Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

asianbystt

Price Asian options using standard trinomial tree

Syntax

Price = asianbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates)
Price = asianbystt(___,AmericanOpt,AvgType,AvgPrice,AvgDate)

Description

example

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

example

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

Examples

collapse all

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 = 

    1.6905
    2.6203

Input Arguments

collapse all

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.

Note

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.

Note

Use this argument when AvgDate < Settle.

Data Types: double

Date averaging period begins, specified as a scalar.

Data Types: double

Output Arguments

collapse all

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.

References

[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 R2015b

Was this topic helpful?