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Price Asian options using implied trinomial tree (ITT)


Price = asianbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates)
Price = asianbyitt(___,AmericanOpt,AvgType,AvgPrice,AvgDate)



Price = asianbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates) prices Asian options using an implied trinomial tree (ITT).


Price = asianbyitt(___,AmericanOpt,AvgType,AvgPrice,AvgDate) adds optional arguments for AmericanOpt, AvgType, AvgPrice, and AvgDate.


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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

Input Arguments

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Stock tree structure, specified by using itttree.

Data Types: struct

Definition of option, specified as 'call' or 'put' using a character vector or a cell array of character vectors.

Data Types: char | cell

Option strike price value, specified with a nonnegative integer using a NINST-by-1 matrix of strike price values.

To compute the value of a floating-strike Asian option, Strike must be specified as NaN. Floating-strike Asian options are also known as average strike options.

Data Types: double

Settlement date or trade date for the Asian option, specified as a NINST-by-1 matrix of settlement or trade dates using serial date numbers or date character vectors.


The Settle date for every Asian option is set to the ValuationDate of the stock tree. The Asian 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 aNINST-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 a 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 a NINST-by-1 vector, 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 NINST-by-1 positive integer flags with values:

  • 0 — European

  • 1 — American

Data Types: double

Average types, specified as arithmetic for arithmetic average, or geometric for geometric average.

Data Types: char

Average price of underlying asset at Settle, specified as a scalar.


Use this argument when AvgDate < Settle.

Data Types: double

Date averaging period begins, specified as a scalar.

Data Types: char | double

Output Arguments

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Expected prices for Asian options at time 0, returned as a NINST-by-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.


[1] Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.

Introduced in R2007a

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