asiansensbyhhm

Calculate price and sensitivities of European discrete arithmetic fixed Asian options using Haug, Haug, Margrabe model

Syntax

PriceSens = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)

PriceSens = asiansensbyhhm(___,Name,Value)

Description

PriceSens = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates) calculates prices and sensitivities for European discrete arithmetic fixed Asian options using the Haug, Haug, Margrabe model.

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

Examples

Compute Price and Sensitivities for Asian Option with Averaging Period Starting 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 Haug, Haug, Margrabe approximation. Assume that the averaging period has started before the Settle date.

OptSpec = 'Call';
ExerciseDates = datetime(2013,10,1);
NumFixings = 12;
AvgDate = datetime(2013,1,1);
AvgPrice = 100;
OutSpec = {'Price','Delta','Gamma'};

[Price,Delta,Gamma] = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ...
'NumFixings',NumFixings,'AvgDate',AvgDate,'AvgPrice',AvgPrice,'OutSpec',OutSpec)

Price = 5.8216

Delta = 0.5907

Gamma = 0.0143

Compute Price and Sensitivities for Asian Option with Averaging Period Starting 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 Haug, Haug, Margrabe approximation. Assume that the averaging period started after the Settle date.

OptSpec = 'Call';
ExerciseDates = 'Oct-1-2013';
NumFixings = 15;
AvgDate = 'Jan-1-2013';
OutSpec = {'Price','Delta','Gamma'};

[Price,Delta,Gamma] = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ...
'NumFixings',NumFixings,'AvgDate',AvgDate,'OutSpec',OutSpec)

Price = 1.3785e-07

Delta = 1.1438e-07

Gamma = 9.0830e-08

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, asiansensbyhhm 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, asiansensbyhhm 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 = asiansensbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'OutSpec',{'All'},'NumFixings',15)

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

character vector | datetime | string array

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

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

NumFixings — Total number of fixings or averaging points

10 (default) | vector

Total number of fixings or averaging points, specified as the comma-separated pair consisting of 'NumFixings' and a NINST-by-1 vector.

Data Types: double

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. asianbyhhm calculates prices of European arithmetic fixed (average price) Asian options with discretely monitoring.

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] Haug, E. G. The Complete Guide to Option Pricing Formulas. McGraw-Hill Education, 2007.

Version History

Introduced in R2018a

R2022b: Serial date numbers not recommended

Although asiansensbyhhm 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.