assetsensbybls
Determine price or sensitivities of asset-or-nothing digital options using Black-Scholes model
Syntax
Description
computes asset-or-nothing European digital options or
sensitivities using the Black-Scholes option pricing model.PriceSens
= assetsensbybls(RateSpec
,StockSpec
,Settle
,Maturity
,OptSpec
,Strike
)
Note
Alternatively, you can use the Binary
object to calculate price or
sensitivities for digital options. For more
information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
specifies options using one or more name-value pair
arguments in addition to the input arguments in the previous
syntax.PriceSens
= assetsensbybls(___,Name,Value
)
Examples
Compute Asset-Or-Nothing Digital Option Prices and Sensitivities 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 and sensitivity 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 delta, price, and gamma.
OutSpec = { 'delta';'price';'gamma'}; [Delta, Price, Gamma] = assetsensbybls(RateSpec, StockSpec, Settle,... Maturity, OptSpec, Strike, 'OutSpec', OutSpec)
Delta = 2×1
-3.0833
-2.8337
Price = 2×1
33.7666
26.9662
Gamma = 2×1
0.0941
0.1439
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, assetsensbybls
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, assetsensbybls
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
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: [Gamma,Delta] =
assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',{'gamma';
'delta'})
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'
Define outputs, specified as the
comma-separated pair consisting of
'OutSpec'
and a
NOUT
- by-1
or a
1
-by-NOUT
cell array of character vectors 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
Output Arguments
PriceSens
— Expected prices or sensitivities for asset-or-nothing option
vector
Expected prices or sensitivities (defined
using OutSpec
) for
asset-or-nothing option, returned as a
NINST
-by-1
vector.
Version History
Introduced in R2009aR2022b: Serial date numbers not recommended
Although assetsensbybls
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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