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SABRInterpolation excel vs linux differences‏‏

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piers august

SABRInterpolation excel vs linux differences‏‏

Hi All

I'm getting significant differences (about 0.2 vol in some places) between the
SABR interpolation in excel and linux for release 0.9.7.

For the same input data below, I'm finding alpha, rho and nu have
small differences giving about a 0.2% difference between the interpolated
curves at the money and elsewhere. Beta is fixed at 1. They should be
bang on identical right?

I'm probably doing something wrong - could anyone make any suggestions
as where to go from here to nail it?

The windows computer is a 64bit athlon and the linux is 64 bit intel btw.

cheers,
Piers

	ql version	0.9.7
		=qlSABRInterpolation(,G11:G25,H11:H25,C9,D9,,1,,,,TRUE)
		obj_00000#0300

	sabr	excel outputted params	linux outputted params
	alpha	0.207442	alpha=0.205598
	beta	1.000	beta=1
	rho	-0.389061	rho=-0.394466
	nu	4.0176907	nu=4.16071
	tau	0.0305936	tau=0.0305936
	fwd	3826.25	forward=3826.25

input strikes	input vols	sabr excel	sabr linux	linux sabr – excel sabr
3400	0.368624622242282	0.354604292668933	0.359178	0.46%
3500	0.321037653604485	0.318275231545040	0.321538	0.33%
3550	0.299501682381891	0.300303657851484	0.302877	0.26%
3600	0.279643985001476	0.282569848982833	0.284426	0.19%
3650	0.261615469316373	0.265235824583730	0.266342	0.11%
3700	0.245580215704548	0.248582585887819	0.248912	0.03%
3750	0.231712426785790	0.233087499691996	0.232633	-0.05%
3800	0.220204595933114	0.219519711494862	0.218336	-0.12%
3850	0.211257342746155	0.208967123228945	0.207239	-0.17%
3900	0.205096538218055	0.202578259521284	0.200651	-0.19%
3950	0.201943526100016	0.200931625388894	0.199217	-0.17%
4000	0.202049566014993	0.203604828891783	0.202397	-0.12%
4050	0.205673850628091	0.209520147602468	0.208939	-0.06%
4100	0.213089315877449	0.217573188533236	0.217628	0.01%
4200	0.240440352051281	0.237060304926802	0.238270	0.12%

#include <ql/quantlib.hpp>
#include <iostream>
#include <vector>

using namespace QuantLib;
using namespace std;

int main(int argc, char *argv[])
{
    Real forward = 3826.25;
    Time tau = 0.0305936;

    vector<double> strikes;
    vector<double> vols;

    strikes.push_back(3400); vols.push_back(0.368624622242282);
    strikes.push_back(3500); vols.push_back(0.321037653604485);
    strikes.push_back(3550); vols.push_back(0.299501682381891);
    strikes.push_back(3600); vols.push_back(0.279643985001476);
    strikes.push_back(3650); vols.push_back(0.261615469316373);
    strikes.push_back(3700); vols.push_back(0.245580215704548);
    strikes.push_back(3750); vols.push_back(0.231712426785790);
    strikes.push_back(3800); vols.push_back(0.220204595933114);
    strikes.push_back(3850); vols.push_back(0.211257342746155);
    strikes.push_back(3900); vols.push_back(0.205096538218055);
    strikes.push_back(3950); vols.push_back(0.201943526100016);
    strikes.push_back(4000); vols.push_back(0.202049566014993);
    strikes.push_back(4050); vols.push_back(0.205673850628091);
    strikes.push_back(4100); vols.push_back(0.213089315877449);
    strikes.push_back(4200); vols.push_back(0.240440352051281);



    SABRInterpolation sabr(    strikes.begin(),
                strikes.end(),
                vols.begin(),
                tau,
                forward,
                Null<Real>(),
                1,
                Null<Real>(),
                Null<Real>(),
                false,
                true,
                false,
                false ) ;

    sabr.update();

    cout << "forward=" <<sabr.forward() << endl;
    cout << "expiry=" << sabr.expiry() << endl;
    cout << "alpha=" << sabr.alpha() << endl;
    cout << "beta=" << sabr.beta() << endl;
    cout << "nu=" << sabr.nu() << endl;
    cout << "rho=" << sabr.rho() << endl;
    cout << "rmsError=" << sabr.rmsError() << endl;
    cout << "atmVol=" << sabr(forward) << endl;
    cout << "endCriteria=" << sabr.endCriteria() << endl;

    for( unsigned int i = 0; i < strikes.size(); ++i )
        cout << strikes[i] << " " << vols[i] << " " << sabr( strikes[i] ) << endl;


    return 0;
}

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piers august

Re: SABRInterpolation excel vs linux differences‏‏

Thanks for your suggestion Joe, the problem was due to the differing default value for the vegaWeightings arg across the c++ and excel versions!

Piers

Excel
Parameters:

	ObjectId	id of object to be created
	XArray	x array.
	YArray	y array.
	Expiry	expiry time in years.
	Forward	forward.
	Alpha	alpha (fixed value or guess). Default value = QuantLib::Null<QuantLib::Real>().
	Beta	beta (fixed value or guess). Default value = QuantLib::Null<QuantLib::Real>().
	Nu	nu (fixed value or guess). Default value = QuantLib::Null<QuantLib::Real>().
	Rho	rho (fixed value or guess). Default value = QuantLib::Null<QuantLib::Real>().
	AlphaIsFixed	TRUE if the alpha value provided is to be kept fixed, FALSE if it is just a guess. Default value = false.
	BetaIsFixed	TRUE if the beta value provided is to be kept fixed, FALSE if it is just a guess. Default value = false.
	NuIsFixed	TRUE if the nu value provided is to be kept fixed, FALSE if it is just a guess. Default value = false.
	RhoIsFixed	TRUE if the rho value provided is to be kept fixed, FALSE if it is just a guess. Default value = false.
	VegaWeighted	TRUE if the interpolation is weighted using options Vega. Default value = true.
	EndCriteria	EndCriteria object ID. Default value = .
	OptimizationMethod	OptimizationMethod object ID. Default value = .
	Permanent	object permanent/nonpermanent
	Trigger	dependency tracking trigger
	Overwrite	overwrite flag

c++
SABRInterpolation (const I1 &xBegin, const I1 &xEnd, const I2 &yBegin, Time t, const Real &forward, Real alpha, Real beta, Real nu, Real rho, bool alphaIsFixed, bool betaIsFixed, bool nuIsFixed, bool rhoIsFixed, bool vegaWeighted=false, const boost::shared_ptr< EndCriteria > &endCriteria=boost::shared_ptr< EndCriteria >(), const boost::shared_ptr< OptimizationMethod > &optMethod=boost::shared_ptr< OptimizationMethod >())

Date: Mon, 7 Dec 2009 16:41:13 -0500
Subject: Re: [Quantlib-users] SABRInterpolation excel vs linux differences‏‏
From: [hidden email]
To: [hidden email]

The floating point rounding mode (fegetround()/fesetround()) and math optimization differences
(gcc -mieee-fp and cl.exe /Op) are some usual suspects.

2009/12/7 piers august <[hidden email]>

Hi All

I'm getting significant differences (about 0.2 vol in some places) between the
SABR interpolation in excel and linux for release 0.9.7.

For the same input data below, I'm finding alpha, rho and nu have
small differences giving about a 0.2% difference between the interpolated
curves at the money and elsewhere. Beta is fixed at 1. They should be
bang on identical right?

I'm probably doing something wrong - could anyone make any suggestions
as where to go from here to nail it?

The windows computer is a 64bit athlon and the linux is 64 bit intel btw.

cheers,
Piers

ql version 0.9.7

=qlSABRInterpolation(,G11:G25,H11:H25,C9,D9,,1,,,,TRUE)

obj_00000#0300

sabr excel outputted params linux outputted params

alpha 0.207442 alpha=0.205598

beta 1.000 beta=1

rho -0.389061 rho=-0.394466

nu 4.0176907 nu=4.16071

tau 0.0305936 tau=0.0305936

fwd 3826.25 forward=3826.25

input strikes input vols sabr excel sabr linux linux sabr – excel sabr

3400 0.368624622242282 0.354604292668933 0.359178 0.46%

3500 0.321037653604485 0.318275231545040 0.321538 0.33%

3550 0.299501682381891 0.300303657851484 0.302877 0.26%

3600 0.279643985001476 0.282569848982833 0.284426 0.19%

3650 0.261615469316373 0.265235824583730 0.266342 0.11%

3700 0.245580215704548 0.248582585887819 0.248912 0.03%

3750 0.231712426785790 0.233087499691996 0.232633 -0.05%

3800 0.220204595933114 0.219519711494862 0.218336 -0.12%

3850 0.211257342746155 0.208967123228945 0.207239 -0.17%

3900 0.205096538218055 0.202578259521284 0.200651 -0.19%

3950 0.201943526100016 0.200931625388894 0.199217 -0.17%

4000 0.202049566014993 0.203604828891783 0.202397 -0.12%

4050 0.205673850628091 0.209520147602468 0.208939 -0.06%

4100 0.213089315877449 0.217573188533236 0.217628 0.01%

4200 0.240440352051281 0.237060304926802 0.238270 0.12%

#include <ql/quantlib.hpp>
#include <iostream>
#include <vector>

using namespace QuantLib;
using namespace std;

int main(int argc, char *argv[])
{
    Real forward = 3826.25;
    Time tau = 0.0305936;

    vector<double> strikes;
    vector<double> vols;

    strikes.push_back(3400); vols.push_back(0.368624622242282);
    strikes.push_back(3500); vols.push_back(0.321037653604485);
    strikes.push_back(3550); vols.push_back(0.299501682381891);
    strikes.push_back(3600); vols.push_back(0.279643985001476);
    strikes.push_back(3650); vols.push_back(0.261615469316373);
    strikes.push_back(3700); vols.push_back(0.245580215704548);
    strikes.push_back(3750); vols.push_back(0.231712426785790);
    strikes.push_back(3800); vols.push_back(0.220204595933114);
    strikes.push_back(3850); vols.push_back(0.211257342746155);
    strikes.push_back(3900); vols.push_back(0.205096538218055);
    strikes.push_back(3950); vols.push_back(0.201943526100016);
    strikes.push_back(4000); vols.push_back(0.202049566014993);
    strikes.push_back(4050); vols.push_back(0.205673850628091);
    strikes.push_back(4100); vols.push_back(0.213089315877449);
    strikes.push_back(4200); vols.push_back(0.240440352051281);



    SABRInterpolation sabr(    strikes.begin(),
                strikes.end(),
                vols.begin(),
                tau,
                forward,
                Null<Real>(),
                1,
                Null<Real>(),
                Null<Real>(),
                false,
                true,
                false,
                false ) ;

    sabr.update();

    cout << "forward=" <<sabr.forward() << endl;
    cout << "expiry=" << sabr.expiry() << endl;
    cout << "alpha=" << sabr.alpha() << endl;
    cout << "beta=" << sabr.beta() << endl;
    cout << "nu=" << sabr.nu() << endl;
    cout << "rho=" << sabr.rho() << endl;
    cout << "rmsError=" << sabr.rmsError() << endl;
    cout << "atmVol=" << sabr(forward) << endl;
    cout << "endCriteria=" << sabr.endCriteria() << endl;

    for( unsigned int i = 0; i < strikes.size(); ++i )
        cout << strikes[i] << " " << vols[i] << " " << sabr( strikes[i] ) << endl;


    return 0;
}

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