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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.

    • When using a BlackScholes model, use finpricer to specify a Rubinstein pricing method for one or more Cliquet instruments.

    • When using a BlackScholes, Heston, Bates, or Merton model, use finpricer to specify an AssetMonteCarlo pricing method for one or more Cliquet 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 Cliquet instrument, see Choose Instruments, Models, and Pricers.

Creation

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 pair argument for ResetDates.

example

TouchOpt = fininstrument(___,Name,Value) sets optional properties using additional name-value pair 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 pair 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

Cliquet Name-Value Pair Arguments

Specify required and optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: CliquetOpt = fininstrument("Cliquet",'ResetDates',ResetDates,'Name',"Cliquet_option")
Required Cliquet Name-Value Pair Arguments

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Reset dates when option strike is set, specified as the comma-separated pair consisting of '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 Pair Arguments

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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 | string

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.

Data Types: string | char

Option type, specified as the comma-separated pair consisting of '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 the comma-separated pair consisting of 'InitialStrike' and a scalar nonnegative numeric value or an NINST-by-1 vector of nonnegative numeric values.

Data Types: double

Local cap, specified as the comma-separated pair consisting of 'LocalCap' and a scalar nonnegative numeric value or an NINST-by-1 vector of nonnegative numeric values.

Data Types: double

Local floor, specified as the comma-separated pair consisting of 'LocalFloor' and a scalar nonnegative numeric value or an NINST-by-1 vector of nonnegative numeric values.

Data Types: double

Global cap, specified as the comma-separated pair consisting of 'GlobalCap' and a scalar nonnegative numeric value or an NINST-by-1 vector of nonnegative numeric values.

Data Types: double

Global floor, specified as the comma-separated pair consisting of '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 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

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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);

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',.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 = 13.0616
outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results 
ans=1×7 table
    Price      Delta        Gamma       Lambda     Rho      Theta     Vega 
    ______    _______    ___________    ______    ______    _____    ______

    13.062    0.13062    -8.8818e-15      1       59.313      0      64.687

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',.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',"VanillaCliquet")
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: "VanillaCliquet"

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

    0.0339
    0.1716
    0.1030

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    0.02066    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    0.011132    1.6851    93.219    51.616    -7.511

More About

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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:

Rn={STnSTn1STn1relative returnSTnSTn1absolute return}

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:

Payoff cliquet=i=1n(Ri)

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:

LCLFCliquetPayoff=i=1nmax(LF,min(LC,Ri))

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:

GCGFCliquetPayoff=max[GF,min(GC,i=1nmax(LF,min(LC,RI))]

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:

GCLFCliquetPayoff=min(GC,i=1nmax(LF,Ri))

GFLCCliquetPayoff=max(GF,i=1nmin(LF,Ri))

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

Introduced in R2021b