Price Asian options using implied trinomial tree (ITT)
This example shows how to price a floating-strike Asian option using an ITT equity tree by loading the file deriv.mat, which provides ITTTree. The ITTTree structure contains the stock specification and time information needed to price the option.
load deriv.mat; OptSpec = 'put'; Strike = NaN; Settle = '01-Jan-2006'; ExerciseDates = '01-Jan-2007'; Price = asianbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDates)
Price = 1.0778
ITTTree— 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
1 vector. 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.
An Asian option is a path-dependent option with a payoff linked to the average value of the underlying asset during the life (or some part of the life) of the option.
Asian options are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option. For more information, see Asian Option.
 Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.