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Price Portfolio of Bond and Bond Option Instruments

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This example shows the workflow to create and price a portfolio of bond and bond option instruments. You can usefinportfolioandpricePortfolioto priceFixedBond,FixedBondOption,OptionEmbeddedFixedBond, andFloatBondinstruments using anIRTreepricing method.

CreateratecurveObject

创建一个ratecurveobject usingratecurve.

Settle = datetime(2018, 1, 1); ZeroTimes = calyears(1:4)'; ZeroRates = [0.035; 0.042147; 0.047345; 0.052707]; ZeroDates = Settle + ZeroTimes; Compounding = 1; ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,"Compounding",Compounding)
ZeroCurve = ratecurve with properties: Type: "zero" Compounding: 1 Basis: 0 Dates: [4x1 datetime] Rates: [4x1 double] Settle: 01-Jan-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"

Create Bond and Option Instruments

Usefininstrumentto create aFixedBond,FixedBondOption,OptionEmbeddedFixedBond, andFloatBondinstrument objects.

CDates = datetime([2020,1,1 ; 2022,1,1]); CRates = [.0425; .0750]; CouponRate = timetable(CDates,CRates); Maturity = datetime(2022,1,1); Period = 1;% Vanilla FixedBondVBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',0.0425,'Period',Period,'Name',"vanilla_fixed")
VBond = FixedBond with properties: CouponRate: 0.0425 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2022 Name: "vanilla_fixed"
% Stepped coupon bondSBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period,'Name',"stepped_coupon_bond")
SBond = FixedBond with properties: CouponRate: [2x1 timetable] Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2022 Name: "stepped_coupon_bond"
% FloatBondSpread = 0; Reset = 1; Float = fininstrument("FloatBond",'Maturity',Maturity,'Spread',Spread,'Reset', Reset,...'ProjectionCurve'ZeroCurve,'Name',"floatbond")
Float = FloatBond with properties: Spread: 0 ProjectionCurve: [1x1 ratecurve] ResetOffset: 0 Reset: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" LatestFloatingRate: NaN Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2022 Name: "floatbond"
% Call optionStrike = 100; ExerciseDates = datetime(2020,1,1); OptionType ='call'; Period = 1; CallOption = fininstrument("FixedBondOption",'Strike'罢工,'ExerciseDate',ExerciseDates,...'OptionType',OptionType,'ExerciseStyle',"american",'Bond', VBond,'Name',"fixed_bond_option")
CallOption = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "american" ExerciseDate: 01-Jan-2020 Strike: 100 Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option"
% Option for embedded bond (callable bond)CDates = datetime([2020,1,1 ; 2022,1,1]); CRates = [.0425; .0750]; CouponRate = timetable(CDates,CRates); StrikeOE = [100; 100]; ExerciseDatesOE = [datetime(2020,1,1); datetime(2021,1,1)]; CallSchedule = timetable(ExerciseDatesOE,StrikeOE,'VariableNames',{'Strike Schedule'}); CallableBond = fininstrument("OptionEmbeddedFixedBond",'Maturity',Maturity,...'CouponRate',CouponRate,'Period', Period,...'CallSchedule',CallSchedule,'Name',"option_embedded_fixedbond")
CallableBond = OptionEmbeddedFixedBond with properties: CouponRate: [2x1 timetable] Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2022 CallDates: [2x1 datetime] PutDates: [0x1 datetime] CallSchedule: [2x1 timetable] PutSchedule: [0x0 timetable] CallExerciseStyle: "american" PutExerciseStyle: [0x0 string] Name: "option_embedded_fixedbond"

CreateHullWhiteModel

Usefinmodelto create aHullWhitemodel object.

VolCurve = 0.01; AlphaCurve = 0.1; HWModel = finmodel("hullwhite",'alpha',AlphaCurve,'sigma',VolCurve)
HWModel = HullWhite with properties: Alpha: 0.1000 Sigma: 0.0100

CreateIRTreePricer forHullWhiteModel

Usefinpricerto create anIRTreepricer object for aHullWhitemodel and use theratecurveobject for the'DiscountCurve'name-value pair argument.

HWTreePricer = finpricer("IRTree",'Model',HWModel,'DiscountCurve'ZeroCurve,'TreeDates',ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [4x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]

CreatefinportfolioObject and Add Callable Bond Instrument

创建一个finportfolioobject with the vanilla bond, stepped coupon bond, float bond, and the call option.

myportfolio = finportfolio([VBond,SBond,Float,CallOption],HWTreePricer, [1,2,2,1])
myportfolio = finportfolio with properties: Instruments: [4x1 fininstrument.FinInstrument] Pricers: [1x1 finpricer.irtree.HWBKTree] PricerIndex: [4x1 double] Quantity: [4x1 double]

UseaddInstrumentto add the callable bond instrument to the existing portfolio.

myportfolio = addInstrument(myportfolio,CallableBond,HWTreePricer,1)
myportfolio = finportfolio with properties: Instruments: [5x1 fininstrument.FinInstrument] Pricers: [1x1 finpricer.irtree.HWBKTree] PricerIndex: [5x1 double] Quantity: [5x1 double]
myportfolio.PricerIndex
ans =5×11 1 1 1 1

ThePricerIndexproperty has a length equal to the length of instrument objects in thefinportfolioobject and stores the index of which pricer is used for each instrument object. In this case, because there is only one pricer, each instrument must use that pricer.

Price Portfolio

UsepricePortfolioto compute the price and sensitivities for the portfolio and the bond and option instruments in the portfolio.

formatbank[PortPrice,InstPrice,PortSens,InstSens] = pricePortfolio(myportfolio)
PortPrice = 600.55
InstPrice =5×196.59 204.14 200.00 0.05 99.77
PortSens=1×4 tablePrice Vega Gamma Delta ______ ______ _______ ________ 600.55 -63.40 5759.65 -1297.48
InstSens=5×4 tablePrice Vega Gamma Delta ______ ______ _______ _______ vanilla_fixed 96.59 -0.00 1603.49 -344.81 stepped_coupon_bond 204.14 0.00 3364.60 -725.96 floatbond 200.00 -0.00 -0.00 0.00 fixed_bond_option 0.05 12.48 24.15 -3.69 option_embedded_fixedbond 99.77 -75.88 767.41 -223.03