assetsensbybls

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

Syntax

PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)

PriceSens = assetsensbybls(___,Name,Value)

Description

PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) computes asset-or-nothing European digital options or sensitivities using the Black-Scholes option pricing model.

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.

PriceSens = assetsensbybls(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

Compute Asset-Or-Nothing Digital Option Prices and Sensitivities Using the Black-Scholes Option Pricing Model

Consider two asset-or-nothing put options on a nondividend paying stock with a strike of 95 and 93 and expiring on January 30, 2009. On November 3, 2008 the stock is trading at 97.50. Using this data, calculate the price and sensitivity of the asset-or-nothing put options if the risk-free rate is 4.5% and the volatility is 22%. First, create the RateSpec.

Settle = datetime(2008,11,3);
Maturity = datetime(2009,1,30);
Rates = 0.045;
Compounding = -1;
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9893
            Rates: 0.0450
         EndTimes: 0.2391
       StartTimes: 0
         EndDates: 733803
       StartDates: 733715
    ValuationDate: 733715
            Basis: 0
     EndMonthRule: 1

Define the StockSpec.

AssetPrice = 97.50;
Sigma = .22;
StockSpec = stockspec(Sigma, AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.2200
         AssetPrice: 97.5000
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Define the put options.

OptSpec = {'put'};
Strike = [95;93];

Calculate the delta, price, and gamma.

OutSpec = { 'delta';'price';'gamma'};
[Delta, Price, Gamma] = assetsensbybls(RateSpec, StockSpec, Settle,...
Maturity, OptSpec, Strike, 'OutSpec', OutSpec)

Delta = 2×1

   -3.0833
   -2.8337

Price = 2×1

   33.7666
   26.9662

Gamma = 2×1

    0.0941
    0.1439

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, assetsensbybls 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, assetsensbybls 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 — Pay-off strike value

vector

Pay-off strike value, 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,Delta] = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',{'gamma'; 'delta'})

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 asset-or-nothing option

vector

Expected prices or sensitivities (defined using OutSpec) for asset-or-nothing option, returned as a NINST-by-1 vector.

More About

Asset-or-Nothing Digital Option

An asset-or-nothing digital option a type of exotic option that pays a fixed amount (the asset) if the underlying asset meets certain conditions at expiration, specifically if the asset's price is above (or below) a predetermined strike price.

If the condition is not met, the option pays nothing. These options are a simplified form of binary options and are primarily used in financial markets for hedging and speculative purposes.

Version History

Introduced in R2009a

R2022b: Serial date numbers not recommended

Although assetsensbybls 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.