Simple Bond Math with QuantLib-Python

[Carter Page]

Hello,

I am new to QuantLib and am trying to get it to replicate some simple bond math using QuantLib-Python.

Suppose we have a 5-year bond with annual coupon payments of $5 and face value of $100, and interest rate of 4%. Classic calculations yield that the present value of the bond is $104.45. When I try to do this simple example in QuantLib-Python, I get $104.70--despite my attempts to strip out calendar conventions.

How can I use QuantLib to line up with this simple bond math?

from QuantLib import *

# Construct yield curve
calc_date = Date(1, 1, 2017)
Settings.instance().evaluationDate = calc_date

spot_dates = [Date(1,1,2017), Date(1,1,2018), Date(1,1,2027)]
spot_rates = [0.0, 0.04, 0.04]

day_count = SimpleDayCounter()
calendar = NullCalendar()
interpolation = Linear()
compounding = Compounded
compounding_frequency = Annual
spot_curve = ZeroCurve(spot_dates, spot_rates, day_count, calendar, interpolation, compounding, compounding_frequency)

spot_curve_handle = YieldTermStructureHandle(spot_curve)

# Construct bond schedule
issue_date = Date(1, 1, 2017)
maturity_date = Date(1, 1, 2022)
tenor = Period(Semiannual)
calendar = NullCalendar()
business_convention = Unadjusted
date_generation = DateGeneration.Backward
month_end = False

schedule = Schedule(issue_date, maturity_date, tenor, calendar, business_convention, business_convention, date_generation, month_end)

# Create FixedRateBond Object

coupon_rate = 0.05
coupons = [coupon_rate]
settlement_days = 0
face_value = 100

fixed_rate_bond = FixedRateBond(settlement_days,
                                face_value,
                                schedule,
                                coupons,
                                day_count)

# Set Valuation engine
bond_engine = DiscountingBondEngine(spot_curve_handle)
fixed_rate_bond.setPricingEngine(bond_engine)

# Calculate present value
value = fixed_rate_bond.NPV()
print(value)

Link to the question on http://quant.stackexchange.com/q/32539/17936.

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[Luigi Ballabio]

For future reference: answered at <http://quant.stackexchange.com/questions/32539/simple-quantlib-bond-math> before the post to the mailing list was cleared.

On Tue, Feb 21, 2017 at 10:01 AM Carter Page <[hidden email]> wrote:

Hello,

I am new to QuantLib and am trying to get it to replicate some simple bond math using QuantLib-Python.

Suppose we have a 5-year bond with annual coupon payments of $5 and face value of $100, and interest rate of 4%. Classic calculations yield that the present value of the bond is $104.45. When I try to do this simple example in QuantLib-Python, I get $104.70--despite my attempts to strip out calendar conventions.

How can I use QuantLib to line up with this simple bond math?

from QuantLib import *

# Construct yield curve
calc_date = Date(1, 1, 2017)
Settings.instance().evaluationDate = calc_date

spot_dates = [Date(1,1,2017), Date(1,1,2018), Date(1,1,2027)]
spot_rates = [0.0, 0.04, 0.04]

day_count = SimpleDayCounter()
calendar = NullCalendar()
interpolation = Linear()
compounding = Compounded
compounding_frequency = Annual
spot_curve = ZeroCurve(spot_dates, spot_rates, day_count, calendar, interpolation, compounding, compounding_frequency)

spot_curve_handle = YieldTermStructureHandle(spot_curve)

# Construct bond schedule
issue_date = Date(1, 1, 2017)
maturity_date = Date(1, 1, 2022)
tenor = Period(Semiannual)
calendar = NullCalendar()
business_convention = Unadjusted
date_generation = DateGeneration.Backward
month_end = False

schedule = Schedule(issue_date, maturity_date, tenor, calendar, business_convention, business_convention, date_generation, month_end)

# Create FixedRateBond Object

coupon_rate = 0.05
coupons = [coupon_rate]
settlement_days = 0
face_value = 100

fixed_rate_bond = FixedRateBond(settlement_days,
                                face_value,
                                schedule,
                                coupons,
                                day_count)

# Set Valuation engine
bond_engine = DiscountingBondEngine(spot_curve_handle)
fixed_rate_bond.setPricingEngine(bond_engine)

# Calculate present value
value = fixed_rate_bond.NPV()
print(value)

Link to the question on http://quant.stackexchange.com/q/32539/17936.

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