// crr.cc
//
// Simple binomial option pricing model: implementation
// (following Cox, Ross, and Rubinstein)
//
#include <math.h>
#include <iostream.h>
#include "crr.h"
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
crr::crr(double ttm,int npers,double r,double sigma) {
  nper = npers;
  tinc = ttm/(double) nper;
  r1per = 1.0 + r * tinc;
  disc = 1.0/r1per;
  up = r1per + sigma * sqrt(tinc);
  down = r1per - sigma * sqrt(tinc);
  prup = disc * 0.5;
  prdn = disc * 0.5;}

double crr::eurcall(double S0,double X) {
  int i,j;
// initialize terminal payoffs
// i is the number of up moves over the whole life
  for(i=0;i<=nper;i++) {
    Sprice = S0*pow(up,(double) i)*pow(down,(double) (nper-i));
    val[i] = MAX(Sprice - 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;j++) {
    for(i=0;i<nper-j;i++) {
      val[i] = prdn * val[i] + prup * val[i+1];}}
  return(val[0]);}

double crr::binopt(double S0,double lower,double upper) {
  int i,j;
// initialize terminal payoffs
// i is the number of up moves over the whole life
  for(i=0;i<=nper;i++) {
    Sprice = S0*pow(up,(double) i)*pow(down,(double) (nper-i));
    val[i] = (((Sprice>=lower) && (Sprice<=upper)) ? 1.0 : 0.0);}
// 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;j++) {
    for(i=0;i<nper-j;i++) {
      val[i] = prdn * val[i] + prup * val[i+1];}}
  return(val[0]);}