// fut.cc
//
// Binomial futures option pricing model: implementation
//
#include <math.h>
#include "fut.h"
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
fut::fut(double ttm,int npers,double r,double sigma) {
  nper = npers;
  tinc = ttm/(double) nper;
  r1per = exp(r * tinc);
  disc = 1.0/r1per;
  disctm = exp(-r * ttm);
  up = 1.0 + sigma * sqrt(tinc);
  down = 1.0 - sigma * sqrt(tinc);
  prcup = 0.5*disc;
  prcdn = 0.5*disc;}

valhedge fut::eurcall(double f0,double X) {
  int i,j;
  double futprice;
  valhedge x1;
// initialize terminal payoffs
// i is the number of up moves over the whole life
  for(i=0;i<=nper;i++) {
    futprice = f0 * pow(up,(double) i) * pow(down,(double) (nper-i));
    val[i] = MAX(futprice - X,0);}
// compute prices back through the tree
// j+1 is the number of periods from the end
// i is the number of up moves from the start
  for(j=0;j<nper-1;j++) {
    for(i=0;i<nper-j;i++) {
      val[i] = prcdn * val[i] + prcup * val[i+1];}}
  x1.value = prcdn * val[0] + prcup * val[1];
  x1.delta = (val[1]-val[0]) / (f0*(up-down));
  return(x1);}