lookbackbystt

Price lookback options using standard trinomial tree

Syntax

Price = lookbackbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates)

Price = lookbackbystt(___,AmericanOpt)

Description

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

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

Examples

Price a Lookback Option Using the Standard Trinomial Tree Model

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 lookback option and compute the price.

Settle = '1/1/09';
ExerciseDates = [datenum('1/1/12');datenum('1/1/13')];
OptSpec = 'call';
Strike = [90;95];

Price= lookbackbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)

Price = 2×1

   11.7296
   12.9120

Input Arguments

STTTree — Stock tree structure for standard trinomial tree

structure

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

Data Types: struct

OptSpec — Definition of option

character vector with value 'call' or 'put' | cell array of character vectors with values 'call' or 'put'

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

Strike — Option strike price value

matrix of nonnegative integers

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

Settle — Settlement date or trade date

serial date number | date character vector

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

Note

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

Data Types: double | char

ExerciseDates — Option exercise dates

serial date number | date character vector

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

AmericanOpt — Option type

0 European (default) | scalar with values [0,1]

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

• 0 — European

• 1 — American

Data Types: single | double

Output Arguments

Price — Expected prices for lookback options at time 0

matrix

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

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.

References

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