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Price of European arithmetic Asian options using Levy model



Price = asianbylevy(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates) returns European arithmetic average pricing for Asian options using the Levy model.


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Define the RateSpec.

Rates = 0.07;
StartDates = 'Jan-1-2013';
EndDates = 'Jan-1-2014';
RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates, 'EndDates', ...
EndDates, 'Rates', Rates, 'Compounding', -1)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9324
            Rates: 0.0700
         EndTimes: 1
       StartTimes: 0
         EndDates: 735600
       StartDates: 735235
    ValuationDate: 735235
            Basis: 0
     EndMonthRule: 1

Define the StockSpec for the asset.

AssetPrice = 6.8;
Sigma = 0.14;
DivType = 'continuous';
DivAmounts = 0.09;
StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmounts)
StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1400
         AssetPrice: 6.8000
       DividendType: {'continuous'}
    DividendAmounts: 0.0900
    ExDividendDates: []

Define two options for 'call' and 'put'.

Settle = 'Jan-1-2013';
Maturity = 'July-1-2013';
Strike = 6.9;
OptSpec = {'call'; 'put'};

Compute the European arithmetic average price for the Asian option using the Levy model.

Price= asianbylevy(RateSpec, StockSpec, OptSpec, Strike, Settle, Maturity)
Price = 2×1


Input Arguments

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Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

Stock specification for underlying asset, specified using StockSpec obtained from stockspec. For information on the stock specification, see stockspec.

stockspec can handle other types of underlying assets. For example, stocks, stock indices, and commodities. If dividends are not specified in StockSpec, dividends are assumed to be 0.

Data Types: struct

Definition of option, specified as 'call' or 'put' using a NINST-by-1 cell array of character vectors.

Data Types: char | cell

Option strike price values, specified with nonnegative integers as a NINST-by-1 vector.

Data Types: single | double

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

Data Types: double | char | cell

Option exercise dates, specified as serial date numbers or date character vectors using a NINST-by-1 vector or cell array of character vector dates. For a European option, there is only one ExerciseDates on the option expiry date.

Data Types: double | char | cell

Output Arguments

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Expected prices of the Asian option, returned as a NINST-by-1 vector.

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.

Version History

Introduced in R2013b