Learn more about Financial Derivatives Toolbox

assetsensbybls - Calculate price and sensitivities of asset-or-nothing digital options using Black-Scholes model

Syntax

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

Arguments

`RateSpec`	The annualized, continuously compounded rate term structure. For information on the interest rate specification, see `intenvset`.
`StockSpec`	Stock specification. See `stockspec`.
`Settle`	`NINST`-by-`1` vector of settlement or trade dates.
`Maturity`	`NINST`-by-`1` vector of maturity dates.
`OptSpec`	`NINST`-by-`1` cell array of strings `'call'` or `'put'`.
`Strike`	`NINST`-by-`1` vector of strike price values.
`OutSpec`	(Optional) All optional inputs are specified as matching parameter name/value pairs. The parameter name is specified as a character string, followed by the corresponding parameter value. You can specify parameter name/value pairs in any order. Names are case-insensitive and partial string matches are allowed provided no ambiguities exist. Valid parameter names are: `NOUT`-by-`1` or `1`-by-`NOUT` cell array of strings indicating the nature and order of the outputs for the function. Possible values are `'Price'`, `'Delta'`, `'Gamma'`, `'Vega'`, `'Lambda'`, `'Rho'`, `'Theta'`, or `'All'`. For example, `OutSpec = {'Price'; 'Lamba'; 'Rho'}` specifies that the output should be `Price`, `Lambda`, and `Rho`, in that order. To invoke from a function: `[Price, Lambda, Rho] = assetsensbybls(..., 'OutSpec', {'Price', 'Lamba', 'Rho'})` `OutSpec = {'All'}` specifies that the output should be `Delta`, `Gamma`, `Vega`, `Lambda`, `Rho`, `Theta`, and `Price`, in that order. This is the same as specifying `OutSpec` as `OutSpec = {'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', 'Price'};`. Default is `OutSpec` = `{'Price'}`.

Description

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

PriceSens = assetsensbybls(RateSpec, StockSpec, Settle,Maturity, OptSpec, Strike, OutSpec) includes the parameter/value pairs defined for OutSpec, and computes asset-or-nothing option prices and sensitivities using the Black-Scholes option pricing model.

PriceSens is a NINST-by-1 vector of expected option prices and sensitivities.

Examples

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%.

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);

Define the StockSpec:

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

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 =

   -3.0833
   -2.8337


Price =

   33.7666
   26.9662


Gamma =

    0.0941
    0.1439

assetsensbybls - Calculate price and sensitivities of asset-or-nothing digital options using Black-Scholes model

Syntax

Arguments

Description

Examples

See Also