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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, ¶ms);
opt.set_xtol_rel(1e-4);
std::vector<double> x(d,0);
std::vector<double> g(0);
double maxf;
nlopt::result result = opt.optimize(x, maxf);
return x;
}
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