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

typedef struct option_param {
    double r;
    double T;
    double S0;
    double V;
    int d;
    double K;
}option_param;


std::vector<double> path_gen(std::vector<double> X, option_param *p){
    std::vector<double> S(p->d);
    S[0]= p->S0*exp((p->r-p->V*p->V/2)*(p->T/p->d)+p->V*sqrt(p->T/p->d)*X[0]);
    for(int i=1;i<p->d;i++){
        S[i]=S[i-1]*exp((p->r-p->V*p->V/2)*(p->T/p->d)+p->V*sqrt(p->T/p->d)*X[i]);
    }
    return S;
}

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

double pay_off (double mean, option_param* p){
    return exp(-p->r*p->T)*pos(mean-p->K);
}
    
std::pair<double,double> monte_carl(option_param* p, int N){
    double moyenne=0;
    double variance=0;
    gaussian G(0,1);
    double temp=0;
    std::vector<double> S(p->d);
    std::vector<double> X(p->d);
    for(int i=0; i<N; i++){
        for(int j=0;j<p->d;j++){
            X[j]=G();
        }
        S=path_gen(X, p);
        temp = pay_off(std::accumulate(S.begin(), S.end(), 0.)/p->d, p);
        moyenne+=temp;
        variance+=temp*temp;
    }
    return {moyenne/N, variance/N-(moyenne/N)*(moyenne/N)};
}



    
    

int main(){
    init_alea(1);
    option_param p = {.r=0.05, .T=1.0, .S0=50.0, .V=0.1, .d=16, .K=45};
    int N=1000000;
    
    std::pair<double,double> meanvar = monte_carl(&p, N);
    std::cout<<"espérance "<<meanvar.first<<" IC "<<1.64*sqrt(meanvar.second)/sqrt(N)<<std::endl;

    
    return 0;
}