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Yield, Macaulay duration and Convexity calculation for Notes/Bonds

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Senevi J Kankanamge Don

Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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Smith, Dale (Norcross)

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Thanks for posting your code. It’s refreshing to see someone actually get this close to Bloomberg’s results. I salute you, as I know how hard it is to get this far. What yield curve are you using on Bloomberg – I25? How are you building your yield curve in QuantLib?

Based on my own experience, I would say you are very close to Bloomberg. I suspect it’s simply not worth chasing down the discrepancy, unless you want to fully investigate differences in

· Day counts

· Business rules (modified following, etc)

· Yield curve interpolation

· Compounding

· Max evaluations

· Etc

In other words, subtle differences in, say, Actual/Actual implementations between QuantLib and Bloomberg may be causing these small differences. Is it really worth chasing them down when you can’t necessarily change them to match the Bloomberg implementation?

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

From: Senevi J Kankanamge Don [mailto:[hidden email]]
Sent: Monday, November 04, 2013 10:25 AM
To: [hidden email]
Subject: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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Jean-Mathieu Vermosen

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

In reply to this post by Senevi J Kankanamge Don

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

you passed to the FixedRateBond constructor is not creating discrepancies in the cash-flow table (Just checked the code, it’s used in FixedRateLeg class for cash-flow generation). Otherwise you would prefer to compare to the true yield under the YA screen (after turning the flag to Following: ModifiedFollowing is for the swap guy).

The duration/convexity figures looks quite far from there target. As far as I remember Bloomberg is not adjusting for convention across bonds of different setup (except for the frequency in some screens). Then it might requires further investigation or to contact our friends from the hep desk to check the convention behind...

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg                          QuantLib
Yield                                      0.302775                              0.3027679582
Macaulay Duration          1.928                                     1.9129221698
Convexity                            0.047                                     0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

        double ql_price = 99.8984375;

        Date settlementDate = Date(25, Oct, 2013);
        Date firstCouponDate = Date(31, Mar, 2014);
        Date datedDate = Date(30, Sep, 2013);
        Date maturityDate = Date(30, Sep, 2015);

        //
        // Parameters required to define the bond
        //
        Natural settlementDays = 0;
        Real faceAmount = 100;
        DayCounter bondDayCount = ActualActual(ActualActual::Bond);
        BusinessDayConvention paymentConvention = ModifiedFollowing;
        Real redemption = 100.0;
        Compounding compoundingMethod = SimpleThenCompounded;
        DateGeneration::Rule dateGeneration = DateGeneration::Forward;
        Frequency frequency = Semiannual;
        Real accuracy = 1.0e-11;
        Size maxEvaluations = 100;

        //
        // Create the Schedule
        //
        Schedule fixedBondSchedule(
                                    datedDate,                                  // Dated Date
                                    maturityDate,                               // Maturity Date
                                    Period(Semiannual),                         // Period
                                    UnitedStates(UnitedStates::GovernmentBond), // Calendar
                                    Unadjusted,                                 // BusinessDayConvention - convention
                                    Unadjusted,                                 // BusinessDayConvention - terminationDateConvention
                                    dateGeneration,                             // DateGeneration::Rule rule
                                    false,                                      // endOfMonth
                                    firstCouponDate);                           // First Date

        //
        // Create the Fixed Rate Bond
        //
        FixedRateBond bond(
                            settlementDays,                        // Settlement Days
                            faceAmount,                            // Face Amount
                            fixedBondSchedule,                     // Schedule
                            std::vector<Rate>(1, ql_coupon),       // Coupons
                            bondDayCount,                          // DayCounter
                            paymentConvention,                     // BusinessDayConvention
                            redemption);                           // Redemption

        Real ql_yield       = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

        InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );
        Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

        Compounding compoundingMethod4Duration = Compounded;
        Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks
-Senevi
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Senevi J Kankanamge Don

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

In reply to this post by Smith, Dale (Norcross)

Hi Dale,

I appreciate your time looking into this. Thanks for your response.

We only use QuantLib to compute the yield, duration and convexity for individual instruments and we don’t build yield curve in QuantLib.

Bloomberg being the standard we adhere to, we are trying our best to match QuantLib results with Bloomberg.

Further investigation revealed why QuantLib yield is different to that of Bloomberg.

If the settlement date falls into the last period (i.e. between 31-Mar-2015 and 30-Sep-2015 in my example), Bloomberg discounts the future cash flows (i.e. Redemption + Last coupon payment) to present value using simple discount method. When the settlement is before 31-Mar-2015, Bloomberg discounts all future cash flows using compound discount method.

Using QuantLib, I am not able to figure out how to achieve the same.

If I do in my code,

Compounding compoundingMethod = SimpleThenCompounded;

QuantLib yield match 100% with Bloomberg when the settlement is in the last period. When the settlement is prior to the last period, QuantLib discounts the cash flow next to the settlement in simple discount and the rest in compound method and hence the value is slightly different to Bloomberg which discounts all cash flows using compound method.

If I do in my code,

Compounding compoundingMethod = Compounded;

QuantLib yield match 100% with Bloomberg when the settlement is prior to the last period. When the settlement is in the last period, QuantLib discount the cash flow using compound method and hence the value is different to Bloomberg which does a simple discount.

If this can be resolved, QuantLib yield will match 100% with Bloomberg.

Thanks

-Senevi

From: Smith, Dale (Norcross) [mailto:[hidden email]]
Sent: Wednesday, November 06, 2013 1:26 PM
To: Senevi J Kankanamge Don; [hidden email]
Subject: RE: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Based on my own experience, I would say you are very close to Bloomberg. I suspect it’s simply not worth chasing down the discrepancy, unless you want to fully investigate differences in

· Day counts

· Business rules (modified following, etc)

· Yield curve interpolation

· Compounding

· Max evaluations

· Etc

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

From: Senevi J Kankanamge Don [[hidden email]]
Sent: Monday, November 04, 2013 10:25 AM
To: [hidden email]
Subject: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

Senevi J Kankanamge Don

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

In reply to this post by Jean-Mathieu Vermosen

Hi,

Thanks for your response.

We compare true yield in BBG.

As you said, I had to set BusinessDayConvention paymentConvention = Unadjusted to avoid discrepancies.

Ultimately we implemented a new method isSettlementLastCouponPeriod() in ql/instruments/bonds/fixedratebond.hpp which returns whether the settlement falls into the last coupon period or not.

Then we did…

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);

Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded;

Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

Now QuantLib yield match 100% with Bloomberg.

Duration and convexity don’t match with Bloomberg. It appears that QuantLib doesn’t take the weight of present values into account in computing these two figures whereas Bloomberg does.

Thanks

-Senevi

From: Jean-Mathieu Vermosen [mailto:[hidden email]]
Sent: Wednesday, November 06, 2013 2:37 PM
To: [hidden email]
Subject: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hey there,

Which yield are you comparing to in BBG ? Treasury yield convention doesn’t adjust payments for holidays, so make sure that

BusinessDayConvention paymentConvention = ModifiedFollowing;

Best,

Jean-Mathieu Vermosen

On Nov 4, 2013, at 10:25 AM, Senevi J Kankanamge Don <[hidden email]> wrote:

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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cheng li

答复: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

In reply to this post by Senevi J Kankanamge Don

Hi Senevi,

I have met the same problem when I try to make my yield calculation matching with market quote in China bond market. The difference in compounding style is same. When bond is in last period, simple compounding is used while not then compounded is used.

I think we have no work around. Maybe some new compounding style should be used? It may not be easy in current framework. We have to pass in more information.

Regards,

Cheng

发件人: Senevi J Kankanamge Don [mailto:[hidden email]]
发送时间: 2013年11月6日 22:55
收件人: Smith, Dale (Norcross); [hidden email]
主题: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Dale,

I appreciate your time looking into this. Thanks for your response.

We only use QuantLib to compute the yield, duration and convexity for individual instruments and we don’t build yield curve in QuantLib.

Bloomberg being the standard we adhere to, we are trying our best to match QuantLib results with Bloomberg.

Further investigation revealed why QuantLib yield is different to that of Bloomberg.

Using QuantLib, I am not able to figure out how to achieve the same.

If I do in my code,

Compounding compoundingMethod = SimpleThenCompounded;

If I do in my code,

Compounding compoundingMethod = Compounded;

If this can be resolved, QuantLib yield will match 100% with Bloomberg.

Thanks

-Senevi

From: Smith, Dale (Norcross) [[hidden email]]
Sent: Wednesday, November 06, 2013 1:26 PM
To: Senevi J Kankanamge Don; [hidden email]
Subject: RE: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Thanks for posting your code. It’s refreshing to see someone actually get this close to Bloomberg’s results. I salute you, as I know how hard it is to get this far. What yield curve are you using on Bloomberg �C I25? How are you building your yield curve in QuantLib?

Based on my own experience, I would say you are very close to Bloomberg. I suspect it’s simply not worth chasing down the discrepancy, unless you want to fully investigate differences in

・ Day counts

・ Business rules (modified following, etc)

・ Yield curve interpolation

・ Compounding

・ Max evaluations

・ Etc

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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Senevi J Kankanamge Don

Re: Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Cheng,

As a workaround, I implemented a new method in Bond class to determine if the given settlement date falls into the last period or not.

bool Bond::isSettlementLastCouponPeriod(const Date& settlementDate) const

{

Date refStartDate, refEndDate;

// Reverse iterate the cashflows to determine if the settlement falls into the last coupon period.

for (Size i = cashflows_.size() - 1; i>=0; --i)

{

shared_ptr<Coupon> coupon = boost::dynamic_pointer_cast<Coupon>(cashflows_[i]);

if (coupon)

{

refStartDate = coupon->referencePeriodStart();

refEndDate = coupon->referencePeriodEnd();

return refStartDate <= settlementDate && settlementDate <= refEndDate;

}

return false;

}

Then I did.

bool bIsSettlementLastCouponPeriod = bond.isSettlementLastCouponPeriod(settlementDate);

Compounding compoundingMethod = bIsSettlementLastCouponPeriod ? SimpleThenCompounded : Compounded

Real ql_clean_price = BondFunctions::cleanPrice( bond, ql_yield, bondDayCount, compoundingMethod, frequency, settlementDate);

With this workaround, our prices matched with Bloomberg to a higher precision.

Thanks

-Senevi

From: Cheng Li [mailto:[hidden email]]
Sent: Sunday, December 08, 2013 10:22 AM
To: Senevi J Kankanamge Don; 'Smith, Dale (Norcross)'; [hidden email]
Subject: 答复: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Senevi,

I think we have no work around. Maybe some new compounding style should be used? It may not be easy in current framework. We have to pass in more information.

Regards,

Cheng

发件人: Senevi J Kankanamge Don [[hidden email]]
发送时间: 2013年11月6日 22:55
收件人: Smith, Dale (Norcross); [hidden email]
主题: Re: [Quantlib-users] Yield, Macaulay duration and Convexity calculation for Notes/Bonds

Hi Dale,

I appreciate your time looking into this. Thanks for your response.

We only use QuantLib to compute the yield, duration and convexity for individual instruments and we don’t build yield curve in QuantLib.

Bloomberg being the standard we adhere to, we are trying our best to match QuantLib results with Bloomberg.

Further investigation revealed why QuantLib yield is different to that of Bloomberg.

Using QuantLib, I am not able to figure out how to achieve the same.

If I do in my code,

Compounding compoundingMethod = SimpleThenCompounded;

If I do in my code,

Compounding compoundingMethod = Compounded;

If this can be resolved, QuantLib yield will match 100% with Bloomberg.

Thanks

-Senevi

Thanks for posting your code. It’s refreshing to see someone actually get this close to Bloomberg’s results. I salute you, as I know how hard it is to get this far. What yield curve are you using on Bloomberg �C I25? How are you building your yield curve in QuantLib?

Based on my own experience, I would say you are very close to Bloomberg. I suspect it’s simply not worth chasing down the discrepancy, unless you want to fully investigate differences in

・ Day counts

・ Business rules (modified following, etc)

・ Yield curve interpolation

・ Compounding

・ Max evaluations

・ Etc

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Financial & Risk Management Solutions

Fiserv

Office: 678-375-5315

www.fiserv.com

Hi,

I am attempting to use QuantLib library in order to calculate yield, Macaulay duration and convexity for US Treasury Notes and Bonds.

This is how the values compare in Bloomberg and QuantLib for one example where the price is 99.8984375.

Bloomberg QuantLib

Yield 0.302775 0.3027679582

Macaulay Duration 1.928 1.9129221698

Convexity 0.047 0.0460608896

Can you please let me know what I need to change in my code in order to get the results matching with Bloomberg?

This is a snippet of my code.

double ql_price = 99.8984375;

Date settlementDate = Date(25, Oct, 2013);

Date firstCouponDate = Date(31, Mar, 2014);

Date datedDate = Date(30, Sep, 2013);

Date maturityDate = Date(30, Sep, 2015);

// Parameters required to define the bond

Natural settlementDays = 0;

Real faceAmount = 100;

DayCounter bondDayCount = ActualActual(ActualActual::Bond);

BusinessDayConvention paymentConvention = ModifiedFollowing;

Real redemption = 100.0;

Compounding compoundingMethod = SimpleThenCompounded;

DateGeneration::Rule dateGeneration = DateGeneration::Forward;

Frequency frequency = Semiannual;

Real accuracy = 1.0e-11;

Size maxEvaluations = 100;

// Create the Schedule

Schedule fixedBondSchedule(

datedDate, // Dated Date

maturityDate, // Maturity Date

Period(Semiannual), // Period

UnitedStates(UnitedStates::GovernmentBond), // Calendar

Unadjusted, // BusinessDayConvention - convention

Unadjusted, // BusinessDayConvention - terminationDateConvention

dateGeneration, // DateGeneration::Rule rule

false, // endOfMonth

firstCouponDate); // First Date

// Create the Fixed Rate Bond

FixedRateBond bond(

settlementDays, // Settlement Days

faceAmount, // Face Amount

fixedBondSchedule, // Schedule

std::vector<Rate>(1, ql_coupon), // Coupons

bondDayCount, // DayCounter

paymentConvention, // BusinessDayConvention

redemption); // Redemption

Real ql_yield = BondFunctions::yield( bond, ql_price, bondDayCount, compoundingMethod, frequency, settlementDate, accuracy, maxEvaluations);

InterestRate interestRate(ql_yield, bondDayCount, compoundingMethod, frequency );

Real ql_convexity = BondFunctions::convexity( bond, interestRate, settlementDate );

Compounding compoundingMethod4Duration = Compounded;

Time ql_duration = BondFunctions::duration( bond, ql_yield, bondDayCount, compoundingMethod4Duration, frequency, Duration::Macaulay, settlementDate );

Thanks

-Senevi

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