cashbybls

Determine price of cash-or-nothing digital options using Black-Scholes model

Syntax

Price = cashbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,Payoff)

Description

Price = cashbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,Payoff) computes the price for cash-or-nothing European digital options using the Black-Scholes option pricing model.

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

RateSpec — Interest-rate term structure

structure

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

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.

More About

Cash-or-Nothing Digital Option

A cash-or-nothing digital option is a type of exotic option that provides a fixed cash payout if the underlying asset meets certain conditions at expiration, specifically if the asset's price is above (for a call option) or below (for a put option) a predetermined strike price.

If the condition is not met, the option pays nothing. This binary payoff structure distinguishes cash-or-nothing digital options from traditional options, which have payoffs that depend on the difference between the underlying asset's price and the strike price.

Version History

Introduced in R2009a

R2022b: 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.