FixedBondOption
Description
Create and price a FixedBondOption
instrument object for
one or more Fixed Bond Option instruments using this workflow:
Use
fininstrument
to create aFixedBondOption
instrument object for one or more Fixed Bond Option instruments.Use
finmodel
to specify aHullWhite
,BlackKarasinski
,BlackDermanToy
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
,CoxIngersollRoss
, orLinearGaussian2F
model for theFixedBondOption
instrument object.Choose a pricing method.
When using a
HullWhite
,BlackKarasinski
,CoxIngersollRoss
, orBlackDermanToy
model, usefinpricer
to specify anIRTree
pricing method for one or moreFixedBondOption
instruments.When using a
HullWhite
,BlackKarasinski
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
, orLinearGaussian2F
model, usefinpricer
to specify anIRMonteCarlo
pricing method for one or moreFixedBondOption
instruments.
For more information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
For more information on the available models and pricing methods for a
FixedBondOption
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates a FixedBondOptionObj
= fininstrument(InstrumentType
,'Strike
',strike_value,'ExerciseDate
',exercise_date,'Bond
',bond_obj)FixedBondOption
object for one or more Fixed
Bond Option instruments by specifying InstrumentType
and sets the properties for
the required name-value pair arguments Strike
,
ExerciseDate
, and Bond
.
The FixedBondOption
instrument supports a European or
American option. For more information, see More About.
sets optional properties
using additional name-value pairs in addition to the required arguments in
the previous syntax. For example, FixedBondOptionObj
= fininstrument(___,Name,Value
)FixedBondOptionObj =
fininstrument("FixedBondOption",'Strike',100,'ExerciseDate',datetime(2019,1,30),'Bond',bond_obj,'OptionType','put','ExerciseStyle',"American",'Name',"fixed_bond_option")
creates a FixedBondOption
instrument with a strike of 100
and an American exercise. You can specify multiple name-value pair
arguments.
Input Arguments
InstrumentType
— Instrument type
string with value "FixedBondOption"
| string array with values of
"FixedBondOption"
| character vector with value
'FixedBondOption'
| cell array of character vectors with values of
'FixedBondOption'
Instrument type, specified as a string with the value of
"FixedBondOption"
, a character vector with the
value of 'FixedBondOption'
, an
NINST
-by-1
string array with
values of "FixedBondOption"
, or an
NINST
-by-1
cell array of
character vectors with values of
'FixedBondOption'
.
Data Types: char
| cell
| string
Specify required
and optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where
Name
is the argument name and Value
is
the corresponding value. Name-value arguments must appear after other arguments,
but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: FixedBondOptionObj =
fininstrument("FixedBondOption",'Strike',100,'ExerciseDate',datetime(2019,1,30),'Bond',bond_obj,'OptionType','put','ExerciseStyle',"American",'Name',"fixed_bond_option")
FixedBondOption
Name-Value Pair
ArgumentsStrike
— Option strike value
scalar nonnegative numeric | nonnegative numeric vector
Option strike value, specified as the comma-separated pair
consisting of 'Strike'
and a scalar nonnegative
numeric or an NINST
-by-1
nonnegative numeric vector.
Data Types: double
ExerciseDate
— Option exercise date
datetime array | string array | date character vector
Option exercise date, specified as the comma-separated pair
consisting of 'ExerciseDate'
and a scalar or an
NINST
-by-1
vector using a
datetime array, string array, or date character vectors.
For a European option, there is only one
ExerciseDate
on the option expiry date.For a Bermudan option, there is a
1
-by-NSTRIKES
vector of exercise dates.For an American option, the option can be exercised between
Settle
of theratecurve
and the single listedExerciseDate
.
To support existing code, FixedBondOption
also
accepts serial date numbers as inputs, but they are not recommended.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the ExerciseDate
property is stored as a
datetime
.
Data Types: double
| char
| string
| datetime
Bond
— Underlying FixedBond
instrument
FixedBond
object | vector of FixedBond
objects
Underlying FixedBond
instrument, specified as
the comma-separated pair consisting of 'Bond'
and
a scalar FixedBond
object or an
NINST
-by-1
vector of
FixedBond
objects.
Data Types: object
FixedBondOption
Name-Value Pair
ArgumentsOptionType
— Option type
"call"
(default) | string with value "call"
or
"put"
| string array with values of "call"
or
"put"
| character vector with value 'call'
or
'put'
| cell array of character vectors with values of
'call'
or 'put'
Option type, specified as the comma-separated pair consisting of
'OptionType'
and a scalar string or character
vector or an NINST
-by-1
cell
array of character vectors or string array.
Data Types: char
| cell
| string
ExerciseStyle
— Option exercise style
"European"
(default) | string with value "European"
,
"American"
, or
"Bermudan"
| string array with values of "European"
,
"American"
, or
"Bermudan"
| character vector with value 'European'
,
'American'
, or
'Bermudan'
| cell array of character vectors with values of
'European'
, 'American'
, or
'Bermudan'
Option exercise style, specified as the comma-separated pair
consisting of 'ExerciseStyle'
and a scalar string
or character vector or an
NINST
-by-1
cell array of
character vectors or string array with values of
"European"
, "American"
, or
"Bermudan"
.
Data Types: string
| cell
| char
Name
— User-defined name for instrument
" "
(default) | string | string array | character vector | cell array of character vectors
User-defined name for one of more instruments, specified as the
comma-separated pair consisting of 'Name'
and a
scalar string or character vector or an
NINST
-by-1
cell array of
character vectors or string array.
Data Types: char
| cell
| string
Properties
Strike
— Option strike value
scalar nonnegative numeric | vector of nonnegative numeric
Option strike value, returned as a scalar nonnegative numeric or an
NINST
-by-1
numeric vector of
nonnegative values.
Data Types: double
ExerciseDate
— Option exercise date
scalar datetime | vector of datetimes
Option exercise date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
OptionType
— Option type
"call"
(default) | scalar string with value "call"
or
"put"
| string array with values of "call"
or
"put"
Option type, returned as a scalar string or an
NINST
-by-1
string array with
values of "call"
or "put"
.
Data Types: string
ExerciseStyle
— Option exercise style
"European"
(default) | scalar string with value "European"
,
"American"
| string array with values of "European"
,
"American"
Option exercise style, returned as a scalar string or an
NINST
-by-1
string array with
values of "European"
or "American"
.
Data Types: string
Bond
— Underlying FixedBond
instrument
scalar FixedBond
object | vector of FixedBond
objects
Underlying FixedBond
instrument, returned as a scalar
FixedBond
object or an NINST
-by-1
vector of
FixedBond
objects.
Data Types: object
Name
— User-defined name for instrument
" "
(default) | scalar string | string array
User-defined name for the instrument, returned as a scalar string or an
NINST
-by-1
string array.
Data Types: string
Object Functions
setExercisePolicy | Set exercise policy for FixedBondOption ,
FloatBondOption , or Vanilla instrument |
Examples
Price a FixedBondOption
Instrument Using HullWhite
Model and HullWhite
Tree Pricer
This example shows the workflow to price a FixedBondOption
instrument when you use a HullWhite
model and an IRTree
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object as the underlying bond.
BondInst = fininstrument("FixedBond",'Maturity',datetime(2029,9,15),'CouponRate',.021,'Period',1,'Name',"bond_instrument")
BondInst = FixedBond with properties: CouponRate: 0.0210 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2029 Name: "bond_instrument"
Create FixedBondOption
Instrument Objects
Use fininstrument
to create three callable FixedBondOption
instrument objects with European, American, and Bermudan exercise.
FixedBOptionEuro = fininstrument("FixedBondOption",'ExerciseDate',datetime(2025,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"fixed_bond_option_european")
FixedBOptionEuro = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 15-Sep-2025 Strike: 98 Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option_european"
FixedBOptionAmerican = fininstrument("FixedBondOption",'ExerciseDate',datetime(2025,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"american",'Name',"fixed_bond_option_american")
FixedBOptionAmerican = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "american" ExerciseDate: 15-Sep-2025 Strike: 98 Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option_american"
FixedBOptionBermudan = fininstrument("FixedBondOption",'ExerciseDate',[datetime(2025,9,15) , datetime(2025,11,15)],'Strike',[98,1000],'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"bermudan",'Name',"fixed_bond_option_bermudan")
FixedBOptionBermudan = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "bermudan" ExerciseDate: [15-Sep-2025 15-Nov-2025] Strike: [98 1000] Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option_bermudan"
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2019,9,15); Type = 'zero'; ZeroTimes = [calyears([1:10])]'; ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 15-Sep-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create a HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.05)
HullWhiteModel = HullWhite with properties: Alpha: 0.0100 Sigma: 0.0500
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object and use the ratecurve
object with the 'DiscountCurve'
name-value pair argument.
HWTreePricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [10x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
HWTreePricer.Tree
ans = struct with fields:
tObs: [0 1 1.9973 2.9945 3.9918 4.9918 5.9891 6.9863 7.9836 8.9836]
dObs: [15-Sep-2019 15-Sep-2020 15-Sep-2021 15-Sep-2022 15-Sep-2023 15-Sep-2024 15-Sep-2025 15-Sep-2026 15-Sep-2027 15-Sep-2028]
CFlowT: {[10x1 double] [9x1 double] [8x1 double] [7x1 double] [6x1 double] [5x1 double] [4x1 double] [3x1 double] [2x1 double] [9.9809]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double] [3x9 double] [3x11 double] [3x13 double] [3x15 double] [3x17 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6] [2 3 4 5 6 7 8] [2 3 4 5 6 7 8 9 10] [2 3 4 5 6 7 8 9 10 11 12] [2 3 4 5 6 7 8 9 10 11 12 13 14] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]}
FwdTree: {1x10 cell}
RateTree: {1x10 cell}
Price FixedBondOption
Instruments
Use price
to compute the price and sensitivities for the two FixedBondOption
instruments.
[Price, outPR] = price(HWTreePricer,FixedBOptionEuro,["all"])
Price = 10.7571
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
10.757 -178.78 2207.3 308.87
[Price, outPR] = price(HWTreePricer,FixedBOptionAmerican,["all"])
Price = 19.2984
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
19.298 -459.06 4977.1 437.32
[Price, outPR] = price(HWTreePricer,FixedBOptionBermudan,["all"])
Price = 10.7571
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
10.757 -178.78 2207.3 308.87
Price Multiple FixedBondOption
Instruments Using HullWhite
Model and HullWhite
Tree Pricer
This example shows the workflow to price multiple FixedBondOption
instruments when you use a HullWhite
model and an IRTree
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object as the underlying bond.
BondInst = fininstrument("FixedBond",'Maturity',datetime(2029,9,15),'CouponRate',.021,'Period',1,'Name',"bond_instrument")
BondInst = FixedBond with properties: CouponRate: 0.0210 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2029 Name: "bond_instrument"
Create FixedBondOption
Instrument Objects
Use fininstrument
to create a FixedBondOption
instrument object with European exercise for three Fixed Bond Option instruments.
FixedBOptionEuro = fininstrument("FixedBondOption",'ExerciseDate',datetime([2025,9,15 ; 2025,10,15 ; 2025,11,15]),'Strike',[98 ; 100 ; 102],'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"fixed_bond_option_european")
FixedBOptionEuro=3×1 FixedBondOption array with properties:
OptionType
ExerciseStyle
ExerciseDate
Strike
Bond
Name
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2019,9,15); Type = 'zero'; ZeroTimes = [calyears([1:10])]'; ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 15-Sep-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create a HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.05)
HullWhiteModel = HullWhite with properties: Alpha: 0.0100 Sigma: 0.0500
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object and use the ratecurve
object with the 'DiscountCurve'
name-value pair argument.
HWTreePricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [10x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
HWTreePricer.Tree
ans = struct with fields:
tObs: [0 1 1.9973 2.9945 3.9918 4.9918 5.9891 6.9863 7.9836 8.9836]
dObs: [15-Sep-2019 15-Sep-2020 15-Sep-2021 15-Sep-2022 15-Sep-2023 15-Sep-2024 15-Sep-2025 15-Sep-2026 15-Sep-2027 15-Sep-2028]
CFlowT: {[10x1 double] [9x1 double] [8x1 double] [7x1 double] [6x1 double] [5x1 double] [4x1 double] [3x1 double] [2x1 double] [9.9809]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double] [3x9 double] [3x11 double] [3x13 double] [3x15 double] [3x17 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6] [2 3 4 5 6 7 8] [2 3 4 5 6 7 8 9 10] [2 3 4 5 6 7 8 9 10 11 12] [2 3 4 5 6 7 8 9 10 11 12 13 14] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]}
FwdTree: {1x10 cell}
RateTree: {1x10 cell}
Price FixedBondOption
Instruments
Use price
to compute the prices and sensitivities for the FixedBondOption
instruments.
[Price, outPR] = price(HWTreePricer,FixedBOptionEuro,["all"])
Price = 3×1
10.7571
10.2111
9.6508
outPR=3×1 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
10.757 -178.78 2207.3 308.87
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
10.211 -173.94 2168.8 300.36
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
9.6508 -168.87 2127.8 291.34
Price a FixedBondOption
Instrument on a Stepped FixedBond
Using HullWhite
Model and HullWhite
Tree Pricer
This example shows the workflow to price a FixedBondOption
instrument on a stepped FixedBond
instrument when you use a HullWhite
model and an IRTree
pricing method.
Create Stepped FixedBond
Instrument Object
Use fininstrument
to create a stepped FixedBond
instrument object as the underlying bond.
Maturity = datetime(2027,1,1); Period = 1; CDates = datetime([2022,1,1 ; 2027,1,1]); CRates = [.022; .027]; CouponRate = timetable(CDates,CRates); SBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period,'Name',"stepped_bond_instrument")
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-2027 Name: "stepped_bond_instrument"
Create FixedBondOption
Instrument Object
Use fininstrument
to create a FixedBondOption
instrument object with European exercise.
FixedBOption = fininstrument("FixedBondOption",'ExerciseDate',datetime(2026,1,1),'Strike',90,'Bond',SBond,'OptionType',"call",'ExerciseStyle',"european",'Name',"fixed_bond_option_european")
FixedBOption = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 01-Jan-2026 Strike: 90 Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option_european"
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); ZeroTimes = calyears(1:10)'; ZeroRates = [0.0055 0.0063 0.0071 0.0083 0.0099 0.0131 0.0178 0.0262 0.0343 0.0387]'; ZeroDates = Settle + ZeroTimes; Compounding = 1; ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding);
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
VolCurve = 0.15; AlphaCurve = 0.03; HWModel = finmodel("HullWhite",'Alpha',AlphaCurve,'Sigma',VolCurve)
HWModel = HullWhite with properties: Alpha: 0.0300 Sigma: 0.1500
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object 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: [1x1 struct] TreeDates: [10x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
HWTreePricer.Tree
ans = struct with fields:
tObs: [0 1 2 3.0027 4.0027 5.0027 6.0027 7.0055 8.0055 9.0055]
dObs: [01-Jan-2018 01-Jan-2019 01-Jan-2020 01-Jan-2021 01-Jan-2022 01-Jan-2023 01-Jan-2024 01-Jan-2025 01-Jan-2026 01-Jan-2027]
CFlowT: {[10x1 double] [9x1 double] [8x1 double] [7x1 double] [6x1 double] [5x1 double] [4x1 double] [3x1 double] [2x1 double] [10.0055]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double] [3x9 double] [3x11 double] [3x13 double] [3x15 double] [3x17 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6] [2 3 4 5 6 7 8] [2 3 4 5 6 7 8 9 10] [2 3 4 5 6 7 8 9 10 11 12] [2 3 4 5 6 7 8 9 10 11 12 13 14] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]}
FwdTree: {1x10 cell}
RateTree: {1x10 cell}
Price FixedBondOption
Instrument
Use price
to compute the price and sensitivities for the FixedBondOption
instrument.
[Price, outPR] = price(HWTreePricer,FixedBOption,"all")
Price = 12.2717
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ ______ ______ ______
12.272 -130.1 1438.4 100.91
Price FixedBondOption
Instrument Using HullWhite
Model and IRMonteCarlo
Pricer
This example shows the workflow to price a FixedBondOption
instrument when using a HullWhite
model and an IRMonteCarlo
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object as the underlying bond.
BondInst = fininstrument("FixedBond",'Maturity',datetime(2022,9,15),'CouponRate',.021,'Period',1,'Name',"bond_instrument")
BondInst = FixedBond with properties: CouponRate: 0.0210 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2022 Name: "bond_instrument"
Create FixedBondOption
Instrument Object
Use fininstrument
to create a FixedBondOption
instrument object.
FixedBOptionEuro = fininstrument("FixedBondOption",'ExerciseDate',datetime(2020,3,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"fixed_bond_option_european")
FixedBOptionEuro = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 15-Mar-2020 Strike: 98 Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option_european"
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.32,'Sigma',0.49)
HullWhiteModel = HullWhite with properties: Alpha: 0.3200 Sigma: 0.4900
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2019,1,1); Type = 'zero'; ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 01-Jan-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create IRMonteCarlo
Pricer Object
Use finpricer
to create an IRMonteCarlo
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("IRMonteCarlo",'Model',HullWhiteModel,'DiscountCurve',myRC,'SimulationDates',datetime(2019,3,15)+calmonths(0:6:48)')
outPricer = HWMonteCarlo with properties: NumTrials: 1000 RandomNumbers: [] DiscountCurve: [1x1 ratecurve] SimulationDates: [15-Mar-2019 15-Sep-2019 15-Mar-2020 15-Sep-2020 15-Mar-2021 15-Sep-2021 15-Mar-2022 15-Sep-2022 15-Mar-2023] Model: [1x1 finmodel.HullWhite]
Price FixedBondOption
Instrument
Use price
to compute the price and sensitivities for the FixedBondOption
instrument.
[Price,outPR] = price(outPricer,FixedBOptionEuro,["all"])
Price = 24.0750
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
24.075 -166.42 1456.2 20.329
Price FixedBondOption
Instrument Using CoxIngersollRoss
Model and IRTree
Pricer
This example shows the workflow to price a FixedBondOption
instrument when you use a CoxIngersollRoss
model and an IRTree
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to first create a FixedBond
instrument object.
Maturity = datetime(2027,1,1); Period = 1; CouponRate = 0.035; FixedBond = fininstrument("FixedBond",Maturity=Maturity,CouponRate=CouponRate,Period=Period,Name="FixedBond_inst")
FixedBond = FixedBond with properties: CouponRate: 0.0350 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-2027 Name: "FixedBond_inst"
Create FixedBondOption
Instrument Object
Then use fininstrument
to create a FixedBondOption
instrument object.
Strike = 96; OptionType = 'call'; ExerciseDate = datetime(2025,1,1); FixedBOption = fininstrument("FixedBondOption",ExerciseDate=ExerciseDate,Strike=Strike,Bond=FixedBond,OptionType=OptionType,Name="FixedBondOption_inst")
FixedBOption = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 01-Jan-2025 Strike: 96 Bond: [1x1 fininstrument.FixedBond] Name: "FixedBondOption_inst"
Create CoxIngersollRoss
Model Object
Use finmodel
to create a CoxIngersollRoss
model object.
alpha = 0.03;
theta = 0.02;
sigma = 0.1;
CIRModel = finmodel("CoxIngersollRoss",Sigma=sigma,Alpha=alpha,Theta=theta)
CIRModel = CoxIngersollRoss with properties: Sigma: 0.1000 Alpha: 0.0300 Theta: 0.0200
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Times= [calyears([1 2 3 4 ])]';
Settle = datetime(2023,1,1);
ZRates = [0.035; 0.042147; 0.047345; 0.052707]';
ZDates = Settle + Times;
Compounding = -1;
Basis = 1;
ZeroCurve = ratecurve("zero",Settle,ZDates,ZRates,Compounding = Compounding, Basis = Basis);
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object for the CoxIngersollRoss
model and use the ratecurve
object for the 'DiscountCurve'
name-value argument.
CIRPricer = finpricer("irtree",Model=CIRModel,DiscountCurve=ZeroCurve,Maturity=ZDates(end),NumPeriods=length(ZDates))
CIRPricer = CIRTree with properties: Tree: [1x1 struct] TreeDates: [4x1 datetime] Model: [1x1 finmodel.CoxIngersollRoss] DiscountCurve: [1x1 ratecurve]
Price FixedBondOption
Instrument
Use price
to compute the price for the FixedBondOption
instrument.
[Price,outPR] = price(CIRPricer,FixedBOption,"all")
Price = 1.0251
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
1.0251 -53.957 296.82 13.791
More About
Bond Option
A bond option gives the holder the right to sell a bond back to the issuer (put) or to redeem a bond from its current owner (call) at a specific price and on a specific date.
The FixedBondOption
instrument supports two types of put and
call options on bonds:
American option — An option that you exercise any time until its expiration date.
European option — An option that you exercise only on its expiration date.
For more information, see Bond Options.
Tips
After creating a FixedBondOption
instrument object, you can use
setExercisePolicy
to
change the size of the options. For example, if you have the following
instrument:
FixedBOption = fininstrument("FixedBondOption",'ExerciseDate',datetime(2022,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"European")
FixedBondOption
instrument's size by changing the
ExerciseStyle
from "European"
to
"American"
, use setExercisePolicy
:FixedBOption = setExercisePolicy(FixedBOption,[datetime(2021,1,1) datetime(2022,1,1)],100,'American')
Version History
Introduced in R2020aR2023b: Support for Pricing FixedBondOption
Instruments Using CoxIngersollRoss
Model and IRTree
Pricer
You can price FixedBondOption
instruments using a CoxIngersollRoss
model object
and an IRTree
pricing
method.
R2022b: Serial date numbers not recommended
Although FixedBondOption
supports serial date numbers,
datetime
values are recommended instead. The
datetime
data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.
To convert serial date numbers or text to datetime
values, use the datetime
function. For example:
t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)
y = 2021
There are no plans to remove support for serial date number inputs.
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