NPV calculation in Python from a discounting curve

[asavoldi]

Hello everybody,

I'm trying to calculate the NPV of a couple of bonds, zero coupon and fixed income, using QuantLib in Python, via SWIG interface (QuantLib 1.3, SWIG 1.2). In C++, starting from the discounting curve which is embedded within the code snippet posted below, I obtain the correct values:

NPV (ZCB) = 99.2665
NPV (FRB) = 103.733

However, from Python side, I've got different results:

NPV (ZCB) = 96.45
NPV (FRB) = 100.79

Could you help me to understand the reason of this mis-behaviour?

Thanks in advance,
Antonio








#!/usr/bin/env python

# Copyright (C) 2008 Florent Grenier
# Copyright (C) 2010 Lluis Pujol Bajador
#
# 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
# <[e-mail]>. 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.

#    This example shows how to set up a term structure and then price
#    some simple bonds. The last part is dedicated to peripherical
#    computations such as "Yield to Price" or "Price to Yield"

# this script should be the prototype which demonstrate how to
# use discounting curve for calculating the Net Present Value
# of a Bond (Fixed Rate, Zero Coupon, and Floating Rate)

# Test cases for Bonds pricing module
# Fixed rate bond
# Zero coupon bond
# Floating rate bond

from QuantLib import *

# global data
calendar = TARGET()
settlementDate = Date(01,January,2014)
settlementDate = calendar.adjust(settlementDate)
fixingDays = 0
settlementDays = 0
todaysDate = calendar.adjust(calendar.advance(settlementDate, -fixingDays, Days))
Settings.instance().evaluationDate = todaysDate
termStructureDayCounter =  ActualActual(ActualActual.ISDA)

print 'Today: '  + str(todaysDate)
print 'Settlement Date: ' + str(settlementDate)

# dates and rates vectors
dates = [
         settlementDate,
         settlementDate + 1*QuantLib.Weeks,
         settlementDate + 1*QuantLib.Months,
         settlementDate + 2*QuantLib.Months,
         settlementDate + 3*QuantLib.Months,
         
         settlementDate + 4*QuantLib.Months,
         settlementDate + 5*QuantLib.Months,
         settlementDate + 6*QuantLib.Months,
         settlementDate + 9*QuantLib.Months,
         settlementDate + 1*12*QuantLib.Months,
         
         settlementDate + 18*QuantLib.Months,
         settlementDate + 2*12*QuantLib.Months,
         settlementDate + 3*12*QuantLib.Months,
         settlementDate + 4*12*QuantLib.Months,
         settlementDate + 5*12*QuantLib.Months,
         
         settlementDate + 6*12*QuantLib.Months,
         settlementDate + 7*12*QuantLib.Months,
         settlementDate + 8*12*QuantLib.Months,
         settlementDate + 9*12*QuantLib.Months,
         settlementDate + 10*12*QuantLib.Months,
         
         settlementDate + 11*12*QuantLib.Months,
         settlementDate + 12*12*QuantLib.Months,
         settlementDate + 15*12*QuantLib.Months,
         settlementDate + 20*12*QuantLib.Months,
         settlementDate + 25*12*QuantLib.Months,
         settlementDate + 30*12*30]



rates = [
        0.002762549,
        0.002762549,
        0.002762549,
        0.002762549,
        0.002762549,
       
        0.00347872,        
        0.004126332,
        0.004714056,
        0.006191223,
        0.007362001,
       
        0.009215772,
        0.01082479,
        0.01404554,
        0.01738827,
        0.02061265,
       
        0.02351719,        
        0.02602376,
        0.02813818,
        0.0299055,
        0.03138197,
       
        0.0326213,        
        0.03366947,
        0.03600337,
        0.03835103,
        0.03976059,
        0.04070031
        ]


#######################################
#        BONDS TO BE PRICED           #
#######################################

# common data

faceAmount = 100;

# Discounting curve built up on the provided dates/rates
bondDiscountingTermStructure = ZeroCurve(dates, rates, termStructureDayCounter)
discountingTermStructure = RelinkableYieldTermStructureHandle()
bondEngine = DiscountingBondEngine(discountingTermStructure)

# zero coupon bond
zeroCouponBond = ZeroCouponBond(settlementDays,
                                UnitedStates(UnitedStates.GovernmentBond),
                                faceAmount,
                                Date(01,January,2015),
                                Following,
                                100,
                                Date(01,January,2005))

zeroCouponBond.setPricingEngine(bondEngine)


# fixed 4.5% US Treasury note
fixedBondSchedule = Schedule(Date(01, January, 2005),
                             Date(01, January, 2015),
                             Period(Annual),
                             UnitedStates(UnitedStates.GovernmentBond),
                             Unadjusted,
                             Unadjusted,
                             DateGeneration.Backward,
                             False)

fixedRateBond = FixedRateBond(settlementDays,
                              faceAmount,
                              fixedBondSchedule,
                              [0.045],
                              ActualActual(ActualActual.Bond),
                              ModifiedFollowing,
                              100.0,
                              Date(01, January, 2005))

fixedRateBond.setPricingEngine(bondEngine);


discountingTermStructure.linkTo(bondDiscountingTermStructure)

#############################
#       BOND PRICING        #
#############################

# write column headings
def formatPrice(p,digits=2):
    format = '%%.%df' % digits
    return format % p

def formatRate(r,digits=2):
    format = '%%.%df %%%%' % digits
    return format % (r*100)

def report(Info, Zc, Fix, Frn, format):
    if format== "Price":
        Zc = formatPrice(Zc)
        Fix = formatPrice(Fix)
        Frn = formatPrice(Frn)
    else:
        if Info.find("coupon")==-1:
            Zc  = formatRate(Zc)
        else:
            Zc  = "N/A"
        Fix = formatRate(Fix)
        Frn = formatRate(Frn)
       
    print '%19s' % Info + ' |' + \
          ' |'.join(['%10s' % y for y in [Zc, Fix, Frn] ])



headers = [ "ZC", "Fixed", "Floating" ]
print ''
print '%19s' % '' + ' |' + \
          ' |'.join(['%10s' % y for y in headers])
                     
separator = " | "
widths = [ 18, 10, 10, 10 ]
width = widths[0] + widths[1] + widths[2]  + widths[3] + widths[3];
rule = "-" * width
dblrule = "=" * width
tab = " " * 8

print  rule
report( "Net present value",
        zeroCouponBond.NPV(),
        fixedRateBond.NPV(),
        #floatingRateBond.NPV(),
        0,
        "Price")
print ''

[Luigi Ballabio]

The expression
    settlementDate + 2*QuantLib.Months
doesn't work as you expect in Python, since there's no real
enumeration in the language and QuantLib.Months is just an integer.
You need to use
    settlementDate + QuantLib.Period(2, QuantLib.Months)
instead.

Luigi

On Wed, Feb 12, 2014 at 10:37 AM, asavoldi <[hidden email]> wrote:

> Hello everybody,
>
> I'm trying to calculate the NPV of a couple of bonds, zero coupon and fixed
> income, using QuantLib in Python, via SWIG interface (QuantLib 1.3, SWIG
> 1.2). In C++, starting from the discounting curve which is embedded within
> the code snippet posted below, I obtain the correct values:
>
> NPV (ZCB) = 99.2665
> NPV (FRB) = 103.733
>
> However, from Python side, I've got different results:
>
> NPV (ZCB) = 96.45
> NPV (FRB) = 100.79
>
> Could you help me to understand the reason of this mis-behaviour?
>
> Thanks in advance,
> Antonio
>
>
>
>
>
>
>
>
> #!/usr/bin/env python
>
> # Copyright (C) 2008 Florent Grenier
> # Copyright (C) 2010 Lluis Pujol Bajador
> #
> # 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
> # <[hidden email]>. 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.
>
> #    This example shows how to set up a term structure and then price
> #    some simple bonds. The last part is dedicated to peripherical
> #    computations such as "Yield to Price" or "Price to Yield"
>
> # this script should be the prototype which demonstrate how to
> # use discounting curve for calculating the Net Present Value
> # of a Bond (Fixed Rate, Zero Coupon, and Floating Rate)
>
> # Test cases for Bonds pricing module
> # Fixed rate bond
> # Zero coupon bond
> # Floating rate bond
>
> from QuantLib import *
>
> # global data
> calendar = TARGET()
> settlementDate = Date(01,January,2014)
> settlementDate = calendar.adjust(settlementDate)
> fixingDays = 0
> settlementDays = 0
> todaysDate = calendar.adjust(calendar.advance(settlementDate, -fixingDays,
> Days))
> Settings.instance().evaluationDate = todaysDate
> termStructureDayCounter =  ActualActual(ActualActual.ISDA)
>
> print 'Today: '  + str(todaysDate)
> print 'Settlement Date: ' + str(settlementDate)
>
> # dates and rates vectors
> dates = [
>          settlementDate,
>          settlementDate + 1*QuantLib.Weeks,
>          settlementDate + 1*QuantLib.Months,
>          settlementDate + 2*QuantLib.Months,
>          settlementDate + 3*QuantLib.Months,
>
>          settlementDate + 4*QuantLib.Months,
>          settlementDate + 5*QuantLib.Months,
>          settlementDate + 6*QuantLib.Months,
>          settlementDate + 9*QuantLib.Months,
>          settlementDate + 1*12*QuantLib.Months,
>
>          settlementDate + 18*QuantLib.Months,
>          settlementDate + 2*12*QuantLib.Months,
>          settlementDate + 3*12*QuantLib.Months,
>          settlementDate + 4*12*QuantLib.Months,
>          settlementDate + 5*12*QuantLib.Months,
>
>          settlementDate + 6*12*QuantLib.Months,
>          settlementDate + 7*12*QuantLib.Months,
>          settlementDate + 8*12*QuantLib.Months,
>          settlementDate + 9*12*QuantLib.Months,
>          settlementDate + 10*12*QuantLib.Months,
>
>          settlementDate + 11*12*QuantLib.Months,
>          settlementDate + 12*12*QuantLib.Months,
>          settlementDate + 15*12*QuantLib.Months,
>          settlementDate + 20*12*QuantLib.Months,
>          settlementDate + 25*12*QuantLib.Months,
>          settlementDate + 30*12*30]
>
>
>
> rates = [
>         0.002762549,
>         0.002762549,
>         0.002762549,
>         0.002762549,
>         0.002762549,
>
>         0.00347872,
>         0.004126332,
>         0.004714056,
>         0.006191223,
>         0.007362001,
>
>         0.009215772,
>         0.01082479,
>         0.01404554,
>         0.01738827,
>         0.02061265,
>
>         0.02351719,
>         0.02602376,
>         0.02813818,
>         0.0299055,
>         0.03138197,
>
>         0.0326213,
>         0.03366947,
>         0.03600337,
>         0.03835103,
>         0.03976059,
>         0.04070031
>         ]
>
>
> #######################################
> #        BONDS TO BE PRICED           #
> #######################################
>
> # common data
>
> faceAmount = 100;
>
> # Discounting curve built up on the provided dates/rates
> bondDiscountingTermStructure = ZeroCurve(dates, rates,
> termStructureDayCounter)
> discountingTermStructure = RelinkableYieldTermStructureHandle()
> bondEngine = DiscountingBondEngine(discountingTermStructure)
>
> # zero coupon bond
> zeroCouponBond = ZeroCouponBond(settlementDays,
>                                 UnitedStates(UnitedStates.GovernmentBond),
>                                 faceAmount,
>                                 Date(01,January,2015),
>                                 Following,
>                                 100,
>                                 Date(01,January,2005))
>
> zeroCouponBond.setPricingEngine(bondEngine)
>
>
> # fixed 4.5% US Treasury note
> fixedBondSchedule = Schedule(Date(01, January, 2005),
>                              Date(01, January, 2015),
>                              Period(Annual),
>                              UnitedStates(UnitedStates.GovernmentBond),
>                              Unadjusted,
>                              Unadjusted,
>                              DateGeneration.Backward,
>                              False)
>
> fixedRateBond = FixedRateBond(settlementDays,
>                               faceAmount,
>                               fixedBondSchedule,
>                               [0.045],
>                               ActualActual(ActualActual.Bond),
>                               ModifiedFollowing,
>                               100.0,
>                               Date(01, January, 2005))
>
> fixedRateBond.setPricingEngine(bondEngine);
>
>
> discountingTermStructure.linkTo(bondDiscountingTermStructure)
>
> #############################
> #       BOND PRICING        #
> #############################
>
> # write column headings
> def formatPrice(p,digits=2):
>     format = '%%.%df' % digits
>     return format % p
>
> def formatRate(r,digits=2):
>     format = '%%.%df %%%%' % digits
>     return format % (r*100)
>
> def report(Info, Zc, Fix, Frn, format):
>     if format== "Price":
>         Zc = formatPrice(Zc)
>         Fix = formatPrice(Fix)
>         Frn = formatPrice(Frn)
>     else:
>         if Info.find("coupon")==-1:
>             Zc  = formatRate(Zc)
>         else:
>             Zc  = "N/A"
>         Fix = formatRate(Fix)
>         Frn = formatRate(Frn)
>
>     print '%19s' % Info + ' |' + \
>           ' |'.join(['%10s' % y for y in [Zc, Fix, Frn] ])
>
>
>
> headers = [ "ZC", "Fixed", "Floating" ]
> print ''
> print '%19s' % '' + ' |' + \
>           ' |'.join(['%10s' % y for y in headers])
>
> separator = " | "
> widths = [ 18, 10, 10, 10 ]
> width = widths[0] + widths[1] + widths[2]  + widths[3] + widths[3];
> rule = "-" * width
> dblrule = "=" * width
> tab = " " * 8
>
> print  rule
> report( "Net present value",
>         zeroCouponBond.NPV(),
>         fixedRateBond.NPV(),
>         #floatingRateBond.NPV(),
>         0,
>         "Price")
> print ''
>
>
>
> --
> View this message in context: http://quantlib.10058.n7.nabble.com/NPV-calculation-in-Python-from-a-discounting-curve-tp14960.html
> Sent from the quantlib-users mailing list archive at Nabble.com.
>
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--
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[asavoldi]

Thank you so much Luigi.