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 a
array of character vectors for
Strike— Option strike price value
Option strike price value, specified with a nonnegative integer
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
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 lookback argument,
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 a
of exercise dates. Each row is the schedule for one option. For a
European option, there is only one
the option expiry date.
For an American option, use a
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
NaN date is listed, or if
1 vector of serial
date numbers or cell array of character vectors, the option can be
ValuationDate of the stock tree
and the single listed
AmericanOpt— Option type
0European (default) | integer with values
(Optional) Option type, specified as
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
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.
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.