Cap

`Cap` instrument object

Description

Create and price a `Cap` instrument object for one or more Cap instruments using this workflow:

1. Use `fininstrument` to create a `Cap` instrument object for one or more Cap instruments.

2. Use `finmodel` to specify a `HullWhite`, `BlackKarasinski`, `Black`, `Normal`, `BraceGatarekMusiela`, `SABRBraceGatarekMusiela`, or `LinearGaussian2F` model for the `Cap` instrument object.

3. Choose a pricing method.

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

``CapOpt = fininstrument(InstrumentType,'Strike',strike_value,'Maturity',maturity_date)``
``CapOpt = fininstrument(___,Name,Value)``

Description

example

````CapOpt = fininstrument(InstrumentType,'Strike',strike_value,'Maturity',maturity_date)` creates a `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.```

example

````CapOpt = fininstrument(___,Name,Value)` sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For 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")``` creates a `Cap` option with a strike of 0.65. You can specify multiple name-value pair arguments.```

Input Arguments

expand all

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`

Name-Value Arguments

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")```

Required `Cap` Name-Value Pair Arguments

expand all

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`

Cap maturity date, specified as the comma-separated pair consisting of `'ExerciseDate'` and a scalar datetime, serial date number, date character vector, date string or an `NINST`-by-`1` vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.

If you use date character vectors or date strings, the format must be recognizable by `datetime` because the `Maturity` property is stored as a datetime.

Data Types: `double` | `char` | `cell` | `string` | `datetime`

Optional `Cap` Name-Value Pair Arguments

expand all

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`

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

Data Types: `double`

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`

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`

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`

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 used in computing business days, specified as the comma-separated pair consisting of `'Holidays'` and dates using an `NINST`-by-`1` vector of datetimes, serial date numbers, cell array of date character vectors, or date string array. For example:

```H = holidays(datetime('today'),datetime(2025,12,15)); CapOpt = fininstrument("Cap",'Strike',100,'Maturity',datetime(2025,12,15),'Holidays',H)```

Data Types: `double` | `cell` | `datetime` | `string`

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`

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

expand all

Option strike price value, returned as a scalar nonnegative value or an `NINST`-by-`1` vector of nonnegative values.

Data Types: `double`

Cap maturity date, returned as a scalar datetime or an `NINST`-by-`1` vector of datetimes.

Data Types: `datetime`

Reset frequency payments per year, returned as a scalar numeric or an `NINST`-by-`1` numeric vector.

Data Types: `double`

Day count basis, returned as a scalar integer or an `NINST`-by-`1` vector of integers.

Data Types: `double`

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`

Lag in rate setting, returned as a scalar numeric or an `NINST`-by-`1` numeric vector.

Data Types: `double`

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`

Business day conventions, returned as a scalar string or an `NINST`-by-`1` string array.

Data Types: `string`

Holidays used in computing business days, returned as an `NINST`-by-`1` vector of datetimes.

Data Types: `datetime`

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`

User-defined name for the instrument, returned as a scalar string or an `NINST`-by-`1` string array.

Data Types: `string`

Examples

collapse all

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 ```

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 object 3x1 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 ```

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: [] ```

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 ```

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 Vega Gamma Delta ______ ______ _______ ______ 2.7733 31.655 -49.227 28.932 ```

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 ... ] 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 ```