// cap.cc
//
// Fixed-income binomial option pricing engine
//
#include <math.h>
#include <iostream.h>
#include "cap.h"
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
#define MIN(a,b) (((a) < (b)) ? (a) : (b))

f_i_bin::f_i_bin(double ttm,int npers,double sigma,double rrbar,double k) {
  nper=npers;
  tinc = ttm/(double) nper;
  sig = sigma;
  up = sigma*sqrt(tinc);
  rbar = rrbar;
  kappa = k;
  prfact = kappa*sqrt(tinc)/(2.0*sig);}

double f_i_bin::bprice(double r0) {
  int i,j;
  double prup;
//initialize terminal payoffs
//i is the number of up moves
  for(i=0;i<=nper;i++) {
//  r[i] = r0 + up * (double)(2*i-nper);   not needed for this claim
    val[i] = 1.0;}
//compute prices back through the tree
//j is the number of periods from the end
//i is the number of up moves from the start
  for(j=1;j<=nper;j++) {for(i=0;i<=nper-j;i++) {
      r[i] = r0 + up * (double) (2*i-nper + j);
      prup = 0.5 + prfact*(rbar-r[i]);
      prup = MIN(1.0,MAX(0.0,prup));
      val[i] = (prup*val[i+1]+(1.0-prup)*val[i])*exp(-r[i]*tinc);}}
  return(val[0]);}

double f_i_bin::cap(double level,double r0) {
  int i,j;
  double prup;
//initialize terminal payoffs
//i is the number of up moves
  for(i=0;i<=nper;i++) {
//  r[i] = r0 + up * (double)(2*i-nper);   not needed for this claim
    val[i] = 0.0;}
//compute prices back through the tree
//j is the number of periods from the end
//i is the number of up moves from the start
  for(j=1;j<=nper;j++) {for(i=0;i<=nper-j;i++) {
      r[i] = r0 + up * (double) (2*i-nper + j);
      prup = 0.5 + prfact*(rbar-r[i]);
      prup = MIN(1.0,MAX(0.0,prup));
      val[i] = (prup*val[i+1]+(1.0-prup)*val[i])*exp(-r[i]*tinc)
        + MAX(0.0,(r[i]-level)*tinc);}}
  return(val[0]);}