Price Portfolio of Bond and Bond Option Instruments
This example shows the workflow to create and price a portfolio of bond and bond option instruments. You can use finportfolio
and pricePortfolio
to price FixedBond
, FixedBondOption
, OptionEmbeddedFixedBond
, and FloatBond
instruments using an IRTree
pricing method.
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
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: [4×1 datetime] Rates: [4×1 double] Settle: 01-Jan-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create Bond and Option Instruments
Use fininstrument
to create a FixedBond
, FixedBondOption
, OptionEmbeddedFixedBond
, and FloatBond
instrument objects.
CDates = datetime([2020,1,1 ; 2022,1,1]); CRates = [.0425; .0750]; CouponRate = timetable(CDates,CRates); Maturity = datetime(2022,1,1); Period = 1; % Vanilla FixedBond VBond = 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 bond SBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period,'Name',"stepped_coupon_bond")
SBond = FixedBond with properties: CouponRate: [2×1 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"
% FloatBond Spread = 0; Reset = 1; Float = fininstrument("FloatBond",'Maturity',Maturity,'Spread',Spread,'Reset', Reset, ... 'ProjectionCurve',ZeroCurve,'Name',"floatbond")
Float = FloatBond with properties: Spread: 0 ProjectionCurve: [1×1 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 option Strike = 100; ExerciseDates = datetime(2020,1,1); OptionType ='call'; Period = 1; CallOption = fininstrument("FixedBondOption",'Strike',Strike,'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: [1×1 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: [2×1 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: [2×1 datetime] PutDates: [0×1 datetime] CallSchedule: [2×1 timetable] PutSchedule: [0×0 timetable] CallExerciseStyle: "american" PutExerciseStyle: [0×0 string] Name: "option_embedded_fixedbond"
Create HullWhite
Model
Use finmodel
to create a HullWhite
model object.
VolCurve = 0.01; AlphaCurve = 0.1; HWModel = finmodel("hullwhite",'alpha',AlphaCurve,'sigma',VolCurve)
HWModel = HullWhite with properties: Alpha: 0.1000 Sigma: 0.0100
Create IRTree
Pricer for HullWhite
Model
Use finpricer
to create an IRTree
pricer object for a HullWhite
model and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
HWTreePricer = finpricer("IRTree",'Model',HWModel,'DiscountCurve',ZeroCurve,'TreeDates',ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1×1 struct] TreeDates: [4×1 datetime] Model: [1×1 finmodel.HullWhite] DiscountCurve: [1×1 ratecurve]
Create finportfolio
Object and Add Callable Bond Instrument
Create a finportfolio
object 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: [4×1 fininstrument.FinInstrument] Pricers: [1×1 finpricer.irtree.HWBKTree] PricerIndex: [4×1 double] Quantity: [4×1 double]
Use addInstrument
to add the callable bond instrument to the existing portfolio.
myportfolio = addInstrument(myportfolio,CallableBond,HWTreePricer,1)
myportfolio = finportfolio with properties: Instruments: [5×1 fininstrument.FinInstrument] Pricers: [1×1 finpricer.irtree.HWBKTree] PricerIndex: [5×1 double] Quantity: [5×1 double]
myportfolio.PricerIndex
ans = 5×1
1
1
1
1
1
The PricerIndex
property has a length equal to the length of instrument objects in the finportfolio
object 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
Use pricePortfolio
to compute the price and sensitivities for the portfolio and the bond and option instruments in the portfolio.
format bank
[PortPrice,InstPrice,PortSens,InstSens] = pricePortfolio(myportfolio)
PortPrice = 600.55
InstPrice = 5×1
96.59
204.14
200.00
0.05
99.77
PortSens=1×4 table
Price Delta Gamma Vega
______ ________ _______ ______
600.55 -1297.48 5759.65 -63.40
InstSens=5×4 table
Price Delta Gamma Vega
______ _______ _______ ______
vanilla_fixed 96.59 -344.81 1603.49 -0.00
stepped_coupon_bond 204.14 -725.96 3364.60 0.00
floatbond 200.00 0.00 -0.00 -0.00
fixed_bond_option 0.05 -3.69 24.15 12.48
option_embedded_fixedbond 99.77 -223.03 767.41 -75.88