# Documentation

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# lookbackbycrr

Price lookback option from Cox-Ross-Rubinstein binomial tree

## Syntax

``Price = lookbackbycrr(CRRTree,OptSpec,Strike,Settle,ExerciseDates)``
``Price = lookbackbycrr(___,AmericanOpt)``

## Description

example

````Price = lookbackbycrr(CRRTree,OptSpec,Strike,Settle,ExerciseDates)` prices lookback options using a Cox-Ross-Rubinstein binomial tree.```

example

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

## Examples

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This example shows how to price a lookback option using a CRR binomial tree by loading the file `deriv.mat`, which provides `CRRTree`. The `CRRTree` 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 = lookbackbycrr(CRRTree, OptSpec, Strike, Settle, ... ExerciseDates)```
```Price = 7.6015 ```

## Input Arguments

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Stock tree structure for a Cox-Ross-Rubinstein binomial tree, specified by using `crrtree`.

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

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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.

## 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.