asianbystt
Price Asian options using standard trinomial tree
Syntax
Description
prices Asian options using a standard trinomial (STT) tree.Price
= asianbystt(STTTree
,OptSpec
,Strike
,Settle
,ExerciseDates
)
Note
Alternatively, you can use the Asian
object to price Asian
options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
Examples
Price an Asian Option Using the Standard Trinomial Tree Model
Create a RateSpec
.
StartDates = datetime(2009,1,1); EndDates = datetime(2013,1,1); Rates = 0.035; Basis = 1; Compounding = -1; RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates,... 'EndDates', EndDates, 'Rates', Rates,'Compounding', Compounding, 'Basis', Basis)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.8694
Rates: 0.0350
EndTimes: 4
StartTimes: 0
EndDates: 735235
StartDates: 733774
ValuationDate: 733774
Basis: 1
EndMonthRule: 1
Create a StockSpec
.
AssetPrice = 85; Sigma = 0.15; StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.1500
AssetPrice: 85
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Create an STTTree
.
NumPeriods = 4; TimeSpec = stttimespec(StartDates, EndDates, 4); STTTree = stttree(StockSpec, RateSpec, TimeSpec)
STTTree = struct with fields:
FinObj: 'STStockTree'
StockSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3 4]
dObs: [733774 734139 734504 734869 735235]
STree: {[85] [110.2179 85 65.5520] [142.9174 110.2179 85 65.5520 50.5537] [185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870] [240.2985 185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870 30.0668]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double]}
Define the Asian option and compute the price.
Settle = datetime(2009,1,1);
ExerciseDates = [datetime(2012,1,1) ; datetime(2013,1,1)];
OptSpec = 'call';
Strike = 100;
Price = asianbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)
Price = 2×1
1.6905
2.6203
Input Arguments
STTTree
— Stock tree structure for standard trinomial tree
structure
Stock tree structure for a standard trinomial tree, specified
by using stttree
.
Data Types: struct
OptSpec
— Definition of option
character vector with value 'call'
or 'put'
Definition of option, specified as 'call'
or 'put'
using
a character vector.
Data Types: char
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
should 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
vector of settlement or trade dates
using date character vectors, or a datetime array.
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, asianbystt
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 character vectors:
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 of dates, the option can be exercised betweenValuationDate
of the stock tree and the single listedExerciseDates
.
To support existing code, asianbystt
also
accepts serial date numbers as inputs, but they are not recommended.
AmericanOpt
— Option type
0
European (default) | scalar with values [0,1]
Option type, specified as NINST
-by-1
positive
integer scalar flags with values:
0
— European1
— American
Data Types: single
| 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, asianbystt
also
accepts serial date numbers as inputs, but they are not recommended.
Output Arguments
Price
— Expected prices for Asian options at time 0
matrix
Expected prices for Asian options at time 0, returned as a NINST
-by-1
matrix.
Pricing of Asian options is done using Hull-White (1993). Consequently,
for these options there are no unique prices on the tree nodes with
the exception of 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 R2015bR2022b: Serial date numbers not recommended
Although asianbystt
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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