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.

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

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

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.