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Price lookback options using standard trinomial tree



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


Alternatively, you can use the Lookback object to price lookback options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.


Price = lookbackbystt(___,AmericanOpt) prices lookback options using a standard trinomial (STT) tree with an optional argument for AmericanOpt.


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Create a RateSpec.

StartDates = datetime(2009,1,1); 
EndDates = datetime(2013,1,1); 
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: {[85]  [110.2179 85 65.5520]  [142.9174 110.2179 85 65.5520 50.5537]  [185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870]  [240.2985 185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870 30.0668]}
        Probs: {[3x1 double]  [3x3 double]  [3x5 double]  [3x7 double]}

Define the lookback option and compute the price.

Settle = datetime(2009,1,1);
ExerciseDates = [datetime(2012,1,1) ; datetime(2013,1,1)];
OptSpec = 'call';
Strike = [90;95];

Price= lookbackbystt(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 or a NINST-by-1 cell array of character vectors for 'call' or 'put'.

Data Types: char | cell

Option strike price value, specified with a nonnegative integer using a NINST-by-1 matrix of strike price values. Each row is the schedule for one option. To compute the value of a floating-strike lookback option, Strike should be specified as NaN. Floating-strike lookback options are also known as average strike options.

Data Types: double

Settlement date or trade date for the lookback option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.


The Settle date for every lookback option is set to the ValuationDate of the stock tree. The lookback argument, Settle, is ignored.

To support existing code, lookbackbystt also accepts serial date numbers as inputs, but they are not recommended.

Option exercise dates, specified as a datetime array, string array, or date character vectors:

  • 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 cell array of character vectors, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

To support existing code, lookbackbystt also accepts serial date numbers as inputs, but they are not recommended.

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

  • 0 — European

  • 1 — American

Data Types: double

Output Arguments

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Expected prices for lookback options at time 0, returned as a NINST-by-1 matrix. Pricing of lookback 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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Lookback Option

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.


[1] Hull J. and A. White. "Efficient Procedures for Valuing European and American Path-Dependent Options." Journal of Derivatives. Fall 1993, pp. 21–31.

Version History

Introduced in R2015b

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