Cliquet

`Cliquet` instrument object

Description

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

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

2. Use `finmodel` to specify a `BlackScholes`, `Bates`, `Merton`, or `Heston` model for the `Cliquet` 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 `Cliquet` instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

``CliquetOpt = fininstrument(InstrumentType,ResetDates=reset_dates)``
``CliquetOpt = fininstrument(___,Name=Value)``

Description

example

````CliquetOpt = fininstrument(InstrumentType,ResetDates=reset_dates)` creates a `Cliquet` instrument object for one or more Cliquet instruments by specifying `InstrumentType` and sets properties using the required name-value argument for `ResetDates`.```

example

````CliquetOpt = fininstrument(___,Name=Value)` sets optional properties using additional name-value arguments in addition to the required arguments in the previous syntax. For example, ```CliquetOpt = fininstrument("Cliquet",ResetDates=ResetDates,Name="Cliquet_option")``` creates a `Cliquet` option. You can specify multiple name-value arguments.```

Input Arguments

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Instrument type, specified as a string with the value of `"Cliquet"`, a character vector with the value of `'Cliquet'`, an `NINST`-by-`1` string array with values of `"Cliquet"`, or an `NINST`-by-`1` cell array of character vectors with values of `'Cliquet'`.

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.

Example: ```CliquetOpt = fininstrument("Cliquet",ResetDates=ResetDates,Name="Cliquet_option")```

Required `Cliquet` Name-Value Arguments

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Reset dates when option strike is set, specified as `ResetDates` and a `1`-by-`NumDates` vector of datetimes. The last element corresponds to the maturity date of the `Cliquet` option.

A cliquet option is a path-dependent, exotic option that periodically settles and then resets its strike price at the level of the underlying asset at the time of settlement. The reset of the strike price is not conditional to the value of the underlying asset at the reset date.

Data Types: `datetime`

Optional `Cliquet` Name-Value Arguments

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Option type, specified as `OptionType` and a scalar string or character vector or an `NINST`-by-`1` cell array of character vectors or string array.

Data Types: `char` | `string`

Option exercise style, specified as `ExerciseStyle` and a scalar string or character vector or an `NINST`-by-`1` cell array of character vectors or string array.

Data Types: `string` | `char`

Option type, specified as `ReturnType` and a scalar string or character vector or an `NINST`-by-`1` cell array of character vectors or string array.

Data Types: `char` | `string`

Original strike price used for first reset date, specified as `InitialStrike` and a scalar nonnegative numeric value or an `NINST`-by-`1` vector of nonnegative numeric values.

Data Types: `double`

Local cap, specified as `LocalCap` and a scalar nonnegative numeric value or an `NINST`-by-`1` vector of nonnegative numeric values.

Data Types: `double`

Local floor, specified as `LocalFloor` and a scalar nonnegative numeric value or an `NINST`-by-`1` vector of nonnegative numeric values.

Data Types: `double`

Global cap, specified as `GlobalCap` and a scalar nonnegative numeric value or an `NINST`-by-`1` vector of nonnegative numeric values.

Data Types: `double`

Global floor, specified as `GlobalFloor` and a scalar nonnegative numeric value or an `NINST`-by-`1` vector of nonnegative numeric values.

Data Types: `double`

User-defined name for one or more instruments, specified as `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

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Reset dates when option strike is set, returned as a `1`-by-`NumDates` vector of datetimes.

Data Types: `datetime`

Option type, returned as a scalar string.

Data Types: `string`

Option type, returned as a scalar string.

Data Types: `string`

Original strike price used for first reset date, returned as a scalar nonnegative numeric value.

Data Types: `double`

Option exercise style, returned as a scalar string.

Data Types: `string`

Local cap, returned as a scalar nonnegative numeric value.

Data Types: `double`

Local floor, returned as a scalar nonnegative numeric value.

Data Types: `double`

Global cap, returned as a scalar nonnegative numeric value.

Data Types: `double`

Global floor, returned as a scalar nonnegative numeric value.

Data Types: `double`

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

Data Types: `string`

Examples

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This example shows the workflow to price the absolute return for a `Cliquet` instrument when you use a `BlackScholes` model and an `AssetMonteCarlo` pricing method.

Create `ratecurve` Object

Create a `ratecurve` object using `ratecurve`.

```Settle = datetime(2020,1,1); Date = datetime(2021,1,1); Rates = 0.10; Basis = 1; ZeroCurve = ratecurve('zero',Settle,Date,Rates,Basis=Basis)```
```ZeroCurve = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 1 Dates: 01-Jan-2021 Rates: 0.1000 Settle: 01-Jan-2020 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous" ```

Create `Cliquet` Instrument Object

Use `fininstrument` to create a `Cliquet` instrument object.

```ResetDates = Settle + years(0:0.25:1); CliquetOpt = fininstrument("Cliquet",ResetDates=ResetDates,Name="cliquet_option")```
```CliquetOpt = Cliquet with properties: OptionType: "call" ExerciseStyle: "european" ResetDates: [01-Jan-2020 00:00:00 01-Apr-2020 07:27:18 ... ] LocalCap: Inf LocalFloor: 0 GlobalCap: Inf GlobalFloor: 0 ReturnType: "absolute" InitialStrike: NaN Name: "cliquet_option" ```

Create `BlackScholes` Model Object

Use `finmodel` to create a `BlackScholes` model object.

`BlackScholesModel = finmodel("BlackScholes",Volatility=0.1)`
```BlackScholesModel = BlackScholes with properties: Volatility: 0.1000 Correlation: 1 ```

Create `AssetMonteCarlo` Pricer Object

Use `finpricer` to create an `AssetMonteCarlo` pricer object and use the `ratecurve` object for the `'DiscountCurve'` name-value pair argument.

`outPricer = finpricer("AssetMonteCarlo",DiscountCurve=ZeroCurve,Model=BlackScholesModel,SpotPrice=100,simulationDates=Settle+days(1):days(1):Date)`
```outPricer = GBMMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 100 SimulationDates: [02-Jan-2020 03-Jan-2020 04-Jan-2020 ... ] NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.BlackScholes] DividendType: "continuous" DividendValue: 0 ```

Price `Cliquet` Instrument

Use `price` to compute the price and sensitivities for the `Cliquet` instrument.

`[Price, outPR] = price(outPricer,CliquetOpt,"all")`
```Price = 13.1885 ```
```outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct] ```
`outPR.Results `
```ans=1×7 table Price Delta Gamma Lambda Rho Theta Vega ______ _______ __________ ______ ______ _____ ______ 13.189 0.13189 1.2434e-14 1 59.019 0 66.068 ```

This example shows the workflow to price a `Cliquet` instrument when you use a `BlackScholes` model and an `AssetMonteCarlo` pricing method. This example demonstrates how variations in caps and floors affect option prices on European Cliquet options.

This example uses three 1-year call cliquet options with quarterly observation dates. The first Cliquet option has no caps or floors, the second Cliquet option has a local floor, and the third Cliquet option has a local cap and a local floor.

Create `ratecurve` Object

Create a `ratecurve` object using `ratecurve`.

```Settle = datetime(2020,01,01); Dates = datetime(2021,01,01); Rate = 0.035; Compounding = -1; ZeroCurve = ratecurve('zero',Settle,Dates,Rate,Compounding=Compounding)```
```ZeroCurve = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: 01-Jan-2021 Rates: 0.0350 Settle: 01-Jan-2020 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous" ```

Create `BlackScholes` Model Object

Use `finmodel` to create a `BlackScholes` model object.

`BSModel = finmodel("BlackScholes",Volatility=0.20)`
```BSModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1 ```

Create `Cliquet` Instrument Objects with Quarterly Observation Dates

Use `fininstrument` to create the first `Cliquet` instrument object with no caps or floors.

```ResetDates = Settle + years(0:0.25:1); Cliquet = fininstrument("Cliquet",ResetDates=ResetDates,ReturnType="relative",LocalFloor="-inf",GlobalFloor="-inf",Name="Vanilla_Cliquet")```
```Cliquet = Cliquet with properties: OptionType: "call" ExerciseStyle: "european" ResetDates: [01-Jan-2020 00:00:00 01-Apr-2020 07:27:18 ... ] LocalCap: Inf LocalFloor: -Inf GlobalCap: Inf GlobalFloor: -Inf ReturnType: "relative" InitialStrike: NaN Name: "Vanilla_Cliquet" ```

Use `fininstrument` to create the second `Cliquet` instrument object with a local floor of 0%.

`LFCliquet = fininstrument("Cliquet",ResetDates=ResetDates,ReturnType="relative",GlobalFloor="-inf",Name="LFCliquet")`
```LFCliquet = Cliquet with properties: OptionType: "call" ExerciseStyle: "european" ResetDates: [01-Jan-2020 00:00:00 01-Apr-2020 07:27:18 ... ] LocalCap: Inf LocalFloor: 0 GlobalCap: Inf GlobalFloor: -Inf ReturnType: "relative" InitialStrike: NaN Name: "LFCliquet" ```

Use `fininstrument` to create the third `Cliquet` instrument object with a local cap of 7% and a local floor of 0%.

```LocalCap = 0.07; LFLCCliquet = fininstrument("Cliquet",ResetDates=ResetDates,ReturnType="relative",LocalCap=LocalCap,GlobalFloor="-inf",Name="LFLCCLiquet")```
```LFLCCliquet = Cliquet with properties: OptionType: "call" ExerciseStyle: "european" ResetDates: [01-Jan-2020 00:00:00 01-Apr-2020 07:27:18 ... ] LocalCap: 0.0700 LocalFloor: 0 GlobalCap: Inf GlobalFloor: -Inf ReturnType: "relative" InitialStrike: NaN Name: "LFLCCLiquet" ```

Create `AssetMonteCarlo` Pricer Object

Use `finpricer` to create an `AssetMonteCarlo` pricer object and use the `ratecurve` object for the `'DiscountCurve'` name-value pair argument.

```SpotPrice = 100; NumTrials = 5000; MCPricer = finpricer("AssetMonteCarlo",DiscountCurve=ZeroCurve,Model=BSModel,... SpotPrice=SpotPrice,SimulationDates=[Settle+years(0:0.25:1),Settle+calmonths(0:1:12)],NumTrials=NumTrials)```
```MCPricer = GBMMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 100 SimulationDates: [01-Jan-2020 00:00:00 01-Feb-2020 00:00:00 ... ] NumTrials: 5000 RandomNumbers: [] Model: [1x1 finmodel.BlackScholes] DividendType: "continuous" DividendValue: 0 ```

Price `Cliquet` Instruments

Use `price` to compute the prices for the three `Cliquet` instruments.

`Price = price(MCPricer,[Cliquet;LFCliquet;LFLCCliquet])`
```Price = 3×1 0.0337 0.1717 0.1042 ```

The underlying asset has good and poor performances when simulating Cliquet option returns. You can observe the effect of caps and floors on these performances when computing the payoff of the three Cliquet instruments:

• The first Cliquet option has no local floor, so it picks up all the poor performances. Since there is no local cap, none of the returns are capped for this Cliquet option.

• The price of the second Cliquet option is higher than the price of the first Cliquet option. The effect of the local floor on the second Cliquet option is that none of the performances below 0% are considered.

• The price of the third Cliquet option is lower than the price of the second Cliquet option because of the capped performances (returns above 7% are not considered), but it is higher than the price of the first Cliquet option with no local floor, since poor performances below 0% are not considered.

This example shows the workflow to price multiple `Cliquet` instruments when you use a `BlackScholes` model and a `Rubinstein` pricing method.

Create `ratecurve` Object

Create a flat `ratecurve` object using `ratecurve`.

```Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,Basis=12)```
```myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous" ```

Create `Cliquet` Instrument Object

Use `fininstrument` to create a `Cliquet` instrument object for three Cliquet instruments.

```ResetDates = Settle + years(0:0.25:1); CliquetOpt = fininstrument("Cliquet",ResetDates=ResetDates,InitialStrike=[140;150;160],ExerciseStyle="european",Name="cliquet_option")```
```CliquetOpt=3×1 object 3x1 Cliquet array with properties: OptionType ExerciseStyle ResetDates LocalCap LocalFloor GlobalCap GlobalFloor ReturnType InitialStrike Name ```

Create `BlackScholes` Model Object

Use `finmodel` to create a `BlackScholes` model object.

`BlackScholesModel = finmodel("BlackScholes",Volatility=0.28)`
```BlackScholesModel = BlackScholes with properties: Volatility: 0.2800 Correlation: 1 ```

Create `Rubinstein` Pricer Object

Use `finpricer` to create a `Rubinstein` pricer object and use the `ratecurve` object for the `'DiscountCurve'` name-value pair argument.

`outPricer = finpricer("analytic",DiscountCurve=myRC,Model=BlackScholesModel,SpotPrice=135,DividendValue=0.025,PricingMethod="Rubinstein")`
```outPricer = Rubinstein with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 135 DividendValue: 0.0250 DividendType: "continuous" ```

Price `Cliquet` Instruments

Use `price` to compute the prices and sensitivities for the three `Cliquet` instruments.

`[Price, outPR] = price(outPricer,CliquetOpt,"all")`
```Price = 3×1 28.1905 25.3226 23.8168 ```
```outPR=3×1 object 3x1 priceresult array with properties: Results PricerData ```
`outPR.Results `
```ans=1×7 table Price Delta Gamma Lambda Vega Rho Theta ______ _______ ________ ______ ______ ______ ______ 28.191 0.59697 0.020662 2.8588 105.38 60.643 -14.62 ```
```ans=1×7 table Price Delta Gamma Lambda Vega Rho Theta ______ _______ ________ ______ ______ ______ _______ 25.323 0.41949 0.016816 2.2364 100.47 55.367 -11.708 ```
```ans=1×7 table Price Delta Gamma Lambda Vega Rho Theta ______ _______ ________ ______ ______ ______ ______ 23.817 0.29729 0.011133 1.6851 93.219 51.616 -7.511 ```

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Algorithms

A cliquet option is constructed as a series of forward start options. The premium and observation (reset) dates are set in advance and its payoff depends on the returns of the underlying asset at given observation or reset dates. This return can be based in terms of absolute or relative returns. The return during the period [Tn-1, Tn] is defined as follows:

Where n = 1,…,Nobs and Nobs is the number of observations (reset dates) during the life of the contract, Sn is the price of the underlying asset at observation time n.

Since the cliquet instrument is built as a series of forward start options, then its payoff is the sum of the returns:

Depending on the underlying asset performance, there would be positive and negative returns, and the presence of caps and floors play a big role in the payoff and price of the cliquet instrument.

If a local cap (LC) and a local floor (LF) of the individual returns are considered, then the payoff of the cliquet option is the sum of the returns, capped and floored by LC and LF, at every observation time tn:

`$\text{LCLFCliquetPayoff}=\sum _{i=1}^{n}\mathrm{max}\left(LF,\mathrm{min}\left(LC,Ri\right)\right)$`

At maturity, the sum of these modified local returns might also be globally capped and floored. If a global cap (GC) and a global floor (GF) are also considered, the cliquet option has a final payoff of:

`$\text{GCGFCliquetPayoff}=\mathrm{max}\left[GF,\mathrm{min}\left(GC,{\sum }_{i=1}^{n}\text{max(LF,min(LC,RI))}\right]$`

In this case the total sum of all the cliquets is now globally capped and floored.

There are two popular cliquets in the market, the globally capped and locally floored cliquet (GCLF) and the globally floored and locally capped cliquet (GFLC). Their payoffs are defined as follows:

`$\text{GCLFCliquetPayoff}=\mathrm{min}\left(GC,{\sum }_{i=1}^{n}\mathrm{max}\left(LF,Ri\right)\right)$`

`$\text{GFLCCliquetPayoff}=\mathrm{max}\left(GF,{\sum }_{i=1}^{n}\mathrm{min}\left(LF,Ri\right)\right)$`

In summary, the payoff of a cliquet instrument is the sum of the capped and floored returns.

Version History

Introduced in R2021b