# 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. require 'QuantLib' include QuantLib SwaptionVols = [ # maturity, length, volatility [Period.new(1, 'Year'), Period.new(1,'Years'), 0.1810], [Period.new(1, 'Year'), Period.new(3,'Years'), 0.1590], [Period.new(1, 'Year'), Period.new(5,'Years'), 0.1400], [Period.new(1, 'Year'), Period.new(10,'Years'), 0.1220], [Period.new(2, 'Years'), Period.new(5, 'Years'), 0.1290], [Period.new(2, 'Years'), Period.new(7, 'Years'), 0.1230], [Period.new(3, 'Years'), Period.new(5, 'Years'), 0.1201], [Period.new(4, 'Years'), Period.new(4, 'Years'), 0.1189], [Period.new(4, 'Years'), Period.new(5, 'Years'), 0.1146], [Period.new(5, 'Years'), Period.new(3, 'Years'), 0.1183], [Period.new(5, 'Years'), Period.new(5, 'Years'), 0.1108], [Period.new(7, 'Years'), Period.new(2, 'Years'), 0.1110], [Period.new(7, 'Years'), Period.new(5, 'Years'), 0.1040], [Period.new(10,'Years'), Period.new(1, 'Year'), 0.1109], [Period.new(10,'Years'), Period.new(5, 'Year'), 0.0977] ] def formatVol(v, digits = 2) format = "%.#{digits}f %%" return sprintf(format, v*100) end def formatPrice(p, digits = 2) format = "%.#{digits}f" return sprintf(format, p) end def calibrate(model, helpers, l, name) format = '%12s |%12s |%12s |%12s |%12s' header = sprintf(format,'maturity','length','volatility','implied','error') rule = '-' * header.length dblrule = '=' * header.length puts puts dblrule puts name puts rule method = Simplex.new(l, 1.0e-9); method.endCriteria = EndCriteria.new(1000, 1.0e-7) model.calibrate!(helpers, method) puts "Parameters: #{model.params}" puts rule puts header puts rule totalError = 0.0 n = helpers.length (0...n).each do |i| maturity, length, vol = SwaptionVols[i] npv = helpers[i].modelValue implied = helpers[i].impliedVolatility(npv, 1.0e-4, 1000, 0.05, 0.50) error = implied - vol totalError += error.abs puts sprintf(format, maturity, length, formatVol(vol,4), formatVol(implied,4), formatVol(error,4)) end averageError = totalError/helpers.length puts rule format = "%#{header.length}s" puts sprintf(format, "Average error: #{formatVol(averageError,4)}") puts dblrule end todaysDate = Date.new(15,2,2002) Settings.instance.evaluationDate = todaysDate calendar = TARGET.new settlementDate = Date.new(19,2,2002); settlementDays = 2 dayCounter = Thirty360.new depositRates = [[1, 'week', 0.03295], [1, 'month', 0.0331], [3, 'months', 0.0329], [6, 'months', 0.0333], [9, 'months', 0.0341], [1, 'year', 0.0353]] depositHelpers = depositRates.map { |n,unit,rate| DepositRateHelper.new(QuoteHandle.new(SimpleQuote.new(rate)), n, unit, settlementDays, calendar, 'mf', dayCounter) } fixedLegFrequency = 1 fixedLegAdjustment = 'unadjusted' fixedLegDayCounter = Thirty360.new floatingLegFrequency = 2 floatingLegAdjustment = 'modifiedfollowing' swapRates = [[2, 'years', 0.04875], [3, 'years', 0.0438], [5, 'years', 0.0474325], [10, 'years', 0.051825], [20, 'years', 0.0545125]] swapHelpers = swapRates.map { |n,unit,rate| SwapRateHelper.new(QuoteHandle.new(SimpleQuote.new(rate)), n, unit, settlementDays, calendar, fixedLegFrequency, fixedLegAdjustment, fixedLegDayCounter, floatingLegFrequency, floatingLegAdjustment) } termStructure = YieldTermStructureHandle.new termStructure.linkTo!(PiecewiseFlatForward.new(settlementDate, depositHelpers+swapHelpers, Actual360.new)) # define the ATM/OTM/ITM swaps payFixed = true fixingDays = 2 swapStart = settlementDate + Period.new(1,'years') index = Euribor.new(6, 'months', termStructure) swapLength = 5 swapEnd = swapStart + Period.new(swapLength,'years') fixedSchedule = Schedule.new(calendar, swapStart, swapEnd, fixedLegFrequency, fixedLegAdjustment) floatingSchedule = Schedule.new(calendar, swapStart, swapEnd, floatingLegFrequency, floatingLegAdjustment) atmRate = SimpleSwap.new(payFixed, 100.0, fixedSchedule, 0.0, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure).fairRate atmSwap = SimpleSwap.new(payFixed, 100.0, fixedSchedule, atmRate, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure) otmSwap = SimpleSwap.new(payFixed, 100.0, fixedSchedule, atmRate*1.2, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure) itmSwap = SimpleSwap.new(payFixed, 100.0, fixedSchedule, atmRate*0.8, fixedLegDayCounter, floatingSchedule, index, fixingDays, 0.0, termStructure) helpers = SwaptionVols.map { |maturity, length, vol| SwaptionHelper.new(maturity, length, QuoteHandle.new(SimpleQuote.new(vol)), index, termStructure) } times = [] helpers.each { |h| times = times + h.times } times.sort!.uniq! grid = TimeGrid.new(times) HW = HullWhite.new(termStructure) HW2 = HullWhite.new(termStructure) BK = BlackKarasinski.new(termStructure) puts "Calibrating..." helpers.each { |h| h.pricingEngine = JamshidianSwaptionEngine.new(HW) } calibrate(HW, helpers, 0.05, "Hull-White (analytic formulae)") helpers.each { |h| h.pricingEngine = TreeSwaptionEngine.new(HW2,grid) } calibrate(HW2, helpers, 0.05, "Hull-White (numerical calibration)") helpers.each { |h| h.pricingEngine = TreeSwaptionEngine.new(BK,grid) } calibrate(BK, helpers, 0.05, "Black-Karasinski (numerical calibration)") # price Bermudan swaptions on defined swaps schedule = Schedule.new(calendar, swapStart, swapEnd, 1, 'mf') bermudanDates = schedule.map { |d| d } exercise = BermudanExercise.new(bermudanDates[0...-1]) format = '%17s |%17s |%17s |%17s' header = sprintf(format,'model','in-the-money', 'at-the-money','out-of-the-money') rule = '-' * header.length dblrule = '=' * header.length puts puts dblrule puts 'Pricing Bermudan swaptions...' puts rule puts header puts rule atmSwaption = Swaption.new(atmSwap, exercise, termStructure, TreeSwaptionEngine.new(HW, 100)) otmSwaption = Swaption.new(otmSwap, exercise, termStructure, TreeSwaptionEngine.new(HW, 100)) itmSwaption = Swaption.new(itmSwap, exercise, termStructure, TreeSwaptionEngine.new(HW, 100)) puts sprintf(format,'HW analytic', formatPrice(itmSwaption.NPV), formatPrice(atmSwaption.NPV), formatPrice(otmSwaption.NPV)) atmSwaption.pricingEngine = TreeSwaptionEngine.new(HW2, 100) otmSwaption.pricingEngine = TreeSwaptionEngine.new(HW2, 100) itmSwaption.pricingEngine = TreeSwaptionEngine.new(HW2, 100) puts sprintf(format,'HW numerical', formatPrice(itmSwaption.NPV), formatPrice(atmSwaption.NPV), formatPrice(otmSwaption.NPV)) atmSwaption.pricingEngine = TreeSwaptionEngine.new(BK, 100) otmSwaption.pricingEngine = TreeSwaptionEngine.new(BK, 100) itmSwaption.pricingEngine = TreeSwaptionEngine.new(BK, 100) puts sprintf(format,'BK numerical', formatPrice(itmSwaption.NPV), formatPrice(atmSwaption.NPV), formatPrice(otmSwaption.NPV)) puts dblrule