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    %% Compute the Implied Volatility Using the Black-Scholes Option Pricing Model
% This example shows how to compute the implied volatility using the
% Black-Scholes option pricing model. Consider a European call and put
% options with an exercise price of $40 that  expires on June 1, 2008. The
% underlying stock is trading at $45 on  January 1, 2008 and the risk-free
% rate is 5% per annum. The option price is $7.10 for the call and $2.85
% for the put. Using this data, calculate the implied volatility of the
% European call and put using the Black-Scholes option pricing model.
%%

% Copyright 2015 The MathWorks, Inc.

AssetPrice = 45;
Settlement = 'Jan-01-2008';
Maturity = 'June-01-2008';
Strike = 40;
Rates = 0.05;
OptionPrice = [7.10; 2.85];
OptSpec = {'call';'put'};

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

StockSpec = stockspec(NaN, AssetPrice);

ImpvVol =  impvbybls(RateSpec, StockSpec, Settlement, Maturity, OptSpec,...
Strike, OptionPrice)
%%
% The implied volatility is 31.75% for the call and 48.78% for the put.