cashbybls
Determine price of cash-or-nothing digital options using Black-Scholes model
Description
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 = 'Jan-1-2008'; Maturity = 'Oct-1-2008'; 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
serial date number | date character vector
Settlement or trade date for the basket option, specified as an
NINST
-by-1
vector of serial date
numbers or date character vectors.
Data Types: double
| char
| cell
Maturity
— Maturity date
serial date number | date character vector
Maturity date for the basket option, specified as an
NINST
-by-1
vector of serial date
numbers or date character vectors.
Data Types: double
| char
| cell
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
MATLAB 명령
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