# compoundbyeqp

Price compound option from Equal Probabilities binomial tree

## Syntax

``````[Price,PriceTree] = compoundbyeqp(EQPTree,UOptSpec,UStrike,USettle,UExerciseDates,UAmericanOpt,COptSpec,CStrike,CSettle,CExerciseDates)``````
``````[Price,PriceTree] = compoundbyeqp(___,CAmericanOpt)``````

## Description

example

``````[Price,PriceTree] = compoundbyeqp(EQPTree,UOptSpec,UStrike,USettle,UExerciseDates,UAmericanOpt,COptSpec,CStrike,CSettle,CExerciseDates)``` prices compound options from a Equal Probabilities binomial tree.```

example

``````[Price,PriceTree] = compoundbyeqp(___,CAmericanOpt)``` adds an optional argument for `CAmericanOpt`.```

## Examples

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This example shows how to price a compound option using a 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 UOptSpec = 'Call'; UStrike = 130; USettle = datetime(2003,1,1); UExerciseDates = datetime(2006,1,1); UAmericanOpt = 1; COptSpec = 'Put'; CStrike = 5; CSettle = datetime(2003,1,1); CExerciseDates = datetime(2005,1,1); Price = compoundbyeqp(EQPTree, UOptSpec, UStrike, USettle, ... UExerciseDates, UAmericanOpt, COptSpec, CStrike, CSettle, ... CExerciseDates)```
```Price = 3.3931 ```

## Input Arguments

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Stock tree structure, specified by using `eqptree`.

Data Types: `struct`

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

Data Types: `char`

Underlying option strike price value, specified with a nonnegative integer using a `1`-by-`1` vector.

Data Types: `double`

Underlying option settlement date or trade date, specified as a `1`-by-`1` vector using a datetime array, string array, or date character vectors.

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

Underlying option exercise date, specified as a datetime array, string array, or date character vectors:

• For a European option, use a`1`-by-`1` vector of the underlying exercise date. For a European option, there is only one `ExerciseDates` on the option expiry date.

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

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

Underlying option type, specified as `NINST`-by-`1` positive integer scalar flags with values:

• `0` — European

• `1` — American

If `UAmericanOpt` is a `NaN` or is unspecified, the option is a European option.

Data Types: `double`

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

Data Types: `char` | `cell`

Compound option strike price values for a European and American option, specified with a nonnegative integer using a `NINST`-by-`1` matrix. Each row is the schedule for one option.

Data Types: `double`

Compound option settlement date or trade date, specified as a `1`-by-`1` vector using a datetime array, string array, or date character vectors.

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

Compound option exercise dates, specified as a datetime array, string array, or date character vectors:

• For a European option, use a`NINST`-by-`1` matrix of the compound 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 the compound 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 `ValuationDate` of the stock tree and the single listed `ExerciseDates`.

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

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

• `0` — European

• `1` — American

If `CAmericanOpt` is a `NaN` or is unspecified, the option is a European option.

Data Types: `double`

## Output Arguments

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Expected prices for compound options at time 0, returned as a `NINST`-by-`1` vector.

Structure with a vector of compound option prices at each node, returned as a tree structure.

`PriceTree` is a MATLAB® structure of trees containing vectors of instrument prices and a vector of observation times for each node.

`PriceTree.PTree` contains the prices.

`PriceTree.tObs` contains the observation times.

`PriceTree.dObs` contains the observation dates.

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### Compound Option

A compound option is basically an option on an option; it gives the holder the right to buy or sell another option.

With a compound option, a vanilla stock option serves as the underlying instrument. Compound options thus have two strike prices and two exercise dates. For more information, see Compound Option.

## References

[1] Rubinstein, Mark. “Double Trouble.” Risk. Vol. 5, 1991, p. 73.

## Version History

Introduced before R2006a

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