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# asiansensbylevy

Calculate prices and sensitivities of European arithmetic Asian options using Levy model

## Syntax

• PriceSens = asiansensbylevy(RateSpec,StockSpec,OptSpec,StrikeSettle,ExerciseDates) example
• PriceSens = asiansensbylevy(___,Name,Value)

## Description

example

PriceSens = asiansensbylevy(RateSpec,StockSpec,OptSpec,StrikeSettle,
ExerciseDates)
returns European average pricing and sensitivities for arithmetic Asian options using the Levy model.

PriceSens = asiansensbylevy(___,Name,Value) returns European average pricing and sensitivities for arithmetic Asian options using the Levy model with optional name-value pair arguments.

## Examples

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### Compute the Price and Sensitivities of an Asian Option Using the Levy Model

Define the RateSpec.

```Rates = 0.07;
StartDates = 'Jan-1-2013';
EndDates = 'Jan-1-2014';
RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates, 'EndDates', ...
EndDates, 'Rates', Rates, 'Compounding', -1)```
```RateSpec =

FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9324
Rates: 0.0700
EndTimes: 1
StartTimes: 0
EndDates: 735600
StartDates: 735235
ValuationDate: 735235
Basis: 0
EndMonthRule: 1```

Define the StockSpec for the asset.

```AssetPrice = 6.8;
Sigma = 0.14;
DivType = 'continuous';
DivAmounts = 0.09;
StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmounts)```
```StockSpec =

FinObj: 'StockSpec'
Sigma: 0.1400
AssetPrice: 6.8000
DividendType: {'continuous'}
DividendAmounts: 0.0900
ExDividendDates: []```

Define two options for a 'call' and 'put'.

```Settle = 'Jan-1-2013';
ExerciseDates = 'Jan-1-2014';
Strike = 6.9;
OptSpec = {'call'; 'put'};```

Compute the European arithmetic average price and sensitivities for the Asian option using the Levy model.

```OutSpec = {'Price', 'Delta', 'Gamma'};
PriceSens = asiansensbylevy(RateSpec, StockSpec, OptSpec, Strike,...
Settle, ExerciseDates,'OutSpec', OutSpec)```
```PriceSens =

4.2895
2.6001```

## Input Arguments

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### RateSpec — Interest-rate term structurestructure

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

### StockSpec — Stock specification for underlying assetstructure

Stock specification for underlying asset, specified using StockSpec obtained from stockspec. For information on the stock specification, see stockspec.

stockspec can handle other types of underlying assets. For example, stocks, stock indices, and commodities. If dividends are not specified in StockSpec, dividends are assumed to be 0.

Data Types: struct

### OptSpec — Definition of option string with values 'call' or 'put' | cell array of strings

Definition of option, specified as 'call' or 'put' using a NINST-by-1 cell array of strings.

Data Types: char | cell

### Strike — Option strike price valuesnonnegative integer | vector of nonnegative integers

Option strike price values, specified with nonnegative integers using a NINST-by-1 vector.

Data Types: single | double

### Settle — Settlement dates or trade datesnonnegative integer | vector of nonnegative integers | date string | cell array of date strings

Settlement dates or trade dates for the Asian option, specified as nonnegative integers or date strings using a NINST-by-1 vector or cell array of dates.

Data Types: char | cell

### ExerciseDates — Option exercise datesnonnegative integer | vector of nonnegative integers | date string | cell array of date strings

Option exercise dates, specified as nonnegative integers or date strings using a NINST-by-1 vector or cell array of exercise dates. For a European option, there is only one ExerciseDates on the option expiry date.

Data Types: char | cell

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: PriceSens = asiansensbylevy(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'OutSpec',{'All'})

### 'OutSpec' — Define outputs{'Price'} (default) | string with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'. | cell array of strings with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'

Define outputs specifying NOUT- by-1 or 1-by-NOUT cell array of strings with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta' and 'All'.

OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to include each sensitivity:

Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types: char | cell

## Output Arguments

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### PriceSens — Expected prices and sensitivities of Asian optionvector

Expected prices and sensitivities of the Asian option, returned as an 1-by-1 vector. If the OutSpec is not specified only the price is returned.