From 43481c09afd990c99106d7efd6fe8a7c9a53d519 Mon Sep 17 00:00:00 2001
From: Bertrand <bertrand.horel@gmail.com>
Date: Sun, 14 Feb 2016 22:04:24 +0000
Subject: ajout option rqmc et correction rqmc.cpp

---
 option.cpp | 50 ++++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 48 insertions(+), 2 deletions(-)

(limited to 'option.cpp')

diff --git a/option.cpp b/option.cpp
index deb8347..016de0b 100644
--- a/option.cpp
+++ b/option.cpp
@@ -3,6 +3,7 @@
 #include "var_alea.hpp"
 #include <algorithm>
 #include <iostream>
+#include "low_discrepancy.hpp"
 
 
 template <typename L>
@@ -25,6 +26,10 @@ double pos (double x){
     return x>0?x:0;
 }
 
+double frac_part(double x){
+    return x - floor(x);
+}
+
 struct asian_option : public var_alea<double>
 {
 	asian_option(double r, double T, double S0, double V, int d, double K)
@@ -50,15 +55,56 @@ struct asian_option : public var_alea<double>
         gaussian G;
 };
 
+struct asian_option_qmc : public var_alea<double>
+{
+	asian_option_qmc(double r, double T, double S0, double V, int d, double K)
+        : r(r), T(T), S0(S0), V(V), d(d), K(K), G(d), U(0,1) {};
+        
+	double operator()() {
+        std::vector<double> S(d);
+        std::vector<double> sob(d); 
+        sob = G();
+        S[0]= S0*exp((r-V*V/2)*(T/d)+V*sqrt(T/d)*gsl_cdf_gaussian_Pinv(frac_part(U()+sob[0]), 1));
+        for(int i=1;i<d;i++){
+            S[i]=S[i-1]*exp((r-V*V/2)*(T/d)+V*sqrt(T/d)*gsl_cdf_gaussian_Pinv(frac_part(U()+sob[i]), 1));
+        }
+        double temp = std::accumulate(S.begin(), S.end(), 0.)/d;
+        return exp(-r*T)*pos(temp-K);
+    };
+    
+	private:
+        double r;
+        double T;
+        double S0;
+        double V;
+        int d;
+        double K;
+        sobol G;
+        uniform U;
+};
 
 
 int main(){
     init_alea(1);
     asian_option A(0.05, 1.0, 50.0, 0.1, 16, 45);
-    int N=1000000;
+    asian_option_qmc B(0.05, 1.0, 50.0, 0.1, 16, 45);
+    int M= 1000000;
+    int N=10000;
+    int I=100;
     
-    std::vector<double> meanvar = monte_carlo(N, A);
+    std::vector<double> meanvar = monte_carlo(M, A);
     std::cout<<"espérance "<<meanvar[0] <<" IC "<<meanvar[2]<<std::endl;
+    std::vector<double> temp;
+    double m = 0;
+    double s = 0;
+    for(int i=0;i<I;i++){
+        temp = monte_carlo(N,B);
+        m+=temp[0];
+        s+=temp[0]*temp[0];
+        }
+    m = m/I;
+    s = s/I - m*m;
+    std::cout<<"espérance "<<m <<" IC "<<sqrt(s)*1.96/10<<std::endl;
 
     
     return 0;
-- 
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