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Price Asian options using standard trinomial tree



Price = asianbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates) prices Asian options using a standard trinomial (STT) tree.


Price = asianbystt(___,AmericanOpt,AvgType,AvgPrice,AvgDate) prices Asian options using a standard trinomial (STT) tree with optional arguments for AmericanOpt, AvgType, AvgPrice, and AvgDate.


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Create a RateSpec.

StartDates = 'Jan-1-2009'; 
EndDates = 'Jan-1-2013'; 
Rates = 0.035; 
Basis = 1; 
Compounding = -1;
RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates,...
'EndDates', EndDates, 'Rates', Rates,'Compounding', Compounding, 'Basis', Basis)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.8694
            Rates: 0.0350
         EndTimes: 4
       StartTimes: 0
         EndDates: 735235
       StartDates: 733774
    ValuationDate: 733774
            Basis: 1
     EndMonthRule: 1

Create a StockSpec.

AssetPrice = 85; 
Sigma = 0.15; 
StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1500
         AssetPrice: 85
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Create an STTTree.

NumPeriods = 4;
TimeSpec = stttimespec(StartDates, EndDates, 4);
STTTree = stttree(StockSpec, RateSpec, TimeSpec)
STTTree = struct with fields:
       FinObj: 'STStockTree'
    StockSpec: [1x1 struct]
     TimeSpec: [1x1 struct]
     RateSpec: [1x1 struct]
         tObs: [0 1 2 3 4]
         dObs: [733774 734139 734504 734869 735235]
        STree: {1x5 cell}
        Probs: {[3x1 double]  [3x3 double]  [3x5 double]  [3x7 double]}

Define the Asian option and compute the price.

Settle = '01-Jan-2009';
ExerciseDates = [datenum('1/1/12');datenum('1/1/13')];
OptSpec = 'call';
Strike = 100;

Price = asianbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)
Price = 2×1


Input Arguments

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Stock tree structure for a standard trinomial tree, specified by using stttree.

Data Types: struct

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

Data Types: char

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 should 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 of serial date numbers or cell array of character vectors, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

Data Types: double | char

Option type, specified as NINST-by-1 positive integer scalar flags with values:

  • 0 — European

  • 1 — American

Data Types: single | 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: double

Output Arguments

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Expected prices for Asian options at time 0, returned as a NINST-by-1 matrix. Pricing of Asian options is done using Hull-White (1993). Consequently, for these options there are no unique prices on the tree nodes with the exception of the root node.

More About

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Asian Option

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.


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

Version History

Introduced in R2015b