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I am trying to understand the rate helper more in detail. In principal I want to build a 3M forward curve based on 6M quotes and 6Mvs3M quotes.

The 6M works and prices to 0. I am not sure whether for the 3M I am doing the proper thing feeding the market quote and the basisswap-spread into the vanilla swap pricer becasue at larger maturities I am getting deviations?

import QuantLib as ql

date = ql.Date(9, ql.February, 2015)
ql.Settings.instance().evaluationDate = date

#Definition of OIS and Libor Index
TONAR_JPY = ql.OvernightIndex("Tonar", 2, ql.JPYCurrency(), ql.Japan(), ql.Actual365Fixed())
Libor_JPY_3M = ql.JPYLibor(ql.Period(3, ql.Months))
Libor_JPY_6M = ql.JPYLibor(ql.Period(6, ql.Months))

#--------------------------------------------------------------------
# Discounting curve
#--------------------------------------------------------------------

#2015-02-09

# setup DepositRateHelper for 0-2 days
helpers_disc = [ql.DepositRateHelper(ql.QuoteHandle(ql.SimpleQuote(rate/100)),
                                     ql.Period(2,ql.Days), fixingDays,
                                     ql.Japan(), ql.ModifiedFollowing, False, ql.Actual365Fixed())
            for rate, fixingDays in [(0.081, 0)]]

# OIS quotes up to 30 years
# setup OISRateHelper from 15 months to 30 years
helpers_disc += [ql.OISRateHelper(2, ql.Period(*tenor),
                                 ql.QuoteHandle(ql.SimpleQuote(rate/100)), TONAR_JPY)
            for rate, tenor in [(0.0713, (1,ql.Weeks)), (0.0688, (2,ql.Weeks)), (0.0663, (3,ql.Weeks)), (0.0656, (1,ql.Months)), 
                                (0.0563, (4,ql.Months)), (0.055, (5,ql.Months)), (0.0538, (6,ql.Months)), (0.05, (11,ql.Months)),
                                (0.0494, (12,ql.Months)), (0.0481, (15,ql.Months)), (0.0506, (18,ql.Months)), (0.0538, (2,ql.Years)),
                                (0.0769, (3,ql.Years)), (0.1119, (4,ql.Years)), (0.2925, (8,ql.Years)), (0.3356, (9,ql.Years)),
                                (0.6888, (15,ql.Years)), (0.965, (20,ql.Years)), (1.1081, (25,ql.Years)), (1.1831, (30,ql.Years))]]

tonar_curve = ql.PiecewiseCubicZero(date, helpers_disc, ql.Actual365Fixed())
tonar_curve.enableExtrapolation()

discount_curve = ql.RelinkableYieldTermStructureHandle()
discount_curve.linkTo(tonar_curve)

#--------------------------------------------------------------------
#6-months JPY Libor
#--------------------------------------------------------------------

#Fixings
helpers_fwd_6M = [ql.DepositRateHelper(ql.QuoteHandle(ql.SimpleQuote(rate/100)),
                                     ql.Period(6,ql.Months), fixingDays,
                                     ql.Japan(), ql.ModifiedFollowing, False, ql.Actual365Fixed())
            for rate, fixingDays in [(0.14214, 0)]]

#FRA Helper
helpers_fwd_6M += [ql.FraRateHelper(ql.QuoteHandle(ql.SimpleQuote(rate/100)), start, Libor_JPY_6M)
            for rate, start in [(0.1444, 1), (0.1456, 2), (0.1463, 3),
                                (0.1475, 4), (0.1488, 5)]]
#Swap Helper
helpers_fwd_6M += [ql.SwapRateHelper(ql.QuoteHandle(ql.SimpleQuote((rate)/100)),
                                  ql.Period(tenor, ql.Years), ql.Japan(),
                                  ql.Semiannual, ql.Unadjusted, ql.Actual365Fixed(),
                                  Libor_JPY_6M, ql.QuoteHandle(), 
                                  ql.Period(0, ql.Days),
                                  discount_curve)
                for rate, tenor in [(0.1475, 1), (0.155, 2), (0.18, 3), (0.21875, 4), (0.2675, 5), (0.32, 6),
                                    (0.375, 7), (0.4325, 8), (0.49, 9), (0.55, 10), (0.67875, 12), (0.8825, 15),
                                    (1.16125, 20), (1.3075, 25), (1.385, 30)]]

jpy_libor_curve_6M = ql.PiecewiseCubicZero(date, helpers_fwd_6M, ql.Actual365Fixed())
jpy_libor_curve_6M.enableExtrapolation()

forward_curve_6M = ql.RelinkableYieldTermStructureHandle()
forward_curve_6M.linkTo(jpy_libor_curve_6M)

#--------------------------------------------------------------------
#3-months JPY Libor
#--------------------------------------------------------------------

#Fixings
helpers_fwd_3M = [ql.DepositRateHelper(ql.QuoteHandle(ql.SimpleQuote(rate/100)),
                                     ql.Period(3,ql.Months), fixingDays,
                                     ql.Japan(), ql.ModifiedFollowing, False, ql.Actual365Fixed())
            for rate, fixingDays in [(0.10429, 0)]]

#FRA Helper
helpers_fwd_3M += [ql.FraRateHelper(ql.QuoteHandle(ql.SimpleQuote(rate/100)), start, Libor_JPY_3M)
            for rate, start in [(0.1113, 1), (0.1138, 2), (0.115, 3), (0.1175, 4), (0.1188, 5), (0.1188, 6),
                                (0.1188, 7), (0.1188, 8)]]


helpers_fwd_3M += [ql.SwapRateHelper(ql.QuoteHandle(ql.SimpleQuote((rate)/100)),
                                  ql.Period(tenor, ql.Years), ql.Japan(),
                                  ql.Quarterly, ql.Unadjusted, ql.Actual365Fixed(),
                                  Libor_JPY_3M, ql.QuoteHandle(ql.SimpleQuote((basis/100/100))), 
                                  ql.Period(0, ql.Days),
                                  discount_curve)
            for rate, basis, tenor in [(0.1475, 3.25, 1), (0.155, 3.25, 2), (0.18, 3.25, 3), (0.21875, 3.375, 4), 
                                       (0.2675, 3.5, 5), (0.32, 3.625, 6), (0.375, 3.875, 7), (0.4325, 4.125, 8), 
                                       (0.49, 4.625, 9), (0.55, 5.125, 10), (0.67875, 6, 12), (0.8825, 6.5, 15),
                                       (1.16125, 6.5, 20), (1.3075, 6.5, 25), (1.385, 6.5, 30)]]

jpy_libor_curve_3M = ql.PiecewiseCubicZero(date, helpers_fwd_3M, ql.Actual365Fixed())
jpy_libor_curve_3M.enableExtrapolation()

forward_curve_3M = ql.RelinkableYieldTermStructureHandle()
forward_curve_3M.linkTo(jpy_libor_curve_3M)

#Swap Pricing 

settle_date = ql.Japan().advance(date, 2, ql.Days)
maturity_date = ql.Japan().advance(settle_date, 1, ql.Years)   
fixed_leg_tenor_6M = ql.Period(6, ql.Months)
float_leg_tenor_6M = ql.Period(6, ql.Months)
float_leg_tenor_3M = ql.Period(3, ql.Months)
fixed_leg_tenor_3M = ql.Period(3, ql.Months)

notional = 1000000

#6M Swap
#1Y market qoute
Market_Swap_Quote_6M = (0.1475/100)

#Fixed Rate
fixed_schedule_6M = ql.Schedule(settle_date, maturity_date, fixed_leg_tenor_6M, ql.Japan(), ql.ModifiedFollowing, ql.ModifiedFollowing,
                             ql.DateGeneration.Backward, True)

#Floating Rate
floating_schedule_6M = ql.Schedule(settle_date, maturity_date, float_leg_tenor_6M, ql.Japan(), ql.ModifiedFollowing, ql.ModifiedFollowing,
                                ql.DateGeneration.Backward, True)

index_complete_6M = ql.JPYLibor(ql.Period(6, ql.Months), forward_curve_6M)

swap_6M = ql.VanillaSwap(ql.VanillaSwap.Payer, notional,
                      fixed_schedule_6M, Market_Swap_Quote_6M, ql.Actual365Fixed(),
                      floating_schedule_6M, index_complete_6M, 0, ql.Actual360())   

swap_6M.setPricingEngine(ql.DiscountingSwapEngine(discount_curve))

#NPV
print('6M Swap NPV =', swap_6M.NPV())
print('6M Swap Fair Rate =', swap_6M.fairRate())

#3M Swap
#1Y market qoute
Market_Swap_Quote_3M = (0.1475/100)
Market_Quote_Spread_6M3M = (3.25/100/100)

#Fixed Rate
fixed_schedule_3M = ql.Schedule(settle_date, maturity_date, fixed_leg_tenor_3M, ql.Japan(), ql.ModifiedFollowing, ql.ModifiedFollowing,
                             ql.DateGeneration.Backward, True)

#Floating Rate
floating_schedule_3M = ql.Schedule(settle_date, maturity_date, float_leg_tenor_3M, ql.Japan(), ql.ModifiedFollowing, ql.ModifiedFollowing,
                                ql.DateGeneration.Backward, True)

index_complete_3M = ql.JPYLibor(ql.Period(3, ql.Months), forward_curve_3M)

swap_3M = ql.VanillaSwap(ql.VanillaSwap.Payer, notional,
                      fixed_schedule_3M, Market_Swap_Quote_3M, ql.Actual365Fixed(),
                      floating_schedule_3M, index_complete_3M, Market_Quote_Spread_6M3M, ql.Actual360())   

swap_3M.setPricingEngine(ql.DiscountingSwapEngine(discount_curve))

#NPV
print('3M Swap NPV =', swap_3M.NPV())
print('3M Swap Fair Rate =', swap_3M.fairRate())
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1 Answer 1

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The NPV fucntion gives you with the market quote the off-market swap. To calculate the par swap fixed rate you have to use the the function 

swap_3M.fairRate()

which results in a NPV euqual to zero (PV Fixed Leg = PV Floating Leg).

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