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# assetsensbyls

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

## Syntax

PriceSens = assetsensbyls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)
PriceSens = assetsensbyls(___,Name,Value)

## Description

example

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

example

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

## Examples

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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 = 'Nov-3-2008';
Maturity = 'Jan-30-2009';
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

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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

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

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 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

Definition of the option as 'call' or 'put', specified as an NINST-by-1 vector.

Data Types: char | cell

Pay-off strike value, specified as an NINST-by-1 vector.

Data Types: double

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

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

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