%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Driver for parameter and implied volatilty fitting under Black-Scholes-Merton
%%% model
%%%
%%% Copyright (C) 2008  Vladimir Surkov
%%%
%%%
%%% This program is free software: you can redistribute it and/or modify
%%% it under the terms of the GNU General Public License as published by
%%% the Free Software Foundation, either version 3 of the License, or
%%% (at your option) any later version.
%%%
%%% This program is distributed in the hope that it will be useful,
%%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%%% GNU General Public License for more details.
%%% 
%%% You should have received a copy of the GNU General Public License
%%% along with this program.  If not, see <http://www.gnu.org/licenses/>.
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [sigma] = Driver_ParameterFitting_BlackScholesMerton()

load('SPY_Option_Prices');
K = SPY_Option_Prices(:,1)';
C = SPY_Option_Prices(:,2)';
P = SPY_Option_Prices(:,3)';

S = 117.5;
T = 1/12;
r = 0.02;
q = 0.0221;

x_0 = 0.1;

f = @(x)(PricingError(S, K, T, x, r, q, C, P));
sigma = lsqnonlin(f,x_0);

[values_call, values_put] = CarrMadanFFT_European_BlackScholesMerton(S, K, T, sigma, r, q);
[sigma_call_model, sigma_put_model] = ImpliedVolatility(S, K, T, r, q, values_call, values_put);
[sigma_call_market, sigma_put_market] = ImpliedVolatility(S, K, T, r, q, C, P);

subplot(2,1,1);
plot(K, sigma_call_model, 'r', K, sigma_call_market, 'b');
subplot(2,1,2);
plot(K, sigma_put_model, 'r', K, sigma_put_market, 'b');


end

function error = PricingError(S, K, T, sigma, r, q, C, P)
    w = blsgamma(S, K, r, T, sigma, q);
    [values_call, values_put] = CarrMadanFFT_European_BlackScholesMerton(S,K,T,sigma,r,q);
    error = [(values_call - C)./w (values_put - P)./w];
end