impvbyrgw - Determine implied volatility using Roll-Geske-Whaley option pricing model for American call option

Syntax

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.
Strike	NINST-by-1 vector of strike price values.
OptPrice	NINST-by-1 vector of American call option prices from which the implied volatility of the underlying asset are derived.
Note   All optional inputs are specified as matching parameter name/parameter value pairs. The parameter name is specified as a character string, followed by the corresponding parameter value. You can specify parameter name/parameter value pairs in any order; names are case-insensitive and partial string matches are allowed provided no ambiguities exist.
Limit	(Optional) Positive scalar representing the upper bound of the implied volatility search interval. Default is 10, or 1000% per annum.
Tolerance	(Optional) Positive scalar implied volatility termination tolerance. Default is 1e-6.

Description

Volatility = impvbyrgw(RateSpec, StockSpec, Settle, Maturity, Strike, OptPrice, 'Name1', Value1...) computes implied volatility using the Roll-Geske-Whaley option pricing model.

Volatility is a NINST-by-1 vector of expected implied volatility values. If no solution is found, a NaN is returned.

Note   impvbyrgw computes implied volatility of American calls with a single cash dividend using the Roll-Geske-Whaley option pricing model.

Examples

Assume that on July 1, 2008 a stock is trading at $13 and pays a single cash dividend of $0.25 on November 1, 2008. The American call option with a strike price of $15 expires on July 1, 2009 and is trading at $1.346. The annualized continuously compounded risk-free rate is 5% per annum. Calculate the implied volatility of the stock using the Roll-Geske-Whaley option pricing model:

AssetPrice = 13;
Strike = 15;
Rates = 0.05;
Settle = 'July-01-08';
Maturity = 'July-01-09';

Define StockSpec and RateSpec:

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
 'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1);

StockSpec = stockspec(NaN, AssetPrice, {'cash'}, 0.25, {'Nov 1,2008'});

Calculate the implied volatility of the option:

Price = [1.346];
Volatility = impvbyrgw(RateSpec, StockSpec, Settle, Maturity, Strike, Price)

Volatility =

    0.3539

See Also

optstockbyrgw | optstocksensbyrgw

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