bin_am_call.cc

来自「Financial Recipes」· CC 代码 · 共 34 行

#include <cmath>                 // standard mathematical library
#include <algorithm>             // defines the max() operator
#include <vector>                // STL vector templates
using namespace std;
    
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];
};