Cliquet

Cliquet instrument object

Since R2021b

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

Syntax

CliquetOpt = fininstrument(InstrumentType,ResetDates=reset_dates)

CliquetOpt = fininstrument(___,Name=Value)

Description

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.

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

InstrumentType — Instrument type

string with value "Cliquet" | string array with values of "Cliquet" | character vector with value 'Cliquet' | cell array of character vectors with values of 'Cliquet'

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

ResetDates — Reset dates when option strike is set

vector of datetimes

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

OptionType — 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 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

ExerciseStyle — Option exercise style

"European" (default) | string with value "European" | string array with values of "European" | character vector with value 'European' | cell array of character vectors with values of 'European'

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

ReturnType — Return calculation type

"absolute" (default) | string with value "absolute" or "relative" | string array with values of "absolute" or "relative" | character vector with value 'absolute' or 'relative' | cell array of character vectors with values of 'absolute' or 'relative'

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

InitialStrike — Original strike price used for first reset date

0 (default) | nonnegative numeric | vector of nonnegative numeric

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

LocalCap — Local cap

inf (default) | nonnegative numeric | vector of nonnegative numeric

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

Data Types: double

LocalFloor — Local floor

0 (default) | nonnegative numeric | vector of nonnegative numeric

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

Data Types: double

GlobalCap — Global cap

inf (default) | nonnegative numeric | vector of nonnegative numeric

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

Data Types: double

GlobalFloor — Global floor

0 (default) | nonnegative numeric | vector of nonnegative numeric

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

Data Types: double

Name — User-defined name for instrument

" " (default) | string | string array | character vector | cell array of character vectors

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

ResetDates — Reset dates when option strike is set

vector of datetimes

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

Data Types: datetime

OptionType — Option type

"call" (default) | string with value "call" or "put"

Option type, returned as a scalar string.

Data Types: string

ReturnType — Return calculation type

"absolute" (default) | string with value "absolute" or "relative"

Option type, returned as a scalar string.

Data Types: string

InitialStrike — Original strike price used for first reset date

0 (default) | nonnegative numeric |

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

Data Types: double

ExerciseStyle — Option exercise style

"European" (default) | string with value "European"

Option exercise style, returned as a scalar string.

Data Types: string

LocalCap — Local cap

inf (default) | nonnegative numeric

Local cap, returned as a scalar nonnegative numeric value.

Data Types: double

LocalFloor — Local floor

0 (default) | nonnegative numeric

Local floor, returned as a scalar nonnegative numeric value.

Data Types: double

GlobalCap — Global cap

inf (default) | nonnegative numeric

Global cap, returned as a scalar nonnegative numeric value.

Data Types: double

GlobalFloor — Global floor

0 (default) | nonnegative numeric

Global floor, returned as a scalar nonnegative numeric value.

Data Types: double

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 Absolute Return for Cliquet Instrument Using a Black-Scholes Model and Asset Monte Carlo Pricer

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    01-Jul-2020 14:54:36    30-Sep-2020 22:21:54    31-Dec-2020 05:49:12]
         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    05-Jan-2020    06-Jan-2020    07-Jan-2020    08-Jan-2020    09-Jan-2020    10-Jan-2020    11-Jan-2020    12-Jan-2020    13-Jan-2020    14-Jan-2020    15-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

Price Relative Return for Cliquet Instrument Using a Black-Scholes Model and Asset Monte Carlo Pricer

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    01-Jul-2020 14:54:36    30-Sep-2020 22:21:54    31-Dec-2020 05:49:12]
         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    01-Jul-2020 14:54:36    30-Sep-2020 22:21:54    31-Dec-2020 05:49:12]
         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    01-Jul-2020 14:54:36    30-Sep-2020 22:21:54    31-Dec-2020 05:49:12]
         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    01-Mar-2020 00:00:00    01-Apr-2020 00:00:00    01-Apr-2020 07:27:18    01-May-2020 00:00:00    01-Jun-2020 00:00:00    01-Jul-2020 00:00:00    01-Jul-2020 14:54:36    ...    ]
          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.

Price Multiple Cliquet Instruments Using Black-Scholes Model and Rubinstein Pricer

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

More About

Cliquet Option

A cliquet option, also called a "ratchet option," is a series of at-the-money (ATM) options, either puts or calls, where each successive option becomes active when the previous one expires.

A cliquet option is a series of forward start options, all related to each other. Each forward start option represents the advance purchase of a put, or call, option with an at-the-money strike price to be determined at a later date, typically when the option becomes active. A forward start option becomes active at a specified date in the future. The premium is paid in advance, while the time to expiration and the underlying security are established at the time the forward start option is purchased.

For example, a comparison of a European cliquet with a European vanilla option illustrates the behavior of a cliquet option. Assume that a cliquet call and put option has these characteristics:

Underlying index = FTST 100 index
Settle = June 19, 2019
Maturity = June 19, 2022
Intial Strike = 3000
% Assume that the underlying asset has the following values at these ResetDates:
ResetDate(1) = Strike = 3300
ResetDate(2) = Strike = 2700
ResetDate(3) = Strike = 2900
Local floor = 0

Assume that a vanilla call and put option has these characteristics:

Underlying index = FTST 100 index
Settle = June 19, 2019
Maturity = June 19, 2022
Strike = 3000

A three-year cliquet call on the FTST with annual resets is a series of three annual at-the-money spot calls. The initial strike is set at 3000. If at the end of year 1, the FTST closes at 3300, the first call matures in-the-money and the holder makes $300 in profit on the one-year start call. The call strike for year 2 is then reset at 3300. If at the end of year 2, the FTST closes at 2700, the call will expire worthless. The call strike for year 3 is then reset at 2700. If at the end of year 3 the underlying asset is trading at 2900, the call matures in-the-money and the holder makes a profit of $200. In summary, the holder has locked $500 in profit.

Year	Strike	Payoff at End of Each Year
1	$3000	$300
2	$3300	$0
3	$2700	$200

On the other hand, a three-year call vanilla option with a strike of 3000 will expire worthless.

A three-year cliquet put on the FTST with annual resets is a series of three annual at-the-money spot puts. The initial strike is set at 3000. If at the end of year 1, the FTST closes at 3300, the first put expires worthless. The put strike for year 2 is then reset at 3300. If at the end of year 2, the FTST closes at 2700, the put matures in-the-money and the holder makes $600 in profit on the second-year start put. The put strike for year 3 is then reset at 2700. If at the end of year 3 the underlying asset is trading at 2900, the put matures worthless. In summary, the holder has locked $600 in profit.

Year	Strike	Payoff at End of Each Year
1	$3000	0
2	$3300	$600
3	$2700	0

On the other hand, a three-year vanilla put option with a strike of $3000 will expire in-the-money with a $100 profit.

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:

$$R_n=\left\{\begin{array}{l}\frac{S_{T_n}-S_{T_{n-1}}}{S_{T_{n-1}}}relativereturn\\ S_{T_n}-S_{T_{n-1}}absolutereturn\end{array}\right\}$$

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:

$$\text{Payoff cliquet}={\displaystyle \sum _{i=1}^n(Ri})$$

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:

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

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:

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

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:

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

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

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

Version History

Introduced in R2021b