impvbyrgw

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

Description

example

Volatility = impvbyrgw(RateSpec,StockSpec,Settle,Maturity,Strike,OptPrice) computes implied volatility using Roll-Geske-Whaley option pricing model for American call option.

Note

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

example

Volatility = impvbyrgw(___,Name,Value) adds optional name-value pair arguments.

Examples

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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

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 date, specified as a NINST-by-1 vector of serial date numbers or a date character vectors.

Data Types: double | char

Maturity date for the American option, specified as a NINST-by-1 vector of serial date numbers or a date character vectors.

Data Types: double | char

Option strike price value, specified as a nonnegative scalar or NINST-by-1 vector of strike price values. Each row is the schedule for one option.

Data Types: double

American option prices from which the implied volatility of the underlying asset is derived, specified as a nonnegative scalar or NINST-by-1 vector.

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: Volatility = impvbyrgw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice,'Limit',5,'Tolerance',1e-5)

Upper bound of implied volatility search interval, specified as the comma-separated pair consisting of 'Limit' and a positive scalar.

Data Types: double

Implied volatility search termination tolerance, specified as the comma-separated pair consisting of 'Tolerance' and a positive scalar.

Data Types: double

Output Arguments

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Expected implied volatility values, returned as a NINST-by-1 vector. If no solution can be found, a NaN is returned.

Introduced in R2008b