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impvbyrgw

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

Syntax

Volatility = impvbyrgw(RateSpec, StockSpec, Settle,
Maturity, Strike, OptPrice, 'Name1', Value1...)

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

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Compute the Implied Volatility Using the Roll-Geske-Whaley Option Pricing Model

This example shows how to compute the implied volatility using the Roll-Geske-Whaley option pricing model. 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 the RateSpec and StockSpec
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
 'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1);

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

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

    0.3539

See Also

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