# asianbyeqp

Price Asian option from Equal Probabilities binomial tree

## Syntax

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

## Arguments

 `EQPTree` Stock tree structure created by `eqptree`. `OptSpec` `NINST`-by-`1` list of string values `'Call'` or `'Put'`. `Strike ` `NINST`-by-`1` vector of strike price values. Each row is the schedule for one option. `Settle` `NINST`-by-`1` vector of `Settle` dates. The settle date for every Asian option is set to the valuation date of the stock tree. The Asian argument `Settle` is ignored. `ExerciseDates` For a European option (`AmericanOpt = 0`):`NINST`-by-`1` vector of exercise dates. Each row is the schedule for one option. For a European option, there is only one exercise date, the option expiry date. For an American option (```AmericanOpt = 1```):`NINST`-by-`2` vector of exercise date boundaries. For each instrument, 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 `NINST`-by-`1`, the option can be exercised between the valuation date of the stock tree and the single listed exercise date. `AmericanOpt` (Optional) If `AmericanOpt = 0`, `NaN`, or is unspecified, the option is a European option. If ```AmericanOpt = 1```, the option is an American option. `AvgType` (Optional) String = `'arithmetic'` for arithmetic average (default) or `'geometric'` for geometric average. `AvgPrice` (Optional) Scalar representing the average price of the underlying asset at `Settle`. This argument is used when `AvgDate < Settle`. Default is the current stock price. `AvgDate` (Optional) Scalar representing the date on which the averaging period begins.

## Description

```Price = asianbyeqp(EQPTree, OptSpec, Strike, Settle,ExerciseDates, AmericanOpt, AvgType, AvgPrice, AvgDate)``` calculates the value of fixed- and floating-strike Asian options. To compute the value of a floating-strike Asian option, specify `Strike` as `NaN`. Fixed-strike Asian options are also known as average price options. Floating-strike Asian options are also known as average strike options.

`Price` is a `NINST`-by-`1` vector of expected prices at time 0.

## Examples

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### Price a Floating-Strike Asian Option Using an EQP Equity Tree

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 ```

## References

Hull, J., and A. White, "Efficient Procedures for Valuing European and American Path-Dependent Options," Journal of Derivatives, Volume 1, pp. 21-31.