# Documentation

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# supersharebybls

Calculate price of supershare digital options using Black-Scholes model

## Syntax

```Price = supersharebybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,StrikeLow,StrikeHigh) ```

## 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. `StrikeLow` `NINST`-by-`1` vector of low strike price values. `StrikeHigh` `NINST`-by-`1` vector of high strike price values.

## Description

`Price = supersharebybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,StrikeLow,StrikeHigh)` computes supershare digital option prices using the Black-Scholes model.

`Price` is a `NINST`-by-`1` vector of expected option prices.

## Examples

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This example shows how to compute the price of supershare digital options using Black-Scholes model. Consider a supershare based on a portfolio of nondividend paying stocks with a lower strike of 350 and an upper strike of 450. The value of the portfolio on November 1, 2008 is 400. The risk-free rate is 4.5% and the volatility is 18%. Using this data, calculate the price of the supershare option on February 1, 2009.

```Settle = 'Nov-1-2008'; Maturity = 'Feb-1-2009'; Rates = 0.045; Basis = 1; Compounding = -1; % create the RateSpec RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis); % define the StockSpec AssetPrice = 400; Sigma = .18; StockSpec = stockspec(Sigma, AssetPrice); % define the high and low strike points StrikeLow = 350; StrikeHigh = 450; % calculate the price Pssh = supersharebybls(RateSpec, StockSpec, Settle, Maturity,... StrikeLow, StrikeHigh)```
```Pssh = 0.9411 ```