cashbybls
Determine price of cash-or-nothing digital options using Black-Scholes model
Description
computes the price for cash-or-nothing European digital options using the
Black-Scholes option pricing model.Price
= cashbybls(RateSpec
,StockSpec
,Settle
,Maturity
,OptSpec
,Strike
,Payoff
)
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 Cash-or-Nothing Option Prices Using the Black-Scholes Option Pricing Model
Consider a European call and put cash-or-nothing options on a futures contract with and exercise strike price of $90, 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 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;
Calculate the prices.
Pcon = cashbybls(RateSpec, StockSpec, Settle,...
Maturity, OptSpec, Strike, Payoff)
Pcon = 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, cashbybls
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, cashbybls
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
Output Arguments
Price
— Expected prices for cash-or-nothing option
vector
Expected prices for cash-or-nothing option, returned as a
NINST
-by-1
vector.
Version History
Introduced in R2009aR2022b: Serial date numbers not recommended
Although cashbybls
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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