# 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 `Touch`

Instrument Using `Heston`

Model and `AssetMonteCarlo`

Pricer

This example shows the workflow to price a `Touch`

instrument when you use a `Heston`

model and an `AssetMonteCarlo`

pricing method.

**Create Touch Instrument Object**

Use `fininstrument`

to create a `Touch`

instrument object.

TouchOpt = fininstrument("Touch",'ExerciseDate',datetime(2022,9,15),'BarrierValue',110,'PayoffValue',140,'BarrierType',"OT",'Name',"touch_option")

TouchOpt = Touch with properties: ExerciseDate: 15-Sep-2022 BarrierValue: 110 PayoffValue: 140 BarrierType: "ot" PayoffType: "expiry" Name: "touch_option"

**Create Heston Model Object**

Use `finmodel`

to create a `Heston`

model object.

HestonModel = finmodel("Heston",'V0',0.032,'ThetaV',0.1,'Kappa',0.003,'SigmaV',0.2,'RhoSV',0.9)

HestonModel = Heston with properties: V0: 0.0320 ThetaV: 0.1000 Kappa: 0.0030 SigmaV: 0.2000 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 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',myRC,"Model",HestonModel,'SpotPrice',112,'simulationDates',datetime(2022,9,15))

outPricer = HestonMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 112 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.Heston] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"

**Price Touch Instrument**

Use `price`

to compute the price and sensitivities for the `Touch`

instrument.

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

Price = 63.5247

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

outPR.Results

`ans=`*1×8 table*
Price Delta Gamma Lambda Rho Theta Vega VegaLT
______ _______ ______ _______ _______ ______ ______ ______
63.525 -7.2363 1.0541 -12.758 -320.21 3.5527 418.94 8.1498

## Input Arguments

`inpPricer`

— Pricer object

`AssetMonteCarlo`

object

Pricer object, specified as a previously created `AssetMonteCarlo`

pricer
object. Create the pricer object using `finpricer`

.

**Data Types: **`object`

`inpInstrument`

— Instrument object

`Vanilla`

object | `Barrier`

object | `Lookback`

object | `Asian`

object | `DoubleBarrier`

object | `Spread`

object | `Touch`

object | `DoubleTouch`

object | `Cliquet`

object | `Binary`

object

Instrument object, specified as a scalar or 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'}
``` |

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

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

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

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

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

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

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

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

`DoubleTouch` | `{'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

**Note**

The `inpPricer`

options that do not support sensitivities do
not return a `PriceResult`

. For example, there is no
`PriceResult`

returned for when you use a
`Black`

, `CDSBlack`

,
`HullWhite`

, `Normal`

, or
`SABR`

pricing method.

## 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 R2020b**

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