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

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

Note

Alternatively, you can use the Asian object to calculate prices or sensitivities for Asian options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

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

Examples

Compute Price and Sensitivities for Asian Option with Averaging Period Before the Settle Date

Define the Asian option parameters.

AssetPrice = 100;
Strike = 95;
Rates = 0.1;
Sigma = 0.15;
Settle = datetime(2013,4,1);
Maturity = datetime(2013,10,1);

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 = datetime(2013,10,1);
AvgDate = datetime(2013,1,1);
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

Compute Price and Sensitivities for Asian Option with Averaging Period After the Settle Date

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

RateSpec — Interest-rate term structure

structure

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

StockSpec — Stock specification for underlying asset

structure

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

OptSpec — Definition of option

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

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

Strike — Option strike price value

nonnegative integer | vector of nonnegative integers

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

Data Types: double

Settle — Settlement dates or trade dates

datetime array | string array | date character vector

Settlement date or trade date for the Asian option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, asiansensbytw also accepts serial date numbers as inputs, but they are not recommended.

ExerciseDates — European option exercise dates

datetime array | string array | date character vector

European option exercise dates, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

Note

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

To support existing code, asiansensbytw also accepts serial date numbers as inputs, but they are not recommended.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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

OutSpec — Define outputs

{'Price'} (default) | character vector with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All' | cell array of character vectors with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All' | string array with values "Price", "Delta", "Gamma", "Vega", "Lambda", "Rho", "Theta", and "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

AvgPrice — Average price of underlying asset at the Settle date

vector

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

AvgDate — Date averaging period begins

datetime array | string array | date character vector

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

To support existing code, asiansensbytw also accepts serial date numbers as inputs, but they are not recommended.

Output Arguments

PriceSens — Expected prices or sensitivities for fixed Asian options

vector

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

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.

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.

Version History

Introduced in R2018a

R2022b: Serial date numbers not recommended

Although asiansensbytw supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.