/*     A procedure that generates evaluates a value function using Monte Carlo
       and writes the values in a .csv file for plotting in Excel.
       Written by Jonathan Goodman for assignment 8 in the class 
	   http://www.math.nyu.edu/faculty/goodman/teaching/DerivSec09/index.html
	   
	   It uses the native C random number generator rand(), which may not be that good.
	   Feel free to replace this with a better one, but remember to set the seed.                */

#include <iostream>
#include <fstream>

using namespace std;

int path( double X[], int n, double tStart,  double T, double xStart);

#define NT 50      // The number of time steps in a path
#define NP 100000      // The number of paths per Monte Carlo 
#define NV 20        // The number of values of f computed
#define XMIN 80      // The smallest x value for which to calculate f
#define XSTEP 10     // The distance between x values at which f is evaluated

int main() {

   ofstream CSVfile;           // Write the output in csv format for Excel to read.
   CSVfile.open( "f.csv");   
   
   double X[NT+1];    // The sample path
   double f;          // The expected payout
   double xStart;     // The starting point for paths.
   
   xStart = XMIN;
   for (int val = 0; val < NV; val++) {   // The loop over x values where f is evaluated
      f = 0;
      for (int p = 0; p < NP; p++) {      // The loop over sample paths.
         path( X, NT, 0, 1, xStart);
         f += X[NT];
	   }
      f = f / NP;
	  CSVfile << xStart << " ,  " << f  << endl;  // Write the xtarting point and value of f into the .csv file
	  xStart += XSTEP;                            // Get ready for the next f evaluation
	}
      
   
   CSVfile.close();
   return 0;
   
}