# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# gapbybls

Determine price of gap digital options using Black-Scholes model

## Syntax

```Price = gapbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold) ```

## 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 character vectors with values of `'call'` or `'put'`. `Strike` `NINST`-by-`1` vector of payoff strike price values. `StrikeThreshold` `NINST`-by-`1` vector of strike values that determine if the option pays off.

## Description

`Price = gapbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold)` computes gap option prices using the Black-Scholes option pricing model.

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

## Examples

collapse all

This example shows how to compute gap option prices using the Black-Scholes option pricing model. Consider a gap call and put options on a nondividend paying stock with a strike of 57 and expiring on January 1, 2008. On July 1, 2008 the stock is trading at 50. Using this data, compute the price of the option if the risk-free rate is 9%, the strike threshold is 50, and the volatility is 20%.

```Settle = 'Jan-1-2008'; Maturity = 'Jul-1-2008'; Compounding = -1; Rates = 0.09; % calculate the RateSpec RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', 1); % define the StockSpec AssetPrice = 50; Sigma = .2; StockSpec = stockspec(Sigma, AssetPrice); % define the call and put options OptSpec = {'call'; 'put'}; Strike = 57; StrikeThreshold = 50; % calculate the price Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,... Strike, StrikeThreshold)```
```Pgap = -0.0053 4.4866 ```