# Documentation

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# asianbyeqp

Price Asian option from Equal Probabilities binomial tree

## Syntax

``Price = asianbyeqp(EQPTree,OptSpec,Strike,Settle,ExerciseDates)``
``Price = asianbyeqp(___,AmericanOpt,AvgType,AvgPrice,AvgDate)``

## Description

example

````Price = asianbyeqp(EQPTree,OptSpec,Strike,Settle,ExerciseDates)` prices Asian options using an Equal Probabilities binomial tree.```

example

````Price = asianbyeqp(___,AmericanOpt,AvgType,AvgPrice,AvgDate)` adds optional arguments for `AmericanOpt`, `AvgType`, `AvgPrice`, and `AvgDate`.```

## Examples

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This example shows how to price a floating-strike Asian option using an EQP equity tree by loading the file deriv.mat, which provides EQPTree. The EQPTree structure contains the stock specification and time information needed to price the option.

```load deriv.mat; OptSpec = 'put'; Strike = NaN; Settle = '01-Jan-2003'; ExerciseDates = '01-Jan-2004'; Price = asianbyeqp(EQPTree, OptSpec, Strike, Settle, ... ExerciseDates)```
```Price = 1.2724 ```

## Input Arguments

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Stock tree structure, specified by using `eqptree`.

Data Types: `struct`

Definition of option, specified as `'call'` or `'put'` using a character vector or a cell array of character vectors.

Data Types: `char` | `cell`

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

To compute the value of a floating-strike Asian option, `Strike` must be specified as `NaN`. Floating-strike Asian options are also known as average strike options.

Data Types: `double`

Settlement date or trade date for the Asian option, specified as a `NINST`-by-`1` matrix of settlement or trade dates using serial date numbers or date character vectors.

### Note

The `Settle` date for every Asian option is set to the `ValuationDate` of the stock tree. The Asian argument, `Settle`, is ignored.

Data Types: `double` | `char`

Option exercise dates, specified as a serial date number or date character vector:

• For a European option, use a`NINST`-by-`1` matrix of exercise dates. Each row is the schedule for one option. For a European option, there is only one `ExerciseDates` on the option expiry date.

• For an American option, use a `NINST`-by-`2` vector of exercise date boundaries. The option can be exercised on any tree date between or including the pair of dates on that row. If only one non-`NaN` date is listed, or if `ExerciseDates` is a `NINST`-by-`1` vector, the option can be exercised between `ValuationDate` of the stock tree and the single listed `ExerciseDates`.

Data Types: `double` | `char`

(Optional) Option type, specified as `NINST`-by-`1` positive integer flags with values:

• `0` — European

• `1` — American

Data Types: `double`

Average types, specified as `arithmetic` for arithmetic average, or `geometric` for geometric average.

Data Types: `char`

Average price of underlying asset at `Settle`, specified as a scalar.

### Note

Use this argument when `AvgDate` < `Settle`.

Data Types: `double`

Date averaging period begins, specified as a scalar.

Data Types: `char` | `double`

## Output Arguments

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Expected prices for Asian options at time 0, returned as a `NINST`-by-`1` vector. Pricing of Asian options is done using Hull-White (1993). Therefore, for these options there are no unique prices on the tree nodes except for the root node.

## References

[1] Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.