asianbyhhm
Price European discrete arithmetic fixed Asian options using Haug, Haug, Margrabe model
Syntax
Description
Examples
Price an 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 = '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 of the Asian option using the Haug, Haug, Margrabe approximation. Assume that the averaging period has started before the Settle
date.
OptSpec = 'Call'; ExerciseDates = 'Oct-1-2013'; NumFixings = 12; AvgDate = 'Jan-1-2013'; AvgPrice = 100; Price = asianbyhhm(RateSpec, StockSpec, OptSpec, Strike, Settle, ExerciseDates, ... 'NumFixings', NumFixings, 'AvgDate', AvgDate, 'AvgPrice', AvgPrice)
Price = 5.8216
Price an 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 of the Asian option using the Haug, Haug, Margrabe approximation. Assume that the averaging period starts after the Settle
date.
OptSpec = 'Call'; ExerciseDates = 'Oct-1-2013'; NumFixings = 15; AvgDate = 'Jan-1-2013'; Price = asianbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates, ... 'NumFixings',NumFixings,'AvgDate',AvgDate)
Price = 1.3785e-07
Input Arguments
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
serial date number | date character vector | datetime | string array
Settlement date or trade date for the Asian option, specified as a
NINST
-by-1
vector using serial date numbers,
date character vectors, datetime, or string arrays.
Data Types: double
| char
| datetime
| string
ExerciseDates
— European option exercise dates
serial date number | date character vector | datetime | string array
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 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: Price =
asianbyhhm(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'NumFixings',15)
AvgDate
— Date averaging period begins
serial date number | date 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 serial date numbers, date character vectors, datetimes, or string
array.
Data Types: char
| double
| datetime
| string
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
Price
— Expected prices for fixed Asian options
vector
Expected prices for fixed Asian options, returned as a
NINST
-by-1
vector.
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
See Also
asiansensbyhhm
| asianbytw
| asianbykv
| asianbyls
| stockspec
| intenvset
| asianbycrr
| asianbylevy
Topics
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