asiansensbytw

Calculate price and sensitivities of European fixed arithmetic Asian options using Turnbull-Wakeman model

Syntax

PriceSens = asiansensbytw(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)
PriceSens = asiansensbytw(___,Name,Value)

Description

example

PriceSens = asiansensbytw(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates) calculates prices and sensitivities for European fixed arithmetic Asian options using the Turnbull-Wakeman model.

example

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

Examples

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Define the Asian option parameters.

AssetPrice = 100;
Strike = 95;
Rates = 0.1;
Sigma = 0.15;
Settle = 'Apr-1-2013';
Maturity = 'Oct-1-2013';

Create a RateSpec using the intenvset function.

 RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', ...
 Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', 1);

Create a StockSpec for the underlying asset using the stockspec function.

DividendType = 'Continuous';
DividendAmounts = 0.05;

StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);

Calculate the price and sensitivities of the Asian option using the Turnbull-Wakeman approximation. Assume that the averaging period has started before the Settle date.

OptSpec = 'Call';
ExerciseDates = 'Oct-1-2013';
AvgDate = 'Jan-1-2013';
AvgPrice = 100;
OutSpec = {'Price','Delta','Gamma'};

[Price,Delta,Gamma] = asiansensbytw(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ...
'AvgDate',AvgDate,'AvgPrice',AvgPrice,'OutSpec',OutSpec)
Price = 5.6731
Delta = 0.5995
Gamma = 0.0135

Define the Asian option parameters.

AssetPrice = 100;
Strike = 95;
Rates = 0.1;
Sigma = 0.15;
Settle = 'Apr-1-2013';
Maturity = 'Oct-1-2013';

Create a RateSpec using the intenvset function.

 RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', ...
 Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', 1);

Create a StockSpec for the underlying asset using the stockspec function.

DividendType = 'Continuous';
DividendAmounts = 0.05;

StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);

Calculate the price and sensitivities of the Asian option using the Turnbull-Wakeman approximation. Assume that the averaging period starts after the Settle date.

OptSpec = 'Call';
ExerciseDates = 'Oct-1-2013';
AvgDate = 'Jan-1-2013';
OutSpec = {'Price','Delta','Gamma'};

[Price,Delta,Gamma] = asiansensbytw(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ...
'AvgDate',AvgDate,'OutSpec',OutSpec)
Price = 1.0774e-08
Delta = 1.0380e-08
Gamma = 9.6246e-09

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 character vector, cell array of character vectors, or string array.

Data Types: char | cell | string

Option strike price value, specified with a nonnegative integer using a NINST-by-1 vector of strike price values.

Data Types: double

Settlement date or trade date for the Asian option, specified as a NINST-by-1 vector using serial date numbers, date character vectors, datetimes, or string arrays.

Data Types: double | char

European option exercise dates, specified as a NINST-by-1 vector using serial date numbers, date character vectors, datetimes, or string arrays.

Note

For a European option, there is only one ExerciseDates on the option expiry date.

Data Types: double | char | datetime | string

Name-Value Pair 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 = asiansensbytw(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 or string array with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output is 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 | string

Average price of underlying asset at the Settle date, specified as the comma-separated pair consisting of 'AvgPrice' and a NINST-by-1 vector.

Note

Use the AvgPrice argument when AvgDate < Settle.

Data Types: double

Date averaging period begins, specified as the comma-separated pair consisting of 'AvgDate' and a NINST-by-1 vector using serial date numbers, date character vectors, datetimes, or string arrays.

Data Types: char | double | datetime | string

Output Arguments

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Expected prices or sensitivities for fixed Asian options, returned as a NINST-by-1 vector. asiansensbytw calculates prices of European arithmetic fixed (average price) Asian options.

More About

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Fixed Asian Options

Fixed Asian options have a specified strike.

The payoff at maturity for a fixed (average price) Asian option is:

  • Fixed call (average price option): max(0,SavX)

  • Fixed put (average price option): max(0,XSav)

where:

is the arithmetic or geometric average price of underlying asset.

is the price at maturity of the underlying asset.

is the strike price.

References

[1] Turnbull, S. M. and L. M. Wakeman. "A Quick Algorithm for Pricing European Average Options."Journal of Financial and Quantitative Analysis Vol. 26(3).1991, pp. 377-389.

Introduced in R2018a