asianbyitt
Price Asian options using implied trinomial tree (ITT)
Syntax
Description
Examples
Price a Floating-Strike Asian Option Using an ITT Equity Tree
This example shows how to price a floating-strike Asian option using an ITT equity tree by loading the file deriv.mat, which provides ITTTree. The ITTTree structure contains the stock specification and time information needed to price the option.
load deriv.mat; OptSpec = 'put'; Strike = NaN; Settle = datetime(2006,1,1); ExerciseDates = datetime(2007,1,1); Price = asianbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDates)
Price = 1.0778
Input Arguments
ITTTree
— Stock tree structure
structure
Stock tree structure, specified by using itttree
.
Data Types: struct
OptSpec
— Definition of option
character vector with value 'call'
or 'put'
| cell array of character vectors with values 'call'
or 'put'
Definition of option, specified as 'call'
or 'put'
using
a character vector or a cell array of character vectors.
Data Types: char
| cell
Strike
— Option strike price value
matrix of nonnegative integers
Option strike price value, specified with a nonnegative integer
using a NINST
-by-1
matrix of
strike price values.
To compute the value of a floating-strike Asian option, Strike
must
be specified as NaN
. Floating-strike Asian options
are also known as average strike options.
Data Types: double
Settle
— Settlement date or trade date
datetime array | string array | date character vector
Settlement date or trade date for the Asian option, specified as a
NINST
-by-1
matrix of settlement or trade dates
using a datetime array, string array, or date character vectors.
Note
The Settle
date for every Asian option is set to the
ValuationDate
of the stock tree. The Asian argument,
Settle
, is ignored.
To support existing code, asianbyitt
also
accepts serial date numbers as inputs, but they are not recommended.
ExerciseDates
— Option exercise dates
datetime array | string array | date character vector
Option exercise dates, specified as a datetime array, string array, or date character vector:
For a European option, use a
NINST
-by-1
matrix of exercise dates. Each row is the schedule for one option. For a European option, there is only oneExerciseDates
on the option expiry date.For an American option, use a
NINST
-by-2
vector of exercise date boundaries. The option can be exercised on any tree date between or including the pair of dates on that row. If only one non-NaN
date is listed, or ifExerciseDates
is aNINST
-by-1
vector, the option can be exercised betweenValuationDate
of the stock tree and the single listedExerciseDates
.
To support existing code, asianbyitt
also
accepts serial date numbers as inputs, but they are not recommended.
AmericanOpt
— Option type
0
European (default) | integer with values 0
or 1
(Optional) Option type, specified as NINST
-by-1
positive
integer flags with values:
0
— European1
— American
Data Types: double
AvgType
— Average types
arithmetic
(default) | character vector with values of arithmetic
or geometric
Average types, specified as arithmetic
for
arithmetic average, or geometric
for geometric
average.
Data Types: char
AvgDate
— Date averaging period begins
datetime scalar | string scalar | date character vector
Date averaging period begins, specified as a scalar datetime, string, or date character vector.
To support existing code, asianbyitt
also
accepts serial date numbers as inputs, but they are not recommended.
Output Arguments
Price
— Expected prices for Asian options at time 0
vector
Expected prices for Asian options at time 0, returned as a
NINST
-by-1
vector. Pricing of Asian options is
done using Hull-White (1993). Therefore, for these options there are no unique prices
on the tree nodes except for the root node.
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] Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.
Version History
Introduced in R2007aR2022b: Serial date numbers not recommended
Although asianbyitt
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.
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