# asiansensbyhhm

Calculate price and sensitivities of European discrete arithmetic fixed Asian options using Haug, Haug, Margrabe model

## Syntax

## Description

adds optional name-value pair arguments.`PriceSens`

= asiansensbyhhm(___,`Name,Value`

)

## Examples

### Compute Price and Sensitivities for Asian Option with Averaging Period Starting Before the Settle Date

Define the Asian option parameters.

AssetPrice = 100; Strike = 95; Rates = 0.1; Sigma = 0.15; Settle = datetime(2013,4,1); Maturity = datetime(2013,10,1);

Create a `RateSpec`

using the `intenvset`

function.

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', ... Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', 1);

Create a `StockSpec`

for the underlying asset using the `stockspec`

function.

```
DividendType = 'Continuous';
DividendAmounts = 0.05;
StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);
```

Calculate the price and sensitivities of the Asian option using the Haug, Haug, Margrabe approximation. Assume that the averaging period has started before the `Settle`

date.

OptSpec = 'Call'; ExerciseDates = datetime(2013,10,1); NumFixings = 12; AvgDate = datetime(2013,1,1); AvgPrice = 100; OutSpec = {'Price','Delta','Gamma'}; [Price,Delta,Gamma] = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ... 'NumFixings',NumFixings,'AvgDate',AvgDate,'AvgPrice',AvgPrice,'OutSpec',OutSpec)

Price = 5.8216

Delta = 0.5907

Gamma = 0.0143

### Compute Price and Sensitivities for Asian Option with Averaging Period Starting After the Settle Date

Define the Asian option parameters.

AssetPrice = 100; Strike = 95; Rates = 0.1; Sigma = 0.15; Settle = 'Apr-1-2013'; Maturity = 'Oct-1-2013';

Create a `RateSpec`

using the `intenvset`

function.

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', ... Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', 1);

Create a `StockSpec`

for the underlying asset using the `stockspec`

function.

```
DividendType = 'Continuous';
DividendAmounts = 0.05;
StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);
```

Calculate the price and sensitivities of the Asian option using the Haug, Haug, Margrabe approximation. Assume that the averaging period started after the `Settle`

date.

OptSpec = 'Call'; ExerciseDates = 'Oct-1-2013'; NumFixings = 15; AvgDate = 'Jan-1-2013'; OutSpec = {'Price','Delta','Gamma'}; [Price,Delta,Gamma] = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ... 'NumFixings',NumFixings,'AvgDate',AvgDate,'OutSpec',OutSpec)

Price = 1.3785e-07

Delta = 1.1438e-07

Gamma = 9.0830e-08

## Input Arguments

`StockSpec`

— Stock specification for underlying asset

structure

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

character vector with value `'call'`

or
`'put'`

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

or
`'put'`

| string array with values `"call"`

or
`"put"`

Definition of option, specified as `'call'`

or
`'put'`

using a character vector, cell array of character vectors, or
string array.

**Data Types: **`char`

| `cell`

| `string`

`Strike`

— Option strike price value

nonnegative integer | vector of nonnegative integers

Option strike price value, specified with a nonnegative integer using a
`NINST`

-by-`1`

vector of strike price values.

**Data Types: **`double`

`Settle`

— Settlement dates or trade dates

datetime array | string array | date character vector

Settlement date or trade date for the Asian option, specified as a
`NINST`

-by-`1`

vector using a datetime array, string
array, or date character vectors.

To support existing code, `asiansensbyhhm`

also
accepts serial date numbers as inputs, but they are not recommended.

`ExerciseDates`

— European option exercise dates

datetime array | string array | date character vector

European option exercise dates, specified as a
`NINST`

-by-`1`

vector using a datetime array, string
array, or date character vectors.

**Note**

For a European option, there is only one `ExerciseDates`

on the
option expiry date.

To support existing code, `asiansensbyhhm`

also
accepts serial date numbers as inputs, but they are not recommended.

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **```
PriceSens =
asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'OutSpec',{'All'},'NumFixings',15)
```

`OutSpec`

— Define outputs

`{'Price'}`

(default) | character vector with values `'Price'`

,
`'Delta'`

, `'Gamma'`

, `'Vega'`

,
`'Lambda'`

, `'Rho'`

, `'Theta'`

,
and `'All'`

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

,
`'Delta'`

, `'Gamma'`

, `'Vega'`

,
`'Lambda'`

, `'Rho'`

, `'Theta'`

,
and `'All'`

| string array with values `"Price"`

, `"Delta"`

,
`"Gamma"`

, `"Vega"`

, `"Lambda"`

,
`"Rho"`

, `"Theta"`

, and
`"All"`

Define outputs, specified as the comma-separated pair consisting of
`'OutSpec'`

and a `NOUT`

- by-`1`

or `1`

-by-`NOUT`

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

,
`'Delta'`

, `'Gamma'`

, `'Vega'`

,
`'Lambda'`

, `'Rho'`

, `'Theta'`

,
and `'All'`

.

`OutSpec = {'All'}`

specifies that the output is
`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`

| `string`

`AvgDate`

— Date averaging period begins

character vector | datetime | string array

Date averaging period begins, specified as the comma-separated pair consisting of
`'AvgDate'`

and a `NINST`

-by-`1`

vector using character vectors, datetimes, or string arrays.

To support existing code, `asiansensbyhhm`

also
accepts serial date numbers as inputs, but they are not recommended.

`NumFixings`

— Total number of fixings or averaging points

`10`

(default) | vector

Total number of fixings or averaging points, specified as the comma-separated pair
consisting of `'NumFixings'`

and a
`NINST`

-by-`1`

vector.

**Data Types: **`double`

## Output Arguments

`PriceSens`

— Expected prices or sensitivities for fixed Asian options

vector

Expected prices or sensitivities for fixed Asian options, returned as a
`NINST`

-by-`1`

vector. `asianbyhhm`

calculates prices of European arithmetic fixed (average price) Asian options with
discretely monitoring.

## More About

### Asian Option

An *Asian* option is a path-dependent option with
a payoff linked to the average value of the underlying asset during the life (or some part
of the life) of the option.

Asian options are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option. For more information, see Asian Option.

## References

[1] Haug, E. G. *The
Complete Guide to Option Pricing Formulas.* McGraw-Hill Education,
2007.

## Version History

**Introduced in R2018a**

### R2022b: Serial date numbers not recommended

Although `asiansensbyhhm`

supports serial date numbers,
`datetime`

values are recommended instead. The
`datetime`

data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.

To convert serial date numbers or text to `datetime`

values, use the `datetime`

function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)

y = 2021

There are no plans to remove support for serial date number inputs.

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