# price

## Syntax

## Description

`[`

computes the equity instrument price and related pricing information based on the pricing
object `Price`

,`PriceResult`

] = price(`inpPricer`

,`inpInstrument`

)`inpPricer`

and the instrument object
`inpInstrument`

.

`[`

adds an optional argument to specify sensitivities. Use this syntax with the input
argument combination in the previous syntax.`Price`

,`PriceResult`

] = price(___,`inpSensitivity`

)

## Examples

### Price `Asian`

Instrument Using `RoughBergomi`

Model and `RoughVolMonteCarlo`

Pricer

This example shows the workflow to price a fixed-strike `Asian`

instrument when you use a `RoughBergomi`

model and an `RoughVolMonteCarlo`

pricing method.

**Create Asian Instrument Object**

Use `fininstrument`

to create an `Asian`

instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2019,1,30),'Strike',1000,'OptionType',"put",'Name',"asian_option")

AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 30-Jan-2019 Name: "asian_option"

**Create RoughBergomi Model Object**

Use `finmodel`

to create a `RoughBergomi`

model object.

`RoughBergomiModel = finmodel("RoughBergomi",Alpha=-0.32, Xi=0.1,Eta=0.003,RhoSV=0.9)`

RoughBergomiModel = RoughBergomi with properties: Alpha: -0.3200 Xi: 0.1000 Eta: 0.0030 RhoSV: 0.9000

**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 RoughVolMonteCarlo Pricer Object**

Use `finpricer`

to create an `RoughVolMonteCarlo`

pricer object and use the `ratecurve`

object for the `'DiscountCurve'`

name-value argument.

`outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughBergomiModel,SpotPrice=900,simulationDates=datetime(2019,1,30))`

outPricer = RoughBergomiMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 900 SimulationDates: 30-Jan-2019 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.RoughBergomi] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"

**Price Asian Instrument**

Use `price`

to compute the price and sensitivities for the `Asian`

instrument.

`[Price, outPR] = price(outPricer,AsianOpt,"all")`

Price = 103.0639

outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]

outPR.Results

`ans=`*1×7 table*
Price Delta Gamma Lambda Rho Theta Vega
______ ________ _________ _______ _______ _______ ______
103.06 -0.77793 0.0024128 -6.7932 -166.05 -1.4838 88.272

### Price `Asian`

Instrument Using `RoughHeston`

Model and `RoughVolMonteCarlo`

Pricer

*Since R2024b*

This example shows the workflow to price a fixed-strike `Asian`

instrument when you use a `RoughHeston`

model and a `RoughVolMonteCarlo`

pricing method.

**Create Asian Instrument Object**

Use `fininstrument`

to create an `Asian`

instrument object.

AsianOpt = fininstrument("Asian",ExerciseDate=datetime(2019,1,30),Strike=1000,OptionType="put",Name="asian_option")

AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 30-Jan-2019 Name: "asian_option"

**Create RoughHeston Model Object**

Use `finmodel`

to create a `RoughHeston`

model object.

`RoughHestonModel = finmodel("RoughHeston",V0=0.4,ThetaV=0.3,Kappa=0.2,SigmaV=0.1,Alpha=-0.02,RhoSV=0.3)`

RoughHestonModel = RoughHeston with properties: Alpha: -0.0200 V0: 0.4000 ThetaV: 0.3000 Kappa: 0.2000 SigmaV: 0.1000 RhoSV: 0.3000

**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 RoughVolMonteCarlo Pricer Object**

Use `finpricer`

to create a `RoughVolMonteCarlo`

pricer object and use the `ratecurve`

object for the `DiscountCurve`

name-value argument.

`outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughHestonModel,SpotPrice=900,simulationDates=datetime(2019,1,30))`

outPricer = RoughHestonMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 900 SimulationDates: 30-Jan-2019 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.RoughHeston] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"

**Price Asian Instrument**

Use `price`

to compute the price and sensitivities for the `Asian`

instrument.

`[Price, outPR] = price(outPricer,AsianOpt,"all")`

Price = 131.2194

outPR = priceresult with properties: Results: [1x8 table] PricerData: [1x1 struct]

outPR.Results

`ans=`*1×8 table*
Price Delta Gamma Lambda Rho Theta Vega VegaLT
______ ________ _______ _______ ______ _______ ______ ______
131.22 -0.67246 0.00155 -4.6122 -152.4 -74.841 105.65 0

## Input Arguments

`inpPricer`

— Pricer object

`RoughVolMonteCarlo`

object

Pricer object, specified as a previously created `RoughVolMonteCarlo`

pricer object. Create the pricer object using `finpricer`

.

**Data Types: **`object`

`inpInstrument`

— Instrument object

`Vanilla`

object | `Asian`

object | object | `Cliquet`

object | `Binary`

object

Instrument object, specified as a scalar or a vector of previously created
instrument objects. Create the instrument objects using `fininstrument`

. The following
instrument objects are supported:

**Data Types: **`object`

`inpSensitivity`

— List of sensitivities to compute

`[]`

(default) | string array with values dependent on pricer object | cell array of character vectors with values dependent on pricer object

(Optional) List of sensitivities to compute, specified as an
`NOUT`

-by-`1`

or
`1`

-by-`NOUT`

cell array of character vectors or
string array.

The supported sensitivities depend on the pricing method.

`inpInstrument` Object | Supported Sensitivities |
---|---|

`Vanilla` | ```
{'delta','gamma','vega',
'theta','rho','price','lambda'}
``` |

`Asian` | `{'delta','gamma','vega','theta','rho','price','lambda'}` |

`Cliquet` | `{'delta','gamma','vega','theta','rho','price','lambda}'` |

`Binary` | `{'delta','gamma','vega','theta','rho','price','lambda'}` |

`inpSensitivity = {'All'}`

or ```
inpSensitivity =
["All"]
```

specifies that all sensitivities for the pricing method are
returned. This is the same as specifying `inpSensitivity`

to include
each sensitivity.

**Example: **```
inpSensitivity =
["delta","gamma","vega","lambda","rho","theta","price"]
```

**Data Types: **`cell`

| `string`

## Output Arguments

`Price`

— Instrument price

numeric

Instrument price, returned as a numeric.

`PriceResult`

— Price result

`PriceResult`

object

Price result, returned as a `PriceResult`

object. The object has
the following fields:

`PriceResult.Results`

— Table of results that includes sensitivities (if you specify`inpSensitivity`

)`PriceResult.PricerData`

— Structure for pricer data

## More About

### Delta

A *delta* sensitivity measures the rate at which
the price of an option is expected to change relative to a $1 change in the price of the
underlying asset.

Delta is not a static measure; it changes as the price of the underlying asset changes (a concept known as gamma sensitivity), and as time passes. Options that are near the money or have longer until expiration are more sensitive to changes in delta.

### Gamma

A *gamma* sensitivity measures the rate of change
of an option's delta in response to a change in the price of the underlying asset.

In other words, while delta tells you how much the price of an option might move, gamma tells you how fast the option's delta itself will change as the price of the underlying asset moves. This is important because this helps you understand the convexity of an option's value in relation to the underlying asset's price.

### Vega

A *vega* sensitivity measures the sensitivity of
an option's price to changes in the volatility of the underlying asset.

Vega represents the amount by which the price of an option would be expected to change for a 1% change in the implied volatility of the underlying asset. Vega is expressed as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls.

### Theta

A *theta* sensitivity measures the rate at which
the price of an option decreases as time passes, all else being equal.

Theta is essentially a quantification of time decay, which is a key concept in options pricing. Theta provides an estimate of the dollar amount that an option's price would decrease each day, assuming no movement in the price of the underlying asset and no change in volatility.

### Rho

A *rho* sensitivity measures the rate at which the
price of an option is expected to change in response to a change in the risk-free interest
rate.

Rho is expressed as the amount of money an option's price would gain or lose for a one percentage point (1%) change in the risk-free interest rate.

### Lambda

A *lambda* sensitivity measures the percentage
change in an option's price for a 1% change in the price of the underlying asset.

Lambda is a measure of leverage, indicating how much more sensitive an option is to price movements in the underlying asset compared to owning the asset outright.

## Version History

**Introduced in R2024a**

### R2024b: Support for `RoughHeston`

model

The `price`

function supports pricing when using a `RoughHeston`

model and a `RoughVolMonteCarlo`

pricing method.

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