# Copyright (C) 2004 StatPro Italia srl # # 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 quantlib-dev@lists.sf.net # The license is also available online at http://quantlib.org/html/license.html # # 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. from QuantLib import * swaptionVols = [ # maturity, length, volatility (Period(1, 'Year'), Period(1,'Years'), 0.1810), (Period(1, 'Year'), Period(3,'Years'), 0.1590), (Period(1, 'Year'), Period(5,'Years'), 0.1400), (Period(1, 'Year'), Period(10,'Years'), 0.1220), (Period(2, 'Years'), Period(5, 'Years'), 0.1290), (Period(2, 'Years'), Period(7, 'Years'), 0.1230), (Period(3, 'Years'), Period(5, 'Years'), 0.1201), (Period(4, 'Years'), Period(4, 'Years'), 0.1189), (Period(4, 'Years'), Period(5, 'Years'), 0.1146), (Period(5, 'Years'), Period(3, 'Years'), 0.1183), (Period(5, 'Years'), Period(5, 'Years'), 0.1108), (Period(7, 'Years'), Period(2, 'Years'), 0.1110), (Period(7, 'Years'), Period(5, 'Years'), 0.1040), (Period(10,'Years'), Period(1, 'Year'), 0.1109), (Period(10,'Years'), Period(5, 'Year'), 0.0977) ] def formatVol(v, digits = 2): format = '%%.%df %%%%' % digits return format % (v * 100) def formatPrice(p, digits = 2): format = '%%.%df %%%%' % digits return format % p def calibrate(model, helpers, l, name): format = '%12s |%12s |%12s |%12s |%12s' header = format % ('maturity','length','volatility','implied','error') rule = '-' * len(header) dblrule = '=' * len(header) print print dblrule print name print rule method = Simplex(l, 1.0e-9); method.setEndCriteria(EndCriteria(1000, 1.0e-7)); model.calibrate(helpers, method); print 'Parameters: %s' % model.params() print rule print header print rule totalError = 0.0 for swaption, helper in zip(swaptionVols, helpers): maturity, length, vol = swaption NPV = helper.modelValue() implied = helper.impliedVolatility(NPV, 1.0e-4, 1000, 0.05, 0.50) error = implied - vol totalError += abs(error) print format % (maturity, length, formatVol(vol,4), formatVol(implied,4), formatVol(error,4)) averageError = totalError/len(helpers) print rule format = '%%%ds' % len(header) print format % ('Average error: ' + formatVol(averageError,4)) print dblrule todaysDate = Date(15,2,2002) Settings.instance().evaluationDate = todaysDate calendar = TARGET() settlementDate = Date(19,2,2002); settlementDays = 2 dayCounter = Thirty360() depositHelpers = [ DepositRateHelper(QuoteHandle(SimpleQuote(rate)), n, unit, settlementDays, calendar, 'mf', dayCounter) for n, unit, rate in [(1, 'week', 0.03295), (1, 'month', 0.0331), (3, 'months', 0.0329), (6, 'months', 0.0333), (9, 'months', 0.0341), (1, 'year', 0.0353)] ] fixedLegFrequency = 1 fixedLegAdjustment = 'unadjusted' fixedLegDayCounter = Thirty360() floatingLegFrequency = 2 floatingLegAdjustment = 'modifiedfollowing' swapHelpers = [ SwapRateHelper(QuoteHandle(SimpleQuote(rate)), n, unit, settlementDays, calendar, fixedLegFrequency, fixedLegAdjustment, fixedLegDayCounter, floatingLegFrequency, floatingLegAdjustment) for n, unit, rate in [(2, 'years', 0.04875), (3, 'years', 0.0438), (5, 'years', 0.0474325), (10, 'years', 0.051825), (20, 'years', 0.0545125)] ] termStructure = YieldTermStructureHandle() termStructure.linkTo(PiecewiseFlatForward(settlementDate, depositHelpers+swapHelpers, Actual360())) # define the ATM/OTM/ITM swaps payFixed = 1 fixingDays = 2 swapStart = settlementDate + (1,'years') index = Euribor(6, 'months', termStructure) swapLength = 5 swapEnd = swapStart + (swapLength,'years') fixedSchedule = Schedule(calendar, swapStart, swapEnd, fixedLegFrequency, fixedLegAdjustment) floatingSchedule = Schedule(calendar, swapStart, swapEnd, floatingLegFrequency, floatingLegAdjustment) atmRate = SimpleSwap(payFixed, 100.0, fixedSchedule, 0.0, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure).fairRate() atmSwap = SimpleSwap(payFixed, 100.0, fixedSchedule, atmRate, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure) otmSwap = SimpleSwap(payFixed, 100.0, fixedSchedule, atmRate*1.2, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure) itmSwap = SimpleSwap(payFixed, 100.0, fixedSchedule, atmRate*0.8, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure) helpers = [ SwaptionHelper(maturity, length, QuoteHandle(SimpleQuote(vol)), index, termStructure) for maturity, length, vol in swaptionVols ] times = {} for h in helpers: for t in h.times(): times[t] = 1 times = times.keys() times.sort() grid = TimeGrid(times) HW = HullWhite(termStructure) HW2 = HullWhite(termStructure) BK = BlackKarasinski(termStructure) print "Calibrating..." for h in helpers: h.setPricingEngine(JamshidianSwaptionEngine(HW)) calibrate(HW, helpers, 0.05, "Hull-White (analytic formulae)") for h in helpers: h.setPricingEngine(TreeSwaptionEngine(HW2,grid)) calibrate(HW2, helpers, 0.05, "Hull-White (numerical calibration)") for h in helpers: h.setPricingEngine(TreeSwaptionEngine(BK,grid)) calibrate(BK, helpers, 0.05, "Black-Karasinski (numerical calibration)") # price Bermudan swaptions on defined swaps schedule = Schedule(calendar, swapStart, swapEnd, 1, 'mf') bermudanDates = [ d for d in schedule ] exercise = BermudanExercise(bermudanDates[:-1]) format = '%17s |%17s |%17s |%17s' header = format % ('model', 'in-the-money', 'at-the-money', 'out-of-the-money') rule = '-' * len(header) dblrule = '=' * len(header) print print dblrule print 'Pricing Bermudan swaptions...' print rule print header print rule atmSwaption = Swaption(atmSwap, exercise, termStructure, TreeSwaptionEngine(HW, 100)) otmSwaption = Swaption(otmSwap, exercise, termStructure, TreeSwaptionEngine(HW, 100)) itmSwaption = Swaption(itmSwap, exercise, termStructure, TreeSwaptionEngine(HW, 100)) print format % ('HW analytic', formatPrice(itmSwaption.NPV()), formatPrice(atmSwaption.NPV()), formatPrice(otmSwaption.NPV())) atmSwaption.setPricingEngine(TreeSwaptionEngine(HW2, 100)) otmSwaption.setPricingEngine(TreeSwaptionEngine(HW2, 100)) itmSwaption.setPricingEngine(TreeSwaptionEngine(HW2, 100)) print format % ('HW numerical', formatPrice(itmSwaption.NPV()), formatPrice(atmSwaption.NPV()), formatPrice(otmSwaption.NPV())) atmSwaption.setPricingEngine(TreeSwaptionEngine(BK, 100)) otmSwaption.setPricingEngine(TreeSwaptionEngine(BK, 100)) itmSwaption.setPricingEngine(TreeSwaptionEngine(BK, 100)) print format % ('BK numerical', formatPrice(itmSwaption.NPV()), formatPrice(atmSwaption.NPV()), formatPrice(otmSwaption.NPV())) print dblrule