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# asianbyhhm

Price European discrete arithmetic fixed Asian options using Haug, Haug, Margrabe model

## Syntax

``Price = asianbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)``
``Price = asianbyhhm(___,Name,Value)``

## Description

example

````Price = asianbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)` prices European discrete arithmetic fixed Asian options using the Haug, Haug, Margrabe model.```

example

````Price = asianbyhhm(___,Name,Value)` adds optional name-value pair arguments.```

## Examples

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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 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; Price = asianbyhhm(RateSpec, StockSpec, OptSpec, Strike, Settle, ExerciseDates, ... 'NumFixings', NumFixings, 'AvgDate', AvgDate, 'AvgPrice', AvgPrice)```
```Price = 5.8216 ```

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 of the Asian option using the Haug, Haug, Margrabe approximation. Assume that the averaging period starts after the `Settle` date.

```OptSpec = 'Call'; ExerciseDates = datetime(2013,10,1); NumFixings = 15; AvgDate = datetime(2013,1,1); Price = asianbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ... 'NumFixings',NumFixings,'AvgDate',AvgDate)```
```Price = 1.3785e-07 ```

## Input Arguments

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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`

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`

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`

Option strike price value, specified with a nonnegative integer using a `NINST`-by-`1` vector of strike price values.

Data Types: `double`

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

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, `asianbyhhm` 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: ```Price = asianbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'NumFixings',15)```

Average price of underlying asset at the `Settle` date, specified as the comma-separated pair consisting of `'AvgPrice'` and a `NINST`-by-`1` vector.

Note

Use the `AvgPrice` argument when `AvgDate` < `Settle`.

Data Types: `double`

Date averaging period begins, specified as the comma-separated pair consisting of `'AvgDate'` and a `NINST`-by-`1` vector using a datetime array, string array, or date character vectors.

To support existing code, `asianbyhhm` also accepts serial date numbers as inputs, but they are not recommended.

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

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Expected prices for fixed Asian options, returned as a `NINST`-by-`1` vector.

## More About

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### 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

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