Cap
Description
Create and price a Cap
instrument object for one or more
Cap instruments using this workflow:
Use
fininstrument
to create aCap
instrument object for one or more Cap instruments.Use
finmodel
to specify aHullWhite
,BlackKarasinski
,BlackDermanToy
,Black
,Normal
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
,CoxIngersollRoss
, orLinearGaussian2F
model for theCap
instrument object.Choose a pricing method.
When using a
HullWhite
,BlackKarasinski
,BlackDermanToy
,Black
,CoxIngersollRoss
, orNormal
model, usefinpricer
for pricing one or moreCap
instruments and specify:When using a
HullWhite
,BlackKarasinski
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
, orLinearGaussian2F
model, usefinpricer
to specify anIRMonteCarlo
pricing method for one or moreCap
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
Cap
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates a CapOpt
= fininstrument(InstrumentType
,'Strike
',strike_value,'Maturity
',maturity_date)Cap
object for one or more Cap instruments by
specifying InstrumentType
and sets the properties for the required
name-value pair arguments Strike
and
Maturity
.
The Cap
instrument supports vanilla and amortizing
caps.
sets optional properties using additional
name-value pairs in addition to the required arguments in the previous
syntax. For example, CapOpt
= fininstrument(___,Name,Value
)CapOpt =
fininstrument("Cap",'Strike',0.65,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'ResetOffset',1,'Basis',1,'DaycountAdjustedCashFlow',true,'BusinessDayConvention',"follow",'ProjectionCurve',ratecurve_object,'Name',"cap_option")
creates a Cap
option with a strike of 0.65. You can
specify multiple name-value pair arguments.
Input Arguments
InstrumentType
— Instrument type
string with value "Cap"
| string array with values of "Cap"
| character vector with value 'Cap'
| cell array of character vectors with values of
'Cap'
Instrument type, specified as a string with the value of
"Cap"
, a character vector with the value of
'Cap'
, an
NINST
-by-1
string array with
values of "Cap"
, or an
NINST
-by-1
cell array of
character vectors with values of 'Cap'
.
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: CapOpt =
fininstrument("Cap",'Strike',0.65,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'ResetOffset',1,'Basis',1,'DaycountAdjustedCashFlow',true,'BusinessDayConvention',"follow",'ProjectionCurve',ratecurve_object,'Name',"cap_option")
Cap
Name-Value Pair ArgumentsStrike
— Cap strike price
nonnegative decimal | vector of nonnegative decimals
Cap strike price, specified as the comma-separated pair consisting
of 'Strike'
and a scalar nonnegative decimal
value or an NINST
-by-1
nonnegative numeric vector.
Data Types: double
Maturity
— Cap maturity date
datetime array | string array | date character vector
Cap maturity 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.
To support existing code, Cap
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 Maturity
property is stored as a
datetime.
Cap
Name-Value Pair ArgumentsReset
— Reset frequency payments per year
1
(default) | numeric with value of 0
, 1
,
2
, 3
,
4
, 6
, or
12
| numeric vector with values of 0
,
1
, 2
,
3
, 4
, 6
, or
12
Reset frequency payments per year, specified as the
comma-separated pair consisting of 'Reset'
and a
scalar numeric or an
NINST
-by-1
numeric
vector.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | integer from 0
to
13
| vector of integers from 0
to
13
Day count basis, specified as the comma-separated pair consisting
of 'Basis'
and a scalar integer or an
NINST
-by-1
vector of
integers with the following values:
0 — actual/actual
1 — 30/360 (SIA)
2 — actual/360
3 — actual/365
4 — 30/360 (PSA)
5 — 30/360 (ISDA)
6 — 30/360 (European)
7 — actual/365 (Japanese)
8 — actual/actual (ICMA)
9 — actual/360 (ICMA)
10 — actual/365 (ICMA)
11 — 30/360E (ICMA)
12 — actual/365 (ISDA)
13 — BUS/252
For more information, see Basis.
Data Types: double
Principal
— Principal amount or principal value schedule
100
(default) | scalar numeric | numeric vector | timetable
Principal amount or principal value schedule, specified as the
comma-separated pair consisting of 'Principal'
and a scalar numeric or an
NINST
-by-1
numeric vector
or a timetable.
Principal
accepts a timetable
, where the
first column is dates and the second column is its associated
principal value. The date indicates the last day that the principal
value is valid.
Note
If you are creating one or more Cap
instruments and use a timetable, the timetable specification
applies to all of the Cap
instruments.
Principal
does not accept an
NINST
-by-1
cell array
of timetables as input.
Data Types: double
| timetable
ResetOffset
— Lag in rate setting
0
(default) | scalar numeric | numeric vector
Lag in rate setting, specified as the comma-separated pair
consisting of 'ResetOffset'
and a scalar numeric
or an NINST
-by-1
numeric
vector.
Data Types: double
DaycountAdjustedCashFlow
— Flag to adjust cash flows based on actual period day count
false
(default) | value of true
or
false
| vector of values of true
or
false
Flag to adjust cash flows based on the actual period day count,
specified as the comma-separated pair consisting of
'DaycountAdjustedCashFlow'
and a scalar or an
NINST
-by-1
vector with
values of true
or
false
.
Data Types: logical
BusinessDayConvention
— Business day conventions
"actual"
(default) | string | string array | character vector | cell array of character vectors
Business day conventions, specified as the comma-separated pair
consisting of 'BusinessDayConvention'
and a
scalar string or character vector or an
NINST
-by-1
cell array of
character vectors or string array for a business day convention. The
selection for business day convention determines how nonbusiness
days are treated. Nonbusiness days are defined as weekends plus any
other date that businesses are not open (for example, statutory
holidays). Values are:
"actual"
— Nonbusiness days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date."follow"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day."modifiedfollow"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day. However, if the following business day is in a different month, the previous business day is adopted instead."previous"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day."modifiedprevious"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However, if the previous business day is in a different month, the following business day is adopted instead.
Data Types: char
| cell
| string
Holidays
— Holidays used in computing business days
NaT
(default) | datetime array | string array | date character vector
Holidays used in computing business days, specified as the
comma-separated pair consisting of 'Holidays'
and
dates using an NINST
-by-1
vector of a datetime array, string array, or date character vectors.
For
example:
H = holidays(datetime('today'),datetime(2025,12,15)); CapOpt = fininstrument("Cap",'Strike',100,'Maturity',datetime(2025,12,15),'Holidays',H)
To support existing code, Cap
also
accepts serial date numbers as inputs, but they are not recommended.
ProjectionCurve
— Rate curve used in generating future cash flows
ratecurve.empty
(default) | ratecurve
object | vector of ratecurve
objects
Rate curve used in projecting the future cash flows, specified as
the comma-separated pair consisting of
'ProjectionCurve'
and a scalar
ratecurve
object or an
NINST
-by-1
vector of
ratecurve
objects. These objects must be
created using ratecurve
. Use
this optional input if the forward curve is different from the
discount curve.
Data Types: object
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 price value
nonnegative value | vector of nonnegative values
Option strike price value, returned as a scalar nonnegative value or an
NINST
-by-1
vector of nonnegative
values.
Data Types: double
Maturity
— Cap maturity date
datetime | vector of datetimes
Cap maturity date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
Reset
— Reset frequency payments per year
1
(default) | scalar numeric | numeric vector
Reset frequency payments per year, returned as a scalar numeric or an
NINST
-by-1
numeric vector.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | integer from 0
to 13
| vector of integers from 0
to
13
Day count basis, returned as a scalar integer or an
NINST
-by-1
vector of
integers.
Data Types: double
Principal
— Principal amount or principal value schedule
100
(default) | scalar numeric | numeric vector | timetable
Principal amount or principal value schedule, returned as a scalar numeric
or an NINST
-by-1
numeric vector for
principal amounts or a timetable for a principal value schedule.
Data Types: double
| timetable
ResetOffset
— Lag in rate setting
0
(default) | scalar numeric | numeric vector
Lag in rate setting, returned as a scalar numeric or an
NINST
-by-1
numeric vector.
Data Types: double
DaycountAdjustedCashFlow
— Flag to adjust cash flows based on actual period day count
false
(default) | value of true
or false
| vector of values of true
or
false
Flag to adjust cash flows based on the actual period day count, returned
as a scalar logical or an NINST
-by-1
vector with values of true
or
false
.
Data Types: logical
BusinessDayConvention
— Business day conventions
"actual"
(default) | string | string array
Business day conventions, returned as a scalar string or an
NINST
-by-1
string array.
Data Types: string
Holidays
— Holidays used in computing business days
NaT
(default) | vector of datetimes
Holidays used in computing business days, returned as an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
ProjectionCurve
— Rate curve used in generating future cash flows
ratecurve.empty
(default) | ratecurve
object | vector of ratecurve
objects
Rate curve used in projecting the future cash flows, returned as a scalar
ratecurve
object or an
NINST
-by-1
vector of
ratecurve
objects.
Data Types: object
Name
— User-defined name for instrument
" "
(default) | string | string array
User-defined name for the instrument, returned as a scalar string or an
NINST
-by-1
string array.
Data Types: string
Examples
Price Vanilla Cap
Instrument Using HullWhite
Model and HullWhite
Pricer
This example shows the workflow to price a vanilla Cap
instrument when using a HullWhite
model and a HullWhite
pricing method.
Create Cap
Instrument Object
Use fininstrument
to create a Cap
instrument object.
CapOpt = fininstrument("Cap",'Strike',0.02,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'Basis',8,'Name',"cap_option")
CapOpt = Cap with properties: Strike: 0.0200 Maturity: 30-Jan-2019 ResetOffset: 0 Reset: 4 Basis: 8 Principal: 100 ProjectionCurve: [0x0 ratecurve] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT Name: "cap_option"
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.62,'Sigma',0.99)
HullWhiteModel = HullWhite with properties: Alpha: 0.6200 Sigma: 0.9900
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); 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: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create HullWhite
Pricer Object
Use finpricer
to create a HullWhite
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'Model',HullWhiteModel,'DiscountCurve',myRC)
outPricer = HullWhite with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.HullWhite]
Price Cap
Instrument
Use price
to compute the price for the Cap
instrument.
Price = price(outPricer,CapOpt)
Price = 2.9366
Price Multiple Vanilla Cap
Instruments Using HullWhite
Model and HullWhite
Pricer
This example shows the workflow to price multiple vanilla Cap
instruments when using a HullWhite
model and a HullWhite
pricing method.
Create Cap
Instrument Object
Use fininstrument
to create a Cap
instrument object for three Cap instruments.
CapOpt = fininstrument("Cap",'Strike',0.02,'Maturity',datetime([2019,1,30 ; 2019,2,30 ; 2019,3,30]),'Reset',4,'Principal',[100 ; 200 ; 300],'Basis',8,'Name',"cap_option")
CapOpt=3×1 Cap array with properties:
Strike
Maturity
ResetOffset
Reset
Basis
Principal
ProjectionCurve
DaycountAdjustedCashFlow
BusinessDayConvention
Holidays
Name
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.62,'Sigma',0.99)
HullWhiteModel = HullWhite with properties: Alpha: 0.6200 Sigma: 0.9900
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); 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: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create HullWhite
Pricer Object
Use finpricer
to create a HullWhite
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'Model',HullWhiteModel,'DiscountCurve',myRC)
outPricer = HullWhite with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.HullWhite]
Price Cap
Instruments
Use price
to compute the prices for the Cap
instruments.
Price = price(outPricer,CapOpt)
Price = 3×1
2.9366
7.4694
17.7915
Price Vanilla Cap
Instrument Using Normal
Model and Normal
Pricer
This example shows the workflow to price a vanilla Cap
instrument when you use a Normal
model and a Normal
pricing method.
Create ratecurve
Object
Create a ratecurve
object using ratecurve
for the underlying interest-rate curve for the cap
instrument.
Settle = datetime(2018,9,15); 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: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create Cap
Instrument Object
Use fininstrument
to create a Cap
instrument object.
CapOpt = fininstrument("Cap",'Maturity',datetime(2022,9,15),'Strike',0.04,'ProjectionCurve',myRC)
CapOpt = Cap with properties: Strike: 0.0400 Maturity: 15-Sep-2022 ResetOffset: 0 Reset: 1 Basis: 0 Principal: 100 ProjectionCurve: [1x1 ratecurve] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT Name: ""
Create Normal
Model Object
Use finmodel
to create a Normal
model object.
NormalModel = finmodel("Normal",'Volatility',0.01)
NormalModel = Normal with properties: Volatility: 0.0100
Create Normal
Pricer Object
Use finpricer
to create a Normal
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',NormalModel)
outPricer = Normal with properties: DiscountCurve: [1x1 ratecurve] Shift: 0 Model: [1x1 finmodel.Normal]
Price Cap
Instrument
Use price
to compute the price for the Cap
instrument.
[Price, outPR] = price(outPricer, CapOpt)
Price = 0.0701
outPR = priceresult with properties: Results: [1x1 table] PricerData: []
Price Amortizing Cap
Instrument Using Black
Model and Black
Pricer
This example shows the workflow to price an amortizing Cap
instrument when you use a Black
model and a Black
pricing method.
Create Cap
Instrument Object
Use fininstrument
to create an amortizing Cap
instrument object.
CADates = [datetime(2020,9,1) ; datetime(2023,9,1)]; CAPrincipal = [100; 85]; Principal = timetable(CADates,CAPrincipal); CapOpt = fininstrument("Cap",'Maturity',datetime(2023,9,1),'Strike',0.015,'Principal',Principal,'Name',"cap_amortizing_option")
CapOpt = Cap with properties: Strike: 0.0150 Maturity: 01-Sep-2023 ResetOffset: 0 Reset: 1 Basis: 0 Principal: [2x1 timetable] ProjectionCurve: [0x0 ratecurve] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT Name: "cap_amortizing_option"
Create Black
Model Object
Use finmodel
to create a Black
model object.
BlackModel = finmodel("Black",'Volatility',0.2)
BlackModel = Black with properties: Volatility: 0.2000 Shift: 0
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,9,1); Type = 'zero'; ZeroTimes = [calyears([1 2 3 4 5 7 10])]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates);
Create Black
Pricer Object
Use finpricer
to create a Black
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'Model',BlackModel,'DiscountCurve',myRC)
outPricer = Black with properties: Model: [1x1 finmodel.Black] DiscountCurve: [1x1 ratecurve]
Price Cap
Instrument
Use price
to compute the price for the Cap
instrument.
Price = price(outPricer,CapOpt)
Price = 0.3897
Price Vanilla Cap
Instrument Using HullWhite
Model and IRTree
Pricer
This example shows the workflow to price a vanilla Cap
instrument when using a HullWhite
model and an IRTree
pricing method.
Create Cap
Instrument Object
Use fininstrument
to create a Cap
instrument object.
CapOpt = fininstrument("Cap",'Strike',0.02,'Maturity',datetime(2020,1,30),'Reset',4,'Principal',100,'Basis',8,'Name',"cap_option")
CapOpt = Cap with properties: Strike: 0.0200 Maturity: 30-Jan-2020 ResetOffset: 0 Reset: 4 Basis: 8 Principal: 100 ProjectionCurve: [0x0 ratecurve] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT Name: "cap_option"
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.10)
HullWhiteModel = HullWhite with properties: Alpha: 0.0100 Sigma: 0.1000
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); 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: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
CFdates = cfdates(Settle, CapOpt.Maturity, CapOpt.Reset, CapOpt.Basis); outPricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',CFdates')
outPricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [6x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
Price Cap
Instrument
Use price
to compute the price and sensitivities for the Cap
instrument.
[Price, outPR] = price(outPricer,CapOpt,["all"])
Price = 2.7733
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ ______ _______ ______
2.7733 28.932 -49.227 31.655
Price Cap
Instrument Using LinearGaussian2F
Model and IRMonteCarlo
Pricer
This example shows the workflow to price a Cap
instrument when using a LinearGaussian2F
model and an IRMonteCarlo
pricing method.
Create Cap
Instrument Object
Use fininstrument
to create a Cap
instrument object.
CapOpt = fininstrument("Cap","Maturity",datetime(2022,9,15),'Strike',0.01,'Reset',2,'Name',"cap_option")
CapOpt = Cap with properties: Strike: 0.0100 Maturity: 15-Sep-2022 ResetOffset: 0 Reset: 2 Basis: 0 Principal: 100 ProjectionCurve: [0x0 ratecurve] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT Name: "cap_option"
Create LinearGaussian2F
Model Object
Use finmodel
to create a LinearGaussian2F
model object.
LinearGaussian2FModel = finmodel("LinearGaussian2F",'Alpha1',0.07,'Sigma1',0.01,'Alpha2',0.5,'Sigma2',0.006,'Correlation',-0.7)
LinearGaussian2FModel = LinearGaussian2F with properties: Alpha1: 0.0700 Sigma1: 0.0100 Alpha2: 0.5000 Sigma2: 0.0060 Correlation: -0.7000
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',LinearGaussian2FModel,'DiscountCurve',myRC,'SimulationDates',ZeroDates)
outPricer = G2PPMonteCarlo with properties: NumTrials: 1000 RandomNumbers: [] DiscountCurve: [1x1 ratecurve] SimulationDates: [01-Jul-2019 01-Jan-2020 01-Jan-2021 01-Jan-2022 01-Jan-2023 01-Jan-2024 01-Jan-2026 01-Jan-2029 01-Jan-2039 01-Jan-2049] Model: [1x1 finmodel.LinearGaussian2F]
Price Cap
Instrument
Use price
to compute the price and sensitivities for the Cap
instrument.
[Price,outPR] = price(outPricer,CapOpt,["all"])
Price = 1.2156
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ ______ _____ ________________
1.2156 131.37 11048 126.5 -157.38
Price Cap
Instrument Using CoxIngersollRoss
Model and IRTree
Pricer
This example shows the workflow to price a Cap
instrument when you use a CoxIngersollRoss
model and an IRTree
pricing method.
Create Cap
Instrument Object
Use fininstrument
to create a Cap
instrument object.
Maturity = datetime(2027,1,1); StrikeCap = 0.055; Reset = 1; Cap = fininstrument("Cap",Strike=StrikeCap,Maturity=Maturity,Reset=Reset,Name="Cap_inst")
Cap = Cap with properties: Strike: 0.0550 Maturity: 01-Jan-2027 ResetOffset: 0 Reset: 1 Basis: 0 Principal: 100 ProjectionCurve: [0x0 ratecurve] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT Name: "Cap_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 Cap
Instrument
Use price
to compute the price for the Cap
instrument.
[Price,outPR] = price(CIRPricer,Cap,"all")
Price = 3.3361
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ ______ _______ ______
3.3361 142.25 -2632.5 26.325
More About
Cap
A cap is a contract that includes a guarantee that sets the maximum interest rate the holder pays, based on an otherwise floating interest rate.
A cap is a contract between two parties, where the buyer pays a premium to the seller in exchange for the right to receive payments if a specified interest rate exceeds a predetermined level (the cap rate) during a specified period. The cap rate is the maximum interest rate level above which the buyer of the cap instrument will receive payments. If the reference interest rate (for example, LIBOR) exceeds the cap rate, the buyer is entitled to receive a payment from the seller.
The payoff for a cap is:
For more information, see Cap.
Version History
Introduced in R2020aR2023b: Support for Pricing Cap
Instruments Using CoxIngersollRoss
Model and IRTree
Pricer
You can price Cap
instruments using a CoxIngersollRoss
model object
and an IRTree
pricing
method.
R2022b: Serial date numbers not recommended
Although Cap
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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