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strange output from zeroRate() ?

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Venkatesh Rao

strange output from zeroRate() ?

Hi, the zeroRate() function (applied to YieldTermStructure object) appears to be returning zero rates that are too large. To illustrate, I constructed a simple example based largely on code snippets from /testsuite/piecewiseyieldcurve.cpp. In brief:

* Input a flat term structure of deposit + swap rates of 5.0% out to 30 years.

Datum depositData[] = { { 1, Weeks, 5.0 }};

Datum swapData[] = {

{ 1, Years, 5.0 }, { 2, Years, 5.0 }, { 3, Years, 5.0 },

.... { 30, Years, 5.0 } };

* Very minor changes to settings in CommonVars, to construction of "rates" and "instruments" vectors [adpated to USDLibor rather than Euribor---conclusions are unaffected by that switch].

-> all the info from this stage goes into "vars".

* PiecewiseYieldCurve set up as follows:

template <class T, class I, template<class C> class B>

CommonVars CurveMake(CommonVars& vars,

const I& interpolator = I(), Real tolerance = 1.0e-9) {

vars.termStructure = boost::shared_ptr<YieldTermStructure>(new

PiecewiseYieldCurve<T,I,B>(vars.settlement, vars.instruments,

Actual360(), interpolator));

...etc....

* Called CurveMake as follows (from main):

CommonVars varsOut =

CurveMake<ZeroYield,Linear,IterativeBootstrap>(vars);

* Retrieve curve info via:

boost::shared_ptr<YieldTermStructure> yc= varsOut.termStructure;

* For output, set up vector of target dates (rTdates), and called zeroRate() and discount(); & computed implied zero from discount() as follows:

d0=varsOut.settlement;

for (Size i=0; i<rtDates.size(); i++) {

Real rx, df; dx=rtDates[i];

rx = Rate(yc->zeroRate(dx,dc, Simple, Annual, true));

df = yc->discount(dx, true);

Real zeroFromDf= -log(df)/((dx-d0)/365.);

wtfil2 << std::setw(7) <<std::setprecision(2) << (dx-d0)/365.

<< std::setw(10) << std::setprecision(4) << rx

<<std::setw(10) << std::setprecision(6) << df

<< std::setw(10) << std::setprecision(4) << zeroFromDf

<<std::endl;

}

* OUTPUT:

[DayCounter= Actual/Actual (ISDA]

Implied

Zero rate from

t (Yrs) zeroRate() discount() discount()

0.5 0.0507 0.975209 0.05007

1 0.05069 0.951751 0.04945

2 0.052 0.905711 0.04945

5 0.05614 0.780837 0.04945

10 0.06402 0.609626 0.04945

20 0.08447 0.371827 0.04943

30 0.1138 0.226552 0.04946

35 0.1331 0.176776 0.04948

********************************************

So, the implied zero from discount() is close to (but not dead on) the expected 5.0%, but the zeroRate() seems to drift away considerably. Similar patterns are observed after toggling various settings and parameters (e.g., DayCounters, call CurveMake with Discount instead of ZeroYield, etc.)

Am I doing something wrong or misunderstanding what zeroRate() is supposed to be returning?

Any help appreciated. Thanks

P.C. Venkatesh
Stress Testing
Division of Banking Supervision & Regulation
Board of Governors of the Federal Reserve System
vox: 202 452 3847
email: [hidden email]

------------------------------------------------------------------------------

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QuantLib-users mailing list
[hidden email]
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Smith, Dale (Norcross)

Re: strange output from zeroRate() ?

Hi,

It would help if you could post a working program. I am also interested in understanding this as well.

Thanks,

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

From: Venkatesh Rao [mailto:[hidden email]]
Sent: Friday, April 04, 2014 8:30 AM
To: [hidden email]
Cc: Venkatesh Rao
Subject: [Quantlib-users] strange output from zeroRate() ?

* Input a flat term structure of deposit + swap rates of 5.0% out to 30 years.

Datum depositData[] = { { 1, Weeks, 5.0 }};

Datum swapData[] = {

{ 1, Years, 5.0 }, { 2, Years, 5.0 }, { 3, Years, 5.0 },

.... { 30, Years, 5.0 } };

* Very minor changes to settings in CommonVars, to construction of "rates" and "instruments" vectors [adpated to USDLibor rather than Euribor---conclusions are unaffected by that switch].

-> all the info from this stage goes into "vars".

* PiecewiseYieldCurve set up as follows:

template <class T, class I, template<class C> class B>

CommonVars CurveMake(CommonVars& vars,

const I& interpolator = I(), Real tolerance = 1.0e-9) {

vars.termStructure = boost::shared_ptr<YieldTermStructure>(new

PiecewiseYieldCurve<T,I,B>(vars.settlement, vars.instruments,

Actual360(), interpolator));

...etc....

* Called CurveMake as follows (from main):

CommonVars varsOut =

CurveMake<ZeroYield,Linear,IterativeBootstrap>(vars);

* Retrieve curve info via:

boost::shared_ptr<YieldTermStructure> yc= varsOut.termStructure;

* For output, set up vector of target dates (rTdates), and called zeroRate() and discount(); & computed implied zero from discount() as follows:

d0=varsOut.settlement;

for (Size i=0; i<rtDates.size(); i++) {

Real rx, df; dx=rtDates[i];

rx = Rate(yc->zeroRate(dx,dc, Simple, Annual, true));

df = yc->discount(dx, true);

Real zeroFromDf= -log(df)/((dx-d0)/365.);

wtfil2 << std::setw(7) <<std::setprecision(2) << (dx-d0)/365.

<< std::setw(10) << std::setprecision(4) << rx

<<std::setw(10) << std::setprecision(6) << df

<< std::setw(10) << std::setprecision(4) << zeroFromDf

<<std::endl;

}

* OUTPUT:

[DayCounter= Actual/Actual (ISDA]

Implied

Zero rate from

t (Yrs) zeroRate() discount() discount()

0.5 0.0507 0.975209 0.05007

1 0.05069 0.951751 0.04945

2 0.052 0.905711 0.04945

5 0.05614 0.780837 0.04945

10 0.06402 0.609626 0.04945

20 0.08447 0.371827 0.04943

30 0.1138 0.226552 0.04946

35 0.1331 0.176776 0.04948

********************************************

Am I doing something wrong or misunderstanding what zeroRate() is supposed to be returning?

Any help appreciated. Thanks

P.C. Venkatesh
Stress Testing
Division of Banking Supervision & Regulation
Board of Governors of the Federal Reserve System
vox: 202 452 3847
email: [hidden email]

Luigi Ballabio

Re: strange output from zeroRate() ?

Hello,
you're asking for zero rates with Simple compounding, that is, df = 1/(1+rT). Use Continuous instead.

Luigi

On Apr 4, 2014 3:00 PM, "Smith, Dale (Norcross)" <[hidden email]> wrote:

Hi,

It would help if you could post a working program. I am also interested in understanding this as well.

Thanks,

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

From: Venkatesh Rao [mailto:[hidden email]]
Sent: Friday, April 04, 2014 8:30 AM
To: [hidden email]
Cc: Venkatesh Rao
Subject: [Quantlib-users] strange output from zeroRate() ?

Hi, the zeroRate() function (applied to YieldTermStructure object) appears to be returning zero rates that are too large. To illustrate, I constructed a simple example based largely on code snippets from /testsuite/piecewiseyieldcurve.cpp. In brief:

* Input a flat term structure of deposit + swap rates of 5.0% out to 30 years.

    Datum depositData[] = { { 1, Weeks, 5.0 }};

    Datum swapData[] = {

        { 1, Years, 5.0 }, { 2, Years, 5.0 }, { 3, Years, 5.0 },

        ....         { 30, Years, 5.0 }     };

* Very minor changes to settings in CommonVars, to construction of "rates" and "instruments" vectors [adpated to USDLibor rather than Euribor---conclusions are unaffected by that switch].

-> all the info from this stage goes into "vars".

*   PiecewiseYieldCurve set up as follows:

    template <class T, class I, template<class C> class B>

    CommonVars CurveMake(CommonVars& vars,

           const I& interpolator = I(), Real tolerance = 1.0e-9) {

        vars.termStructure = boost::shared_ptr<YieldTermStructure>(new

            PiecewiseYieldCurve<T,I,B>(vars.settlement, vars.instruments,

                                       Actual360(), interpolator));

     ...etc....

* Called CurveMake as follows (from main):

     CommonVars varsOut =

      CurveMake<ZeroYield,Linear,IterativeBootstrap>(vars);

* Retrieve curve info via:

     boost::shared_ptr<YieldTermStructure> yc= varsOut.termStructure;

* For output, set up vector of target dates (rTdates), and called zeroRate() and discount(); & computed implied zero from discount() as follows:

     d0=varsOut.settlement;

     for (Size i=0; i<rtDates.size(); i++) {

         Real rx, df;     dx=rtDates[i];

         rx = Rate(yc->zeroRate(dx,dc, Simple, Annual, true));

         df = yc->discount(dx, true);

         Real zeroFromDf= -log(df)/((dx-d0)/365.);

         wtfil2 << std::setw(7) <<std::setprecision(2) << (dx-d0)/365.

                << std::setw(10) << std::setprecision(4) << rx

                <<std::setw(10) << std::setprecision(6) << df

                << std::setw(10) << std::setprecision(4) << zeroFromDf

                <<std::endl;

     }

* OUTPUT:

[DayCounter= Actual/Actual (ISDA]

                                                         Implied

                                                        Zero rate from

t (Yrs) zeroRate() discount() discount()

    0.5       0.0507 0.975209     0.05007

      1      0.05069 0.951751     0.04945

      2        0.052 0.905711     0.04945

      5      0.05614 0.780837     0.04945

     10      0.06402 0.609626     0.04945

     20      0.08447 0.371827     0.04943

     30       0.1138 0.226552     0.04946

     35       0.1331 0.176776     0.04948

********************************************

So, the implied zero from discount() is close to (but not dead on) the expected 5.0%, but the zeroRate() seems to drift away considerably. Similar patterns are observed after toggling various settings and parameters (e.g., DayCounters, call CurveMake with Discount instead of ZeroYield, etc.)

Am I doing something wrong or misunderstanding what zeroRate() is supposed to be returning?

Any help appreciated.   Thanks

P.C. Venkatesh
Stress Testing
Division of Banking Supervision & Regulation
Board of Governors of the Federal Reserve System
vox: 202 452 3847
email: [hidden email]

------------------------------------------------------------------------------

_______________________________________________
QuantLib-users mailing list
[hidden email]
https://lists.sourceforge.net/lists/listinfo/quantlib-users

Venkatesh Rao

Re: strange output from zeroRate() ?

Ah yes. Thought I’d toggled that too but apparently not. Here’re the revised #’s, which are looking MUCH BETTER J was going down the non-obvious rabbit holes!! Much obliged

[Changed rx to; rx = Rate(yc->zeroRate(dx,dc, Continuous, Annual, true));]

Implied

zero from

t (Yrs) zeroRate() discount() discount()

0.5 0.05007 0.975209 0.05007

1 0.04945 0.951751 0.04945

2 0.04947 0.905711 0.04945

5 0.04948 0.780837 0.04945

10 0.04948 0.609626 0.04945

20 0.04947 0.371827 0.04943

30 0.04949 0.226552 0.04946

35 0.04951 0.176776 0.04948

********************************************

From: Luigi Ballabio [mailto:[hidden email]]
Sent: Friday, April 04, 2014 9:55 AM
To: Smith, Dale (Norcross)
Cc: QuantLib users; Venkatesh Rao
Subject: Re: [Quantlib-users] strange output from zeroRate() ?

Hello,
you're asking for zero rates with Simple compounding, that is, df = 1/(1+rT). Use Continuous instead.

Luigi

On Apr 4, 2014 3:00 PM, "Smith, Dale (Norcross)" <[hidden email]> wrote:

Hi,

It would help if you could post a working program. I am also interested in understanding this as well.

Thanks,

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

From: Venkatesh Rao [mailto:[hidden email]]
Sent: Friday, April 04, 2014 8:30 AM
To: [hidden email]
Cc: Venkatesh Rao
Subject: [Quantlib-users] strange output from zeroRate() ?

* Input a flat term structure of deposit + swap rates of 5.0% out to 30 years.

Datum depositData[] = { { 1, Weeks, 5.0 }};

Datum swapData[] = {

{ 1, Years, 5.0 }, { 2, Years, 5.0 }, { 3, Years, 5.0 },

.... { 30, Years, 5.0 } };

* Very minor changes to settings in CommonVars, to construction of "rates" and "instruments" vectors [adpated to USDLibor rather than Euribor---conclusions are unaffected by that switch].

-> all the info from this stage goes into "vars".

* PiecewiseYieldCurve set up as follows:

template <class T, class I, template<class C> class B>

CommonVars CurveMake(CommonVars& vars,

const I& interpolator = I(), Real tolerance = 1.0e-9) {

vars.termStructure = boost::shared_ptr<YieldTermStructure>(new

PiecewiseYieldCurve<T,I,B>(vars.settlement, vars.instruments,

Actual360(), interpolator));

...etc....

* Called CurveMake as follows (from main):

CommonVars varsOut =

CurveMake<ZeroYield,Linear,IterativeBootstrap>(vars);

* Retrieve curve info via:

boost::shared_ptr<YieldTermStructure> yc= varsOut.termStructure;

* For output, set up vector of target dates (rTdates), and called zeroRate() and discount(); & computed implied zero from discount() as follows:

d0=varsOut.settlement;

for (Size i=0; i<rtDates.size(); i++) {

Real rx, df; dx=rtDates[i];

rx = Rate(yc->zeroRate(dx,dc, Simple, Annual, true));

df = yc->discount(dx, true);

Real zeroFromDf= -log(df)/((dx-d0)/365.);

wtfil2 << std::setw(7) <<std::setprecision(2) << (dx-d0)/365.

<< std::setw(10) << std::setprecision(4) << rx

<<std::setw(10) << std::setprecision(6) << df

<< std::setw(10) << std::setprecision(4) << zeroFromDf

<<std::endl;

}

* OUTPUT:

[DayCounter= Actual/Actual (ISDA]

Implied

Zero rate from

t (Yrs) zeroRate() discount() discount()

0.5 0.0507 0.975209 0.05007

1 0.05069 0.951751 0.04945

2 0.052 0.905711 0.04945

5 0.05614 0.780837 0.04945

10 0.06402 0.609626 0.04945

20 0.08447 0.371827 0.04943

30 0.1138 0.226552 0.04946

35 0.1331 0.176776 0.04948

********************************************

Am I doing something wrong or misunderstanding what zeroRate() is supposed to be returning?

Any help appreciated. Thanks

P.C. Venkatesh
Stress Testing
Division of Banking Supervision & Regulation
Board of Governors of the Federal Reserve System
vox: 202 452 3847
email: [hidden email]