Main Content

# lookbackbyeqp

Price lookback option from Equal Probabilities binomial tree

## Syntax

``Price = lookbackbyeqp(EQPTree,OptSpec,Strike,Settle,ExerciseDates)``
``Price = lookbackbyeqp(___,AmericanOpt)``

## Description

example

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

example

````Price = lookbackbyeqp(___,AmericanOpt)` adds an optional argument for `AmericanOpt`.```

## Examples

collapse all

This example shows how to price a lookback 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 = 'Call'; Strike = 115; Settle = '01-Jan-2003'; ExerciseDates = '01-Jan-2006'; Price = lookbackbyeqp(EQPTree, OptSpec, Strike, Settle, ... ExerciseDates)```
```Price = 8.7941 ```

## Input Arguments

collapse all

Stock tree structure for an Equal Probabilities binomial tree, specified by using `eqptree`.

Data Types: `struct`

Definition of option, specified as `'call'` or `'put'` using a character vector or a `NINST`-by-`1` cell array of character vectors for `'call'` or `'put'`.

Data Types: `char` | `cell`

Option strike price value, specified with a nonnegative integer using a `NINST`-by-`1` matrix of strike price values. Each row is the schedule for one option.

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

Data Types: `double`

Settlement date or trade date for the lookback 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 lookback option is set to the `ValuationDate` of the stock tree. The lookback 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 of serial date numbers or cell array of character vectors, 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` integer flags with values:

• `0` — European

• `1` — American

Data Types: `single` | `double`

## Output Arguments

collapse all

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

## More About

collapse all

### Lookback Option

A lookback option is a path-dependent option based on the maximum or minimum value the underlying asset achieves during the entire life of the option.

Financial Instruments Toolbox™ software supports two types of lookback options: fixed and floating. Fixed lookback options have a specified strike price, while floating lookback options have a strike price determined by the asset path. For more information, see Lookback Option.

## References

[1] Hull J. and A. White. "Efficient Procedures for Valuing European and American Path-Dependent Options." Journal of Derivatives. Fall 1993, pp. 21–31.

## Version History

Introduced before R2006a