src/opti.cpp


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#include "opti.hpp"

double pos (double x){
    return x>0?x:0;
};

double f (const std::vector<double> &X, std::vector<double> &grad, void *params) {
    int d = X.size();
    double *p =(double *)params;
    double r=p[0] ; double T=p[1]; double S0=p[2];
    double V=p[3]; double K=p[4];
    double norm = 0;
    for(int i=0; i<d; i++){
        norm+=X[i]*X[i];
    }
    std::vector<double> S(d);
    S[0]= S0*exp((r-V*V/2)*(T/d)+V*sqrt(T/d)*X[0]);
    for(int i=1;i<d;i++){
        S[i]=S[i-1]*exp((r-V*V/2)*(T/d)+V*sqrt(T/d)*X[i]);
    }
    double temp = std::accumulate(S.begin(), S.end(), 0.)/d;
    double value = exp(-r*T)*pos(temp-K);
    return log(value) - 0.5*norm;
};


std::vector<double> argmax(double r, double T, double S0, double V, double K, int d){
    
    double params[5] = {r, T, S0, V, K};
    
    nlopt::opt opt(nlopt::LN_COBYLA, d);

    opt.set_max_objective(f, &params);

    opt.set_xtol_rel(1e-4);

    std::vector<double> x(d,0);
    std::vector<double> g(0);

    
    std::cout<<"valeur au début : "<<f(x, g, &params)<<std::endl;

    double maxf;
    nlopt::result result = opt.optimize(x, maxf);

    return x;
}