cashsensbybls
Determine price or sensitivities of cash-or-nothing digital options using Black-Scholes model
Syntax
Description
computes the price or sensitivities for cash-or-nothing
European digital options using the Black-Scholes option
pricing model.PriceSens
= cashsensbybls(RateSpec
,StockSpec
,Settle
,Maturity
,OptSpec
,Strike
,Payoff
)
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
= cashsensbybls(___,Name,Value
)
Examples
Compute Cash-or-Nothing Option Prices and Sensitivities Using the Black-Scholes Option Pricing Model
Consider a European call and put cash-or-nothing options on a futures contract with an exercise price of $90, and a fixed payoff of $10 that expires on October 1, 2008. Assume that on January 1, 2008 the contract trades at $110, and has a volatility of 25% per annum and the risk-free rate is 4.5% per annum. Using this data, calculate the price and sensitivity of the call and put cash-or-nothing options on the futures contract. First, create the RateSpec
:
Settle = datetime(2008,1,1); Maturity = datetime(2008,10,1); Rates = 0.045; Compounding = -1; Basis = 1; RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9668
Rates: 0.0450
EndTimes: 0.7500
StartTimes: 0
EndDates: 733682
StartDates: 733408
ValuationDate: 733408
Basis: 1
EndMonthRule: 1
Define the StockSpec
.
AssetPrice = 110;
Sigma = .25;
DivType = 'Continuous';
DivAmount = Rates;
StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmount)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.2500
AssetPrice: 110
DividendType: {'continuous'}
DividendAmounts: 0.0450
ExDividendDates: []
Define the call and put options.
OptSpec = {'call'; 'put'}; Strike = 90; Payoff = 10;
Compute the gamma, theta, and price.
OutSpec = { 'gamma';'theta';'price'}; [Gamma, Theta, Price] = cashsensbybls(RateSpec, StockSpec,... Settle, Maturity, OptSpec, Strike, Payoff, 'OutSpec', OutSpec)
Gamma = 2×1
-0.0050
0.0050
Theta = 2×1
-2.2489
1.8139
Price = 2×1
7.6716
1.9965
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, cashsensbybls
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, cashsensbybls
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
— Strike price value
vector
Strike price value, specified as an
NINST
-by-1
vector.
Data Types: double
Payoff
— Payoff values
vector
Payoff values (or the amount to be paid at
expiration), 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,Theta,Price] =
cashsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,Payoff,'OutSpec',{'gamma';'theta';'price'})
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 cash-or-nothing option
vector
Expected prices or sensitivities (defined
using OutSpec
) for
cash-or-nothing option, returned as a
NINST
-by-1
vector.
Version History
Introduced in R2009aR2022b: Serial date numbers not recommended
Although cashsensbybls
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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