Price lookback option from Cox-Ross-Rubinstein binomial tree
This example shows how to price a lookback option using a CRR binomial tree by loading the file
deriv.mat, which provides
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
CRRTree— Stock tree structure
Stock tree structure for a Cox-Ross-Rubinstein binomial tree,
specified by using
OptSpec— Definition of option
'put'| cell array of character vectors with values
Definition of option, specified as
a character vector or an
cell array of character vectors for
Strike— Option strike price value
Option strike price value, specified with a nonnegative integer using an
1 matrix of strike price
values. Each row is the schedule for one option.
To compute the value of a floating-strike lookback option,
be specified as
NaN. Floating-strike lookback options
are also known as average strike options.
Settle— Settlement date or trade date
Settlement date or trade date for the lookback option, specified as an
1 matrix of settlement or
trade dates using serial date numbers or date character vectors.
Settle date for every lookback option is
set to the
ValuationDate of the stock tree. The
Settle, is ignored.
ExerciseDates— Option exercise dates
Option exercise dates, specified as a serial date number or date character vector:
For a European option, use an
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
For an American option, use an
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
1 vector of
serial date numbers or cell array of character vectors, the
option can be exercised between
of the stock tree and the single listed
AmericanOpt— Option type
0European (default) | integer with values
(Optional) Option type, specified as an
integer flags with values:
0 — European
1 — American
Price— Expected prices for lookback options at time
Expected prices for lookback options at time 0, returned as an
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
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.
 Hull J. and A. White. "Efficient Procedures for Valuing European and American Path-Dependent Options." Journal of Derivatives. Fall 1993, pp. 21–31.