#include <vector>
#include <gsl/gsl_cdf.h>
#include "var_alea.hpp"
#include <algorithm>
#include <iostream>

double r;
double T;
double S0;
double V;
int d;

std::vector<double> path_gen(std::vector<double> X){
    d=X.size();
    std::vector<double> S(d);
    S[0]= S0;
    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]);
    }
    return S;
}

double mean_monte_carl(double r, double T, double S0, double V, int N, int d){
    double moyenne=0;
    gaussian G;
    std::vector<double> S(d);
    std::vector<double> X(d);
    for(int i=1; i<N; i++){
        for(int j=1;j<d;i++){
            X[i]=G();
        }
        S=path_gen(X);
        moyenne+=std::accumulate(S.begin(), S.end(), 0 );
    }
    return moyenne/N;
}

int main(){
    init_alea(0);
    double r=0.05;
    double T=1.0;
    double S0=50.0;
    double V=0.1;
    int d=16;
    int N=1000000;
    
    
    double moyenne = mean_monte_carl(r, T, S0, V, N, d);
    std::cout<<moyenne<<std::endl;

    
    return 0;
}