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Price lookback option from Cox-Ross-Rubinstein binomial tree



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


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


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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, ... 
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 an 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 an 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 an NINST-by-1 matrix of settlement or trade dates using serial date numbers or date character vectors.


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 an 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 an 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 an 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 an 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 an 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

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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.


[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