# optstockbybjs

Price American options using Bjerksund-Stensland 2002 option pricing model

## Syntax

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

## 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.

## Description

```Price = optstockbybjs(RateSpec, StockSpec, Settle, Maturity,OptSpec, Strike)``` computes American option prices with continuous dividend yield using the Bjerksund-Stensland 2002 option pricing model.

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

 Note:   `optstockbybjs` computes prices of American options with continuous dividend yield using the Bjerksund-Stensland option pricing model.

## Examples

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### Compute the American Option Prices With Continuous Dividend Yield Using the Bjerksund-Stensland 2002 Option Pricing Model

This example shows how to compute the American option prices with continuous dividend yield using the Bjerksund-Stensland 2002 option pricing model. Consider two American stock options (a call and a put) with an exercise price of \$100. The options expire on April 1, 2008. Assume the underlying stock pays a continuous dividend yield of 4% as of January 1, 2008. The stock has a volatility of 20% per annum and the annualized continuously compounded risk-free rate is 8% per annum. Using this data, calculate the price of the American call and put, assuming the following current prices of the stock: \$90 (for the call) and \$120 (for the put).

```Settle = 'Jan-1-2008'; Maturity = 'April-1-2008'; Strike = 100; AssetPrice = [90;120]; DivYield = 0.04; Rate = 0.08; Sigma = 0.20; % define the RateSpec and StockSpec StockSpec = stockspec(Sigma, AssetPrice, {'continuous'}, DivYield); RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rate, 'Compounding', -1); % define the option type OptSpec = {'call'; 'put'}; Price = optstockbybjs(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike) ```
```Price = 0.8420 0.1108 ```

The first element of the `Price` vector represents the price of the call (\$0.84); the second element represents the price of the put option (\$0.11).

## References

Bjerksund, P. and G. Stensland, Closed-Form Approximation of American Options, Scandinavian Journal of Management, 1993, Vol. 9, Suppl., pp. S88-S99.

Bjerksund, P. and G. Stensland, Closed Form Valuation of American Options, Discussion paper 2002 (http://brage.bibsys.no/nhh/bitstream/URN:NBN:no-bibsys_brage_22301/1/bjerksund%20petter%200902.pdf)