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# optstockbyrgw

Determine American call option prices using Roll-Geske-Whaley option pricing model

## Description

example

Price = optstockbyrgw(RateSpec,StockSpec,Settle,Maturity,Strike) computes the American call option prices using the Roll-Geske-Whaley option pricing model.

### Note

optstockbyrgw computes prices of American calls with a single cash dividend using the Roll-Geske-Whaley option pricing model.

## Examples

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This example shows how to determine American call option prices using Roll-Geske-Whaley option pricing model. Consider an American call option with an exercise price of \$22 that expires on February 1, 2009. The underlying stock is trading at \$20 on June 1, 2008 and has a volatility of 20% per annum. The annualized continuously compounded risk-free rate is 6.77% per annum. The stock pays a single dividend of \$2 on September 1, 2008. Using this data, compute price of the American call option using the Roll-Geske-Whaley option pricing model.

Settle = 'Jun-01-2008';
Maturity = 'Feb-01-2009';
AssetPrice = 20;
Strike = 22;
Sigma  = 0.2;
Rate = 0.0677;
DivAmount = 2;
DivDate = 'Sep-01-2008';

% define the RateSpec and StockSpec
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates',...
Maturity, 'Rates', Rate, 'Compounding', -1, 'Basis', 0);

StockSpec = stockspec(Sigma, AssetPrice, {'cash'}, DivAmount, DivDate);

Price  = optstockbyrgw(RateSpec, StockSpec, Settle, Maturity,Strike)
Price = 0.3359

## 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, specified as serial date number or date character vector using a NINST-by-1 vector.

Data Types: double | char

Maturity date for option, specified as serial date number or date character vector using a NINST-by-1 vector.

Data Types: double | char

Option strike price value, specified as a nonnegative NINST-by-1 vector.

Data Types: double

## Output Arguments

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Expected call option prices, returned as a NINST-by-1 vector.

Data Types: double

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### Vanilla Option

A vanilla option is a category of options that includes only the most standard components.

A vanilla option has an expiration date and straightforward strike price. American-style options and European-style options are both categorized as vanilla options.

The payoff for a vanilla option is as follows:

• For a call: $\mathrm{max}\left(St-K,0\right)$

• For a put: $\mathrm{max}\left(K-St,0\right)$

where:

St is the price of the underlying asset at time t.

K is the strike price.