QuantLib-noBoost/test-suite/margrabeoption.cpp at master · haozhangphd/QuantLib-noBoost

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

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 "utilities.hpp"

#include <ql/time/daycounters/actual360.hpp>

#include <ql/experimental/exoticoptions/margrabeoption.hpp>

#include <ql/experimental/exoticoptions/analyticamericanmargrabeengine.hpp>

#include <ql/experimental/exoticoptions/analyticeuropeanmargrabeengine.hpp>

#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>

#include <ql/utilities/dataformatters.hpp>

using namespace QuantLib;

#define REPORT_FAILURE(greekName, exercise, \

s1, s2, Q1, Q2, q1, q2, r, today, v1, v2, rho, \

expected, calculated, error, tolerance) \

FAIL_CHECK( \

exerciseTypeToString(exercise) << " " \

<< "Call option on Exchange Asset s2 for Asset s1" \

<< " with null payoff:\n" \

<< "1st underlying value: " << s1 << "\n" \

<< "2nd underlying value: " << s2 << "\n" \

<< "1st underlying quantity: " << Q1 << "\n" \

<< "2nd underlying quantity: " << Q2 << "\n" \

<< " 1st dividend yield: " << io::rate(q1) << "\n" \

<< " 2nd dividend yield: " << io::rate(q2) << "\n" \

<< " risk-free rate: " << io::rate(r) << "\n" \

<< " reference date: " << today << "\n" \

<< " maturity: " << exercise->lastDate() << "\n" \

<< "1st asset volatility: " << io::volatility(v1) << "\n" \

<< "2nd asset volatility: " << io::volatility(v2) << "\n" \

<< " correlation: " << rho << "\n\n" \

<< " expected " << greekName << ": " << expected << "\n" \

<< " calculated " << greekName << ": " << calculated << "\n"\

<< " error: " << error << "\n" \

<< " tolerance: " << tolerance);

#define REPORT_FAILURE2(greekName, exercise, s1, s2, q1, q2, r, today, \

v1, v2, expected, calculated, error, tolerance) \

FAIL_CHECK(exerciseTypeToString(exercise) << " " \

<< " European option with " \

<< " null pay off " << "\n" \

<< " spot1 value: " << s1 << "\n" \

<< " spot2 value: " << s2 << "\n" \

<< " strike: 0 " << "\n" \

<< " dividend yield 1: " << io::rate(q1) << "\n" \

<< " dividend yield 2: " << io::rate(q2) << "\n" \

<< " risk-free rate: " << io::rate(r) << "\n" \

<< " reference date: " << today << "\n" \

<< " maturity: " << exercise->lastDate() << "\n" \

<< " volatility 1: " << io::volatility(v1) << "\n\n" \

<< " volatility 2: " << io::volatility(v2) << "\n\n" \

<< " expected " << greekName << ": " << expected << "\n" \

<< " calculated " << greekName << ": " << calculated << "\n"\

<< " error: " << error << "\n" \

<< " tolerance: " << tolerance);

namespace {

struct MargrabeOptionTwoData {

Real s1;

Real s2;

Integer Q1;

Integer Q2;

Rate q1;

Rate q2;

Rate r;

Time t; // years

Volatility v1;

Volatility v2;

Real rho;

Real result;

Real delta1;

Real delta2;

Real gamma1;

Real gamma2;

Real theta;

Real rho_greek;

Real tol;

};

struct MargrabeAmericanOptionTwoData {

Real s1;

Real s2;

Integer Q1;

Integer Q2;

Rate q1;

Rate q2;

Rate r;

Time t; // years

Volatility v1;

Volatility v2;

Real rho;

Real result;

Real tol;

};

Integer timeToDays(Time t) {

// FLOATING_POINT_EXCEPTION

return Integer(t*360+0.5);

}

TEST_CASE("MargrabeOption_EuroExchangeTwoAssets", "[MargrabeOption]") {

INFO("Testing European one-asset-for-another option...");

Exchange-One-Asset-for-Another European Options

MargrabeOptionTwoData values[] = {

//Simplification : we assume that the option always exchanges S2 for S1

//s1, s2, Q1, Q2, q1, q2, r, t, v1, v2, rho, result,

//delta1, delta2, gamma1, gamma2, theta, rho, tol

// data from "given article p.52"

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.15, -0.50, 2.125, 0.841, -0.818, 0.112, 0.135, -2.043, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.20, -0.50, 2.199, 0.813, -0.784, 0.109, 0.132, -2.723, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.25, -0.50, 2.283, 0.788, -0.753, 0.105, 0.126, -3.419, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.15, 0.00, 2.045, 0.883, -0.870, 0.108, 0.131, -1.168, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.20, 0.00, 2.091, 0.857, -0.838, 0.112, 0.135, -1.698, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.25, 0.00, 2.152, 0.830, -0.805, 0.111, 0.134, -2.302, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.15, 0.50, 1.974, 0.946, -0.942, 0.079, 0.096, -0.126, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.20, 0.50, 1.989, 0.929, -0.922, 0.092, 0.111, -0.398, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.25, 0.50, 2.019, 0.902, -0.891, 0.104, 0.125, -0.838, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, -0.50, 2.762, 0.672, -0.602, 0.072, 0.087, -1.207, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, -0.50, 2.989, 0.661, -0.578, 0.064, 0.078, -1.457, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, -0.50, 3.228, 0.653, -0.557, 0.058, 0.070, -1.712, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, 0.00, 2.479, 0.695, -0.640, 0.085, 0.102, -0.874, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, 0.00, 2.650, 0.680, -0.616, 0.077, 0.093, -1.078, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, 0.00, 2.847, 0.668, -0.592, 0.069, 0.083, -1.302, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, 0.50, 2.138, 0.746, -0.713, 0.106, 0.128, -0.416, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, 0.50, 2.231, 0.728, -0.689, 0.099, 0.120, -0.550, 0.0, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, 0.50, 2.374, 0.707, -0.659, 0.090, 0.109, -0.741, 0.0, 1.0e-3},

//Quantity tests from Excel calcuations

{22.0, 10.0, 1, 2, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, 0.50, 2.138, 0.746, -1.426, 0.106, 0.255, -0.987, 0.0, 1.0e-3},

{11.0, 20.0, 2, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, 0.50, 2.231, 1.455, -0.689, 0.198, 0.120, 0.410, 0.0, 1.0e-3},

{11.0, 10.0, 2, 2, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, 0.50, 2.374, 1.413, -1.317, 0.181, 0.219, -0.336, 0.0, 1.0e-3}

};

DayCounter dc = Actual360();

Date today = Settings::instance().evaluationDate();

std::shared_ptr<SimpleQuote> spot1 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<SimpleQuote> spot2 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<SimpleQuote> qRate1 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<YieldTermStructure> qTS1 = flatRate(today, qRate1, dc);

std::shared_ptr<SimpleQuote> qRate2 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<YieldTermStructure> qTS2 = flatRate(today, qRate2, dc);

std::shared_ptr<SimpleQuote> rRate = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);

std::shared_ptr<SimpleQuote> vol1 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(today, vol1, dc);

std::shared_ptr<SimpleQuote> vol2 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<BlackVolTermStructure> volTS2 = flatVol(today, vol2, dc);

for (Size i=0; i<LENGTH(values); i++) {

Date exDate = today + Integer(values[i].t*360+0.5);

std::shared_ptr<Exercise> exercise = std::make_shared<EuropeanExercise>(exDate);

spot1 ->setValue(values[i].s1);

spot2 ->setValue(values[i].s2);

qRate1->setValue(values[i].q1);

qRate2->setValue(values[i].q2);

rRate ->setValue(values[i].r );

vol1 ->setValue(values[i].v1);

vol2 ->setValue(values[i].v2);

std::shared_ptr<BlackScholesMertonProcess> stochProcess1 =

std::make_shared<BlackScholesMertonProcess>(Handle<Quote>(spot1),

Handle<YieldTermStructure>(qTS1),

Handle<YieldTermStructure>(rTS),

Handle<BlackVolTermStructure>(volTS1));

std::shared_ptr<BlackScholesMertonProcess> stochProcess2 =

std::make_shared<BlackScholesMertonProcess>(Handle<Quote>(spot2),

Handle<YieldTermStructure>(qTS2),

Handle<YieldTermStructure>(rTS),

Handle<BlackVolTermStructure>(volTS2));

std::vector<std::shared_ptr<StochasticProcess1D> > procs;

procs.emplace_back(stochProcess1);

procs.emplace_back(stochProcess2);

Matrix correlationMatrix(2,2, values[i].rho);

for (Integer j=0; j < 2; j++) {

correlationMatrix[j][j] = 1.0;

}

std::shared_ptr<PricingEngine> engine =

std::make_shared<AnalyticEuropeanMargrabeEngine>(stochProcess1,

stochProcess2,

values[i].rho);

MargrabeOption margrabeOption(values[i].Q1, values[i].Q2, exercise);

// analytic engine

margrabeOption.setPricingEngine(engine);

Real calculated = margrabeOption.NPV();

Real expected = values[i].result;

Real error = std::fabs(calculated-expected);

Real tolerance = values[i].tol;

if (error > tolerance) {

REPORT_FAILURE("value", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

calculated = margrabeOption.delta1();

expected = values[i].delta1;

error= std::fabs(calculated-expected);

if (error>tolerance) {

REPORT_FAILURE("delta1", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

calculated = margrabeOption.delta2();

expected = values[i].delta2;

error= std::fabs(calculated-expected);

if (error>tolerance) {

REPORT_FAILURE("delta2", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

calculated = margrabeOption.gamma1();

expected = values[i].gamma1;

error= std::fabs(calculated-expected);

if (error>tolerance) {

REPORT_FAILURE("gamma1", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

calculated = margrabeOption.gamma2();

expected = values[i].gamma2;

error= std::fabs(calculated-expected);

if (error>tolerance) {

REPORT_FAILURE("gamma2", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

calculated = margrabeOption.theta();

expected = values[i].theta;

error= std::fabs(calculated-expected);

if (error>tolerance) {

REPORT_FAILURE("theta", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

calculated = margrabeOption.rho();

expected = values[i].rho_greek;

error= std::fabs(calculated-expected);

if (error>tolerance) {

REPORT_FAILURE("rho_greek", exercise,

values[i].s1, values[i].s2, values[i].Q1,

values[i].Q2, values[i].q1, values[i].q2,

values[i].r, today, values[i].v1,

values[i].v2, values[i].rho, expected,

calculated, error, tolerance);

}

TEST_CASE("MargrabeOption_Greeks", "[MargrabeOption]") {

INFO("Testing analytic European exchange option greeks...");

SavedSettings backup;

std::map<std::string,Real> calculated, expected, tolerance;

tolerance["delta1"] = 1.0e-5;

tolerance["delta2"] = 1.0e-5;

tolerance["gamma1"] = 1.0e-5;

tolerance["gamma2"] = 1.0e-5;

tolerance["theta"] = 1.0e-5;

tolerance["rho"] = 1.0e-5;

Real underlyings1[] = { 22.0 };

Real underlyings2[] = { 20.0 };

Rate qRates1[] = { 0.06, 0.16, 0.04 };

Rate qRates2[] = { 0.04, 0.14, 0.02 };

Rate rRates[] = { 0.1, 0.2, 0.08 };

Time residualTimes[] = { 0.1, 0.5 };

Volatility vols1[] = { 0.20 };

Volatility vols2[] = { 0.15, 0.20, 0.25};

DayCounter dc = Actual360();

Date today = Date::todaysDate();

Settings::instance().evaluationDate() = today;

std::shared_ptr<SimpleQuote> spot1 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<SimpleQuote> spot2 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<SimpleQuote> qRate1 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<YieldTermStructure> qTS1 = flatRate(qRate1, dc);

std::shared_ptr<SimpleQuote> qRate2 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<YieldTermStructure> qTS2 = flatRate(qRate2, dc);

std::shared_ptr<SimpleQuote> rRate = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<YieldTermStructure> rTS = flatRate(rRate, dc);

std::shared_ptr<SimpleQuote> vol1 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<BlackVolTermStructure> volTS1 = flatVol(vol1, dc);

std::shared_ptr<SimpleQuote> vol2 = std::make_shared<SimpleQuote>(0.0);

std::shared_ptr<BlackVolTermStructure> volTS2 = flatVol(vol2, dc);

for (Size k=0; k<LENGTH(residualTimes); k++) {

Date exDate = today + timeToDays(residualTimes[k]);

std::shared_ptr<Exercise> exercise = std::make_shared<EuropeanExercise>(exDate);

// option to check

std::shared_ptr<BlackScholesMertonProcess> stochProcess1 =

std::make_shared<BlackScholesMertonProcess>(Handle<Quote>(spot1),

Handle<YieldTermStructure>(qTS1),

Handle<YieldTermStructure>(rTS),

Handle<BlackVolTermStructure>(volTS1));

std::shared_ptr<BlackScholesMertonProcess> stochProcess2 =

std::make_shared<BlackScholesMertonProcess>(Handle<Quote>(spot2),

Handle<YieldTermStructure>(qTS2),

Handle<YieldTermStructure>(rTS),

Handle<BlackVolTermStructure>(volTS2));

std::vector<std::shared_ptr<StochasticProcess1D> > procs;

procs.emplace_back(stochProcess1);

procs.emplace_back(stochProcess2);

//The correlation -0.5 can be different real between -1 and 1 for more tests

Real correlation = -0.5;

Matrix correlationMatrix(2,2, correlation);

for (Integer j=0; j < 2; j++) {

correlationMatrix[j][j] = 1.0;

std::shared_ptr<PricingEngine> engine =

std::make_shared<AnalyticEuropeanMargrabeEngine>(stochProcess1,

stochProcess2,

correlation);

//The quantities of S1 and S2 can be different from 1 & 1 for more tests

MargrabeOption margrabeOption(1, 1, exercise);

// analytic engine

margrabeOption.setPricingEngine(engine);

for (Size l=0; l<LENGTH(underlyings1); l++) {

for (Size m=0; m<LENGTH(qRates1); m++) {

for (Size n=0; n<LENGTH(rRates); n++) {

for (Size p=0; p<LENGTH(vols1); p++) {

Real u1 = underlyings1[l],

u2 = underlyings2[l],

Rate q1 = qRates1[m],

q2 = qRates2[m],

r = rRates[n];

Volatility v1 = vols1[p],

v2 = vols2[p];

spot1 ->setValue(u1);

spot2 ->setValue(u2);

qRate1->setValue(q1);

qRate2->setValue(q2);

rRate ->setValue(r);

vol1 ->setValue(v1);

vol2 ->setValue(v2);

Real value = margrabeOption.NPV();

calculated["delta1"] = margrabeOption.delta1();

calculated["delta2"] = margrabeOption.delta2();

calculated["gamma1"] = margrabeOption.gamma1();

calculated["gamma2"] = margrabeOption.gamma2();

calculated["theta"] = margrabeOption.theta();

calculated["rho"] = margrabeOption.rho();

if (value > spot1->value()*1.0e-5) {

// perturb spot and get delta1 and gamma

u = u1;

Real du = u*1.0e-4;

spot1->setValue(u+du);

Real value_p = margrabeOption.NPV(),

delta_p = margrabeOption.delta1();

spot1->setValue(u-du);

Real value_m = margrabeOption.NPV(),

delta_m = margrabeOption.delta1();

spot1->setValue(u);

expected["delta1"] = (value_p - value_m)/(2*du);

expected["gamma1"] = (delta_p - delta_m)/(2*du);

u = u2;

spot2->setValue(u+du);

value_p = margrabeOption.NPV();

delta_p = margrabeOption.delta2();

spot2->setValue(u-du);

value_m = margrabeOption.NPV();

delta_m = margrabeOption.delta2();

spot2->setValue(u);

expected["delta2"] = (value_p - value_m)/(2*du);

expected["gamma2"] = (delta_p - delta_m)/(2*du);

// perturb rates and get rho

Spread dr = r*1.0e-4;

rRate->setValue(r+dr);

value_p = margrabeOption.NPV();

rRate->setValue(r-dr);

value_m = margrabeOption.NPV();

rRate->setValue(r);

expected["rho"] = (value_p - value_m)/(2*dr);

// perturb date and get theta

Time dT = dc.yearFraction(today-1, today+1);

Settings::instance().evaluationDate() = today-1;

value_m = margrabeOption.NPV();

Settings::instance().evaluationDate() = today+1;

value_p = margrabeOption.NPV();

Settings::instance().evaluationDate() = today;

expected["theta"] = (value_p - value_m)/dT;

// compare

std::map<std::string,Real>::iterator it;

for (it = calculated.begin();

it != calculated.end(); ++it) {

std::string greek = it->first;

Real expct = expected [greek],

calcl = calculated[greek],

tol = tolerance [greek];

Real error = relativeError(expct,calcl,u1);

if (error>tol) {

REPORT_FAILURE2(greek, exercise,

u1, u2, q1, q2, r, today, v1, v2,

expct, calcl, error, tol);

}

TEST_CASE("MargrabeOption_AmericanExchangeTwoAssets", "[MargrabeOption]") {

INFO("Testing American one-asset-for-another option...");

MargrabeAmericanOptionTwoData values[] = {

//Simplification : we assume that the option always exchanges S2 for S1

//s1, s2, Q1, Q2, q1, q2, r, t, v1, v2, rho, result, tol

// data from Haug

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.15, -0.50, 2.1357, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.20, -0.50, 2.2074, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.25, -0.50, 2.2902, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.15, 0.00, 2.0592, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.20, 0.00, 2.1032, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.25, 0.00, 2.1618, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.15, 0.50, 2.0001, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.20, 0.50, 2.0110, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.10, 0.20, 0.25, 0.50, 2.0359, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, -0.50, 2.8051, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, -0.50, 3.0288, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, -0.50, 3.2664, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, 0.00, 2.5282, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, 0.00, 2.6945, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, 0.00, 2.8893, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.15, 0.50, 2.2053, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.20, 0.50, 2.2906, 1.0e-3},

{22.0, 20.0, 1, 1, 0.06, 0.04, 0.10, 0.50, 0.20, 0.25, 0.50, 2.4261, 1.0e-3}