# --- # jupyter: # jupytext: # formats: py:percent # text_representation: # extension: .py # format_name: percent # format_version: '1.3' # jupytext_version: 1.4.2 # kernelspec: # display_name: Python 3 # language: python # name: python3 # --- # %% [markdown] # # Interest-rate swaps # # Copyright (©) 2004, 2005, 2006, 2007 StatPro Italia srl # # This file is part of QuantLib, a free-software/open-source library # for financial quantitative analysts and developers - https://www.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 # . The license is also available online at # . # # 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. # %% import QuantLib as ql # %% [markdown] # ### Global data # %% calendar = ql.TARGET() todaysDate = ql.Date(6, ql.November, 2001) ql.Settings.instance().evaluationDate = todaysDate settlementDate = ql.Date(8, ql.November, 2001) # %% [markdown] # ### Market quotes # %% deposits = { (3, ql.Months): 0.0363, } # %% FRAs = {(3, 6): 0.037125, (6, 9): 0.037125, (9, 12): 0.037125} # %% futures = { ql.Date(19, 12, 2001): 96.2875, ql.Date(20, 3, 2002): 96.7875, ql.Date(19, 6, 2002): 96.9875, ql.Date(18, 9, 2002): 96.6875, ql.Date(18, 12, 2002): 96.4875, ql.Date(19, 3, 2003): 96.3875, ql.Date(18, 6, 2003): 96.2875, ql.Date(17, 9, 2003): 96.0875, } # %% swaps = { (2, ql.Years): 0.037125, (3, ql.Years): 0.0398, (5, ql.Years): 0.0443, (10, ql.Years): 0.05165, (15, ql.Years): 0.055175, } # %% [markdown] # We'll convert them to `Quote` objects... # %% for n, unit in deposits.keys(): deposits[(n, unit)] = ql.SimpleQuote(deposits[(n, unit)]) for n, m in FRAs.keys(): FRAs[(n, m)] = ql.SimpleQuote(FRAs[(n, m)]) for d in futures.keys(): futures[d] = ql.SimpleQuote(futures[d]) for n, unit in swaps.keys(): swaps[(n, unit)] = ql.SimpleQuote(swaps[(n, unit)]) # %% [markdown] # ...and build rate helpers. # %% dayCounter = ql.Actual360() settlementDays = 2 depositHelpers = [ ql.DepositRateHelper( ql.QuoteHandle(deposits[(n, unit)]), ql.Period(n, unit), settlementDays, calendar, ql.ModifiedFollowing, False, dayCounter, ) for n, unit in deposits.keys() ] # %% dayCounter = ql.Actual360() settlementDays = 2 fraHelpers = [ ql.FraRateHelper( ql.QuoteHandle(FRAs[(n, m)]), n, m, settlementDays, calendar, ql.ModifiedFollowing, False, dayCounter ) for n, m in FRAs.keys() ] # %% dayCounter = ql.Actual360() months = 3 futuresHelpers = [ ql.FuturesRateHelper( ql.QuoteHandle(futures[d]), d, months, calendar, ql.ModifiedFollowing, True, dayCounter, ql.makeQuoteHandle(0.0), ) for d in futures.keys() ] # %% [markdown] # The discount curve for the swaps will come from elsewhere. A real application would use some kind of risk-free curve; here we're using a flat one for convenience. # %% discountTermStructure = ql.YieldTermStructureHandle( ql.FlatForward(settlementDate, 0.04, ql.Actual360())) # %% settlementDays = 2 fixedLegFrequency = ql.Annual fixedLegTenor = ql.Period(1, ql.Years) fixedLegAdjustment = ql.Unadjusted fixedLegDayCounter = ql.Thirty360(ql.Thirty360.BondBasis) floatingLegFrequency = ql.Quarterly floatingLegTenor = ql.Period(3, ql.Months) floatingLegAdjustment = ql.ModifiedFollowing swapHelpers = [ ql.SwapRateHelper( ql.QuoteHandle(swaps[(n, unit)]), ql.Period(n, unit), calendar, fixedLegFrequency, fixedLegAdjustment, fixedLegDayCounter, ql.Euribor3M(), ql.QuoteHandle(), ql.Period("0D"), discountTermStructure, ) for n, unit in swaps.keys() ] # %% [markdown] # ### Term structure construction # %% forecastTermStructure = ql.RelinkableYieldTermStructureHandle() # %% helpers = depositHelpers + futuresHelpers + swapHelpers[1:] depoFuturesSwapCurve = ql.PiecewiseFlatForward(settlementDate, helpers, ql.Actual360()) # %% helpers = depositHelpers + fraHelpers + swapHelpers depoFraSwapCurve = ql.PiecewiseFlatForward(settlementDate, helpers, ql.Actual360()) # %% [markdown] # ### Swap pricing # %% swapEngine = ql.DiscountingSwapEngine(discountTermStructure) # %% nominal = 1000000 length = 5 maturity = calendar.advance(settlementDate, length, ql.Years) payFixed = True # %% fixedLegFrequency = ql.Annual fixedLegAdjustment = ql.Unadjusted fixedLegDayCounter = ql.Thirty360(ql.Thirty360.BondBasis) fixedRate = 0.04 # %% floatingLegFrequency = ql.Quarterly spread = 0.0 fixingDays = 2 index = ql.Euribor3M(forecastTermStructure) floatingLegAdjustment = ql.ModifiedFollowing floatingLegDayCounter = index.dayCounter() # %% fixedSchedule = ql.Schedule( settlementDate, maturity, fixedLegTenor, calendar, fixedLegAdjustment, fixedLegAdjustment, ql.DateGeneration.Forward, False, ) floatingSchedule = ql.Schedule( settlementDate, maturity, floatingLegTenor, calendar, floatingLegAdjustment, floatingLegAdjustment, ql.DateGeneration.Forward, False, ) # %% [markdown] # We'll build a 5-years swap starting spot... # %% spot = ql.VanillaSwap( ql.Swap.Payer, nominal, fixedSchedule, fixedRate, fixedLegDayCounter, floatingSchedule, index, spread, floatingLegDayCounter, ) spot.setPricingEngine(swapEngine) # %% [markdown] # ...and one starting 1 year forward. # %% forwardStart = calendar.advance(settlementDate, 1, ql.Years) forwardEnd = calendar.advance(forwardStart, length, ql.Years) fixedSchedule = ql.Schedule( forwardStart, forwardEnd, fixedLegTenor, calendar, fixedLegAdjustment, fixedLegAdjustment, ql.DateGeneration.Forward, False, ) floatingSchedule = ql.Schedule( forwardStart, forwardEnd, floatingLegTenor, calendar, floatingLegAdjustment, floatingLegAdjustment, ql.DateGeneration.Forward, False, ) # %% forward = ql.VanillaSwap( ql.Swap.Payer, nominal, fixedSchedule, fixedRate, fixedLegDayCounter, floatingSchedule, index, spread, floatingLegDayCounter, ) forward.setPricingEngine(swapEngine) # %% [markdown] # We'll price them both on the bootstrapped curves. # # This is the quoted 5-years market rate; we expect the fair rate of the spot swap to match it. # %% print(swaps[(5, ql.Years)].value()) # %% def show(swap): print("NPV = %.2f" % swap.NPV()) print("Fair spread = %.4f %%" % (swap.fairSpread()*100)) print("Fair rate = %.4f %%" % (swap.fairRate()*100)) # %% [markdown] # These are the results for the 5-years spot swap on the deposit/futures/swap curve... # %% forecastTermStructure.linkTo(depoFuturesSwapCurve) show(spot) # %% [markdown] # ...and these are on the deposit/fra/swap curve. # %% forecastTermStructure.linkTo(depoFraSwapCurve) show(spot) # %% [markdown] # The same goes for the 1-year forward swap, except for the fair rate not matching the spot rate. # %% forecastTermStructure.linkTo(depoFuturesSwapCurve) show(forward) # %% forecastTermStructure.linkTo(depoFraSwapCurve) show(forward) # %% [markdown] # Modifying the 5-years swap rate and repricing will change the results: # %% swaps[(5, ql.Years)].setValue(0.046) # %% forecastTermStructure.linkTo(depoFuturesSwapCurve) # %% show(spot) # %% show(forward) # %% forecastTermStructure.linkTo(depoFraSwapCurve) # %% show(spot) # %% show(forward)