Price Asian option from Cox-Ross-Rubinstein binomial tree
Price = asianbycrr(CRRTree,OptSpec,Strike,Settle,ExerciseDates)
Price = asianbycrr(___,AmericanOpt,AvgType,AvgPrice,AvgDate)
This example shows how to price a floating-strike Asian option using a CRR binomial tree using 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 = 'put'; Strike = NaN; Settle = '01-Jan-2003'; ExerciseDates = '01-Jan-2004'; Price = asianbycrr(CRRTree, OptSpec, Strike, Settle, ... ExerciseDates)
Price = 1.2177
CRRTree— Stock tree structure
Stock tree structure, 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 cell array of character vectors.
Strike— Option strike price value
Option strike price value, specified with a nonnegative integer
1 matrix of
strike price values.
To compute the value of a floating-strike Asian option,
be specified as
NaN. Floating-strike Asian options
are also known as average strike options.
Settle— Settlement date or trade date
Settlement date or trade date for the Asian option, specified
1 matrix of settlement
or trade dates using serial date numbers or date character vectors.
Settle date for every Asian 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 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, the option
can be exercised between
ValuationDate of the stock
tree and the single listed
AmericanOpt— Option type
0European (default) | integer with values
(Optional) Option type, specified as
integer flags with values:
0 — European
1 — American
AvgType— Average types
arithmetic(default) | character vector with values of
Average types, specified as
arithmetic average, or
geometric for geometric
AvgDate— Date averaging period begins
Date averaging period begins, specified as a scalar.
Price— Expected prices for Asian options at time
Expected prices for Asian options at time 0, returned as a
Pricing of Asian 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.
 Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.