assetbybls
Determine price of asset-or-nothing digital options using Black-Scholes model
Description
computes asset-or-nothing European digital options using the Black-Scholes option
pricing model.Price
= assetbybls(RateSpec
,StockSpec
,Settle
,Maturity
,OptSpec
,Strike
)
Note
Alternatively, you can use the Binary
object
to price digital options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
Examples
Compute Asset-Or-Nothing Digital Option Prices Using the Black-Scholes Option Pricing Model
Consider two asset-or-nothing put options on a nondividend paying stock with a strike of 95 and 93 and expiring on January 30, 2009. On November 3, 2008 the stock is trading at 97.50. Using this data, calculate the price of the asset-or-nothing put options if the risk-free rate is 4.5% and the volatility is 22%. First, create the RateSpec
.
Settle = datetime(2008,11,3); Maturity = datetime(2009,1,30); Rates = 0.045; Compounding = -1; RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9893
Rates: 0.0450
EndTimes: 0.2391
StartTimes: 0
EndDates: 733803
StartDates: 733715
ValuationDate: 733715
Basis: 0
EndMonthRule: 1
Define the StockSpec
.
AssetPrice = 97.50; Sigma = .22; StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.2200
AssetPrice: 97.5000
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Define the put options.
OptSpec = {'put'};
Strike = [95;93];
Calculate the price.
Paon = assetbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)
Paon = 2×1
33.7666
26.9662
Input Arguments
StockSpec
— Stock specification for underlying asset
structure
Stock specification for the underlying asset. For information on the stock
specification, see stockspec
.
stockspec
handles several
types of underlying assets. For example, for physical commodities the price
is StockSpec.Asset
, the volatility is
StockSpec.Sigma
, and the convenience yield is
StockSpec.DividendAmounts
.
Data Types: struct
Settle
— Settlement or trade date
datetime array | string array | date character vector
Settlement or trade date for the basket option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, assetbybls
also
accepts serial date numbers as inputs, but they are not recommended.
Maturity
— Maturity date
datetime array | string array | date character vector
Maturity date for the basket option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, assetbybls
also
accepts serial date numbers as inputs, but they are not recommended.
OptSpec
— Definition of option
character vector with values 'call'
or
'put'
| cell array of character vectors with values 'call'
or
'put'
Definition of the option as 'call'
or
'put'
, specified as an
NINST
-by-1
vector.
Data Types: char
| cell
Strike
— Pay-off strike value
vector
Pay-off strike value, specified as an
NINST
-by-1
vector.
Data Types: double
Output Arguments
Price
— Expected prices for asset-or-nothing option
vector
Expected prices for asset-or-nothing option, returned as a
NINST
-by-1
vector.
Version History
Introduced in R2009aR2022b: Serial date numbers not recommended
Although assetbybls
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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