# Cliquet

## Description

Create and price a `Cliquet`

instrument object for one or
more Cliquet instruments using this workflow:

Use

`fininstrument`

to create a`Cliquet`

instrument object for one or more Cliquet instruments.Use

`finmodel`

to specify a`BlackScholes`

,`Bates`

,`Merton`

,`RoughBergomi`

, or`Heston`

model for the`Cliquet`

instrument object.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.When using a

`RoughBergomi`

model, use`finpricer`

to specify a`RoughVolMonteCarlo`

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

### Description

creates a `CliquetOpt`

= fininstrument(`InstrumentType`

,`ResetDates`

=reset_dates)`Cliquet`

instrument object for one or more
Cliquet instruments by specifying `InstrumentType`

and
sets properties using the
required name-value argument for `ResetDates`

.

sets optional properties using
additional name-value arguments in addition to the required arguments in the
previous syntax. For example, `CliquetOpt`

= fininstrument(___,`Name=Value`

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

creates a `Cliquet`

option. You can specify multiple
name-value arguments.

### Input Arguments

## Properties

## Examples

## More About

## 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:

$${R}_{n}=\left\{\begin{array}{l}\frac{{S}_{{T}_{n}}-{S}_{{T}_{n-1}}}{{S}_{{T}_{n-1}}}relative\text{}return\\ {S}_{{T}_{n}}-{S}_{{T}_{n-1}}absolute\text{}return\end{array}\right\}$$

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:

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

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*:

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

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:

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

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:

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

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

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

## Version History

**Introduced in R2021b**