// calculate the binomial option pricing formula for an American call
#include <cmath> // standard mathematical library
#include <algorithm> // defining the max() operator
#include <vector> // STL vector templates
double option_price_call_american_binomial( double S, // spot price
double X, // exercice price
double r, // interest rate
double sigma, // volatility
double t, // time to maturity
int steps) { // no steps in binomial tree
double R = exp(r*(t/steps)); // interest rate for each step
double Rinv = 1.0/R; // inverse of interest rate
double u = exp(sigma*sqrt(t/steps)); // up movement
double uu = u*u;
double d = 1.0/u;
double p_up = (R-d)/(u-d);
double p_down = 1.0-p_up;
vector<double> prices(steps+1); // price of underlying
vector<double> call_values(steps+1); // value of corresponding call
prices[0] = S*pow(d, steps); // fill in the endnodes.
for (int i=1; i<=steps; ++i) prices[i] = uu*prices[i-1];
for (int i=0; i<=steps; ++i) call_values[i] = max(0.0, (prices[i]-X));
// call payoffs at maturity
for (int step=steps-1; step>=0; --step)
{
for (int i=0; i<=step; ++i) {
call_values[i] = (p_up*call_values[i+1]+p_down*call_values[i])*Rinv;
prices[i] = d*prices[i+1];
call_values[i] = max(call_values[i],prices[i]-X); // check for exercise
};
};
return call_values[0];
};
