to calculate 25C strike, got " << vvss.k_c());
    if (fabs(vvss.vol_atm() - 0.0905) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to calculate ATM vol, got " << vvss.vol_atm());
    if (fabs(vvss.vol_p() - 0.0943) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to calculate 25P vol, got " << vvss.vol_p());
    if (fabs(vvss.vol_c() - 0.0893) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to calculate 25C vol, got " << vvss.vol_c());
 
    // Now check that our smile returns these
    if (fabs(vvss.volatility(vvss.k_atm()) - vvss.vol_atm()) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to recover ATM vol, got " << vvss.volatility(vvss.k_atm()));
    if (fabs(vvss.volatility(vvss.k_p()) - vvss.vol_p()) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to recover 25P vol, got " << vvss.volatility(vvss.k_p()));
    if (fabs(vvss.volatility(vvss.k_c()) - vvss.vol_c()) > tolerance)
        BOOST_FAIL("VannaVolgaSmileSection failed to recover 25C vol, got " << vvss.volatility(vvss.k_c()));
 
    // To graph the smile, uncomment this code
    /*
    cout << "strike,vol" << endl;
    //for (Real k = 1.1; k < 1.35; k += 0.002) // normal (as per paper)
    //for (Real k = 0.9; k < 1.5; k += 0.01) // large
    for (Real k = 0.1; k < 3; k += 0.05) // extreme
        cout << k << "," << vvss.volatility(k) << endl;
    */
}
 
BOOST_AUTO_TEST_CASE(testVannaVolgaFxVolSurface) {
 
    BOOST_TEST_MESSAGE("Testing fx vanna volga surface");
 
    SavedSettings backup;
 
    // Data from
    // "Consistent pricing and hedging of an FX options book" (2005)
    // L. Bisesti, A. Castagna and F. Mercurio
    // http://www.fabiomercurio.it/fxbook.pdf
    Date asof(12, Feb, 2004);
    Settings::instance().evaluationDate() = asof;
 
    Handle<Quote> fxSpot(QuantLib::ext::shared_ptr<Quote>(new SimpleQuote(1.2832)));
 
    // vols are % here
    // tenor, atm, rr, bf, T, p_d, p_f
    VolData volData[] = { { "1W", 11.75, 0.50, 0.190, 0.0192, 0.999804, 0.999606 },
                          { "2W", 11.60, 0.50, 0.190, 0.0384, 0.999595, 0.999208 },
                          { "1M", 11.50, 0.60, 0.190, 0.0877, 0.999044, 0.998179 },
                          { "2M", 11.25, 0.60, 0.210, 0.1726, 0.998083, 0.996404 },
                          { "3M", 11.00, 0.60, 0.220, 0.2493, 0.997187, 0.994803 },
                          { "6M", 10.87, 0.65, 0.235, 0.5014, 0.993959, 0.989548 },
                          { "9M", 10.83, 0.69, 0.235, 0.7589, 0.990101, 0.984040 },
                          { "1Y", 10.80, 0.70, 0.240, 1.0110, 0.985469, 0.978479 },
                          { "2Y", 10.70, 0.65, 0.255, 2.0110, 0.960102, 0.951092 } };
 
    // Assume act/act
    DayCounter dc = ActualActual(ActualActual::ISDA);
    Calendar cal = TARGET();
 
    // set up vectors
    Size len = sizeof(volData) / sizeof(volData[0]);
    vector<Date> dates(len);
    vector<Volatility> atm(len);
    vector<Volatility> rr(len);
    vector<Volatility> bf(len);
    // For DiscountCurve we need the T=0 points.
    vector<Date> discountDates(len + 1);
    vector<DiscountFactor> dfDom(len + 1);
    vector<DiscountFactor> dfFor(len + 1);
    discountDates[0] = asof;
    dfDom[0] = 1.0;
    dfFor[0] = 1.0;
 
    for (Size i = 0; i < sizeof(volData) / sizeof(volData[0]); i++) {
        dates[i] = asof + PeriodParser::parse(volData[i].tenor);
        // check time == volData[i].time
        /*
        if (fabs(dc.yearFraction(asof, dates[i]) - volData[i].time) > 0.001)
            BOOST_FAIL("Did not match vol data time (" << volData[i].time <<
                       ") with aosf " << asof << " and maturity " << dates[i] <<
                       " got year fraction of " << dc.yearFraction(asof, dates[i]));
         */
 
        atm[i] = volData[i].atm / 100;
        rr[i] = volData[i].rr / 100;
        bf[i] = volData[i].bf / 100;
 
        discountDates[i + 1] = dates[i];
        dfDom[i + 1] = volData[i].df_d;
        dfFor[i + 1] = volData[i].df_f;
    }
 
    // Now build discount curves
    Handle<YieldTermStructure> domYTS(
        QuantLib::ext::shared_ptr<YieldTermStructure>(new DiscountCurve(discountDates, dfDom, dc)));
    Handle<YieldTermStructure> forYTS(
        QuantLib::ext::shared_ptr<YieldTermStructure>(new DiscountCurve(discountDates, dfFor, dc)));
 
    // build surface
    FxBlackVannaVolgaVolatilitySurface volSurface(asof, dates, atm, rr, bf, dc, cal, fxSpot, domYTS, forYTS);
 
    // 1.55,1.75,0.121507
    Real vol = volSurface.blackVol(1.75, 1.55);
    Real expected = 0.121507;
    if (fabs(vol - expected) > 0.00001)
        BOOST_FAIL("Failed to get expected vol from surface " << vol);
    /*
    cout << "strike,time,vol" << endl;
    for (Real k = 1.0; k < 1.6; k += 0.01) // extreme
        for (Time tt = 0.1; tt < 2; tt+= 0.05)
            cout << k << "," << tt << "," << volSurface.blackVol(tt, k) << endl;
     */
 
    // Test if Null<Real>() or 0 strike returns atm vol
    for (Size i = 0; i < len; i++) {
        Real vol = volSurface.blackVol(dates[i], Null<Real>());
        Real vol2 = volSurface.blackVol(dates[i], 0);
        if (fabs(vol - atm[i]) > 0.00001)
            BOOST_FAIL("Failed to get expected atm vol from surface: " << vol);
        if (fabs(vol2 - atm[i]) > 0.00001)
            BOOST_FAIL("Failed to get expected atm vol from surface: " << vol);
    }
}
 
BOOST_AUTO_TEST_CASE(testInvertedVolTermStructure) {
 
    BOOST_TEST_MESSAGE("Testing inverted vol term structure");
 
    SavedSettings backup;
 
    CommonVars vars;
 
    Handle<BlackVolTermStructure> surface(QuantLib::ext::shared_ptr<BlackVolTermStructure>(
        new BlackVarianceSurface(vars.today, TARGET(), vars.dates, vars.strikes, vars.vols, vars.dc)));
 
    BlackInvertedVolTermStructure bivt(surface);
 
    if (surface->maxDate() != bivt.maxDate())
        BOOST_FAIL("inverted maxDate() vol surface does not match base");
 
    if (surface->referenceDate() != bivt.referenceDate())
        BOOST_FAIL("inverted referenceDate() vol surface does not match base");
 
    // base spot is 100
    // test cases <Time, Strike>
    double testCases[][2] = { { 0.1, 104 }, { 0.5, 90 },  { 0.6, 110 }, { 0.9, 90 },
                              { 0.9, 95 },  { 0.9, 100 }, { 0.9, 105 }, { 0.9, 110 } };
 
    for (Size i = 0; i < sizeof(testCases) / sizeof(testCases[0]); i++) {
        Time t = testCases[i][0];
        Real k = testCases[i][1];
 
        Real vol1 = surface->blackVol(t, k);
 
        Real invertedStrike = 1.0 / k;
        Real vol2 = bivt.blackVol(t, invertedStrike);
        if (fabs(vol1 - vol2) > 0.00001)
            BOOST_FAIL("Failed to get expected vol (" << vol1 << ") from inverted vol surface, got (" << vol2 << ")");
    }
}
 
BOOST_AUTO_TEST_SUITE_END()
 
BOOST_AUTO_TEST_SUITE_END()