# price

## Syntax

## Description

`[`

computes the 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.`Price`

,`PriceResult`

] = price(___,`inpSensitivity`

)

## Examples

### Use `FFT`

Pricer and `Heston`

Model to Price `Vanilla`

Instrument

This example shows the workflow to price a `Vanilla`

instrument when you use a `Heston`

model and an `FFT`

pricing method.

**Create Vanilla Instrument Object**

Use `fininstrument`

to create a `Vanilla`

instrument object.

VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2022,9,15),'Strike',105,'ExerciseStyle',"european",'Name',"vanilla_option")

VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Strike: 105 Name: "vanilla_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 FFT Pricer Object**

Use `finpricer`

to create an `FFT`

pricer object and use the `ratecurve`

object for the `'DiscountCurve'`

name-value pair argument.

outPricer = finpricer("fft",'DiscountCurve',myRC,'Model',HestonModel,'SpotPrice',100,'CharacteristicFcnStep', 0.2,'NumFFT',2^13)

outPricer = FFT with properties: Model: [1x1 finmodel.Heston] DiscountCurve: [1x1 ratecurve] SpotPrice: 100 DividendType: "continuous" DividendValue: 0 NumFFT: 8192 CharacteristicFcnStep: 0.2000 LogStrikeStep: 0.0038 CharacteristicFcn: @characteristicFcnHeston DampingFactor: 1.5000 Quadrature: "simpson" VolRiskPremium: 0 LittleTrap: 1

**Price Vanilla Instrument**

Use `price`

to compute the price and sensitivities for the `Vanilla`

instrument.

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

Price = 14.7545

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

outPR.Results

`ans=`*1×7 table*
Price Delta Gamma Theta Rho Vega VegaLT
______ _______ ________ ________ ______ ______ ______
14.754 0.44868 0.021649 -0.20891 120.45 88.192 1.3248

## Input Arguments

`inpInstrument`

— Instrument object

`Vanilla`

object

Instrument object, specified as a scalar or vector of `Vanilla`

instrument objects.
Use `fininstrument`

to create
`Vanilla`

instrument
objects.

**Data Types: **`object`

`inpSensitivity`

— List of sensitivities to compute

`[ ]`

(default) | string array with values `"Price"`

, `"Delta"`

,
`"Gamma"`

, `"Vega"`

, `"Rho"`

,
`"Theta"`

, `"Vegalt"`

, and
`"All"`

| cell array of character vectors with values `'Price'`

,
`'Delta'`

, `'Gamma'`

, `'Vega'`

,
`'Rho'`

, `'Theta'`

, `'Vegalt'`

, and
`'All'`

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

-by-`1`

or a
`1`

-by-`NOUT`

cell array of character vectors or
string array with possible values of `'Price'`

,
`'Delta'`

, `'Gamma'`

, `'Vega'`

,
`'Rho'`

, `'Theta'`

, `'Vegalt'`

, and
`'All'`

.

`inpSensitivity = {'All'}`

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

specifies that the output is `'Delta'`

,
`'Gamma'`

, `'Vega'`

, `'Rho'`

,
`'Theta'`

, `'Vegalt'`

, and
`'Price'`

. This is the same as specifying
`inpSensitivity`

to include each sensitivity.

**Example: **```
inpSensitivity =
{'delta','gamma','vega','rho','theta','vegalt','price'}
```

**Data Types: **`string`

| `cell`

## 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.

### Vegalt

A *vegalt* sensitivity measures the sensitivity of
an option's price to changes in the long-term volatility of the underlying asset.

## Version History

**Introduced in R2020a**

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