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Calculate prices or sensitivities of European arithmetic Asian options using Levy model



PriceSens = asiansensbylevy(RateSpec,StockSpec,OptSpec,StrikeSettle,ExerciseDates) returns European average pricing or sensitivities for arithmetic Asian options using the Levy model.

PriceSens = asiansensbylevy(___,Name,Value) adds optional name-value pair arguments.


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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 a 'call' and 'put'.

Settle = 'Jan-1-2013';
ExerciseDates = 'Jan-1-2014';
Strike = 6.9;
OptSpec = {'call'; 'put'};

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

OutSpec = {'Price', 'Delta', 'Gamma'};
PriceSens = asiansensbylevy(RateSpec, StockSpec, OptSpec, Strike,...
Settle, ExerciseDates,'OutSpec', OutSpec)
PriceSens = 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 using 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

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: PriceSens = asiansensbylevy(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'OutSpec',{'All'})

Define outputs, specified as the comma-separated pair consisting of 'OutSpec' and a NOUT- by-1 or 1-by-NOUT cell array of character vectors with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to include each sensitivity:

Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types: char | cell

Output Arguments

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Expected prices or sensitivities (defined by OutSpec) of the Asian option, returned as an 1-by-1 vector. If the OutSpec is not specified only the price is returned.

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.

Introduced in R2013b