binomial_tree.hpp

/*
 * Copyright (c) 2019 alpha group, CS department, University of Torino.
 * 
 * This file is part of pico 
 * (see https://github.com/alpha-unito/pico).
 * 
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program. If not, see <http://www.gnu.org/licenses/>.
 */

#ifndef EXAMPLES_STOCK_MARKET_BINOMIAL_TREE_HPP_
#define EXAMPLES_STOCK_MARKET_BINOMIAL_TREE_HPP_

#include <algorithm>
#include <cmath>
#include <fstream>
#include <iostream>
#include <vector>

#include "defs.h"

/* Template code for the binomial tree
 * Instructions to build the code are here
 * http://www.maths.manchester.ac.uk/~pjohnson/Tutorials/node1.html
 */

// return the value of the binomial tree
double binomialTree(double S0,  // price
                    double X,   // strike price
                    double T,  // time to maturity or option expiration in years
                    double r,  // risk-free interest rate
                    double sigma,  // volatility
                    int n)         // tree paramaters (steps in tree)
{
  // declare and initialise local variables (u,d,q)
  double dt, u, d, q;
  dt = T / n;
  u = exp(sigma * sqrt(dt));
  d = exp(-sigma * sqrt(dt));
  q = (exp(r * dt) - d) / (u - d);
  // create storage for the stock price tree and option price tree
  double stockTree[n + 1][n + 1];
  // setup and initialise the stock price tree
  for (int i = 0; i <= n; i++) {
    for (int j = 0; j <= i; j++) {
      stockTree[i][j] = S0 * pow(u, j) * pow(d, i - j);
    }
  }
  double valueTree[n + 1][n + 1];
  for (int j = 0; j <= n; j++) {
    valueTree[n][j] = payoff(stockTree[n][j], X);
  }
  for (int i = n - 1; i >= 0; i--) {
    for (int j = 0; j <= i; j++) {
      valueTree[i][j] = exp(-r * dt) * (q * valueTree[i + 1][j + 1] +
                                        (1 - q) * valueTree[i + 1][j]);
    }
  }
  return valueTree[0][0];
}

StockPrice binomial_tree(const OptionData &opt, int steps) {
  return binomialTree(opt.s, opt.strike, opt.t, opt.r, opt.v, steps);
}

// int main()
//{
//  // declare and initialise Black Scholes parameters
//   // declare and initialise Black Scholes parameters
//  double S0=100.,X=100.,T=1.,r=0.06,sigma=0.2;
//  // declare and initialise tree paramaters (steps in tree)
//  int n=3;
//  cout << " V(S="<<S0<<",t=0) = " << binomialTree(S0,X,T,r,sigma,n) << endl;
///** OUTPUT
// V(S=100,t=0) = 11.552
// */
//}

#endif /* EXAMPLES_STOCK_MARKET_BINOMIAL_TREE_HPP_ */