bin_am_prop_div_call.cc

Financial Recipes

#include <cmath>
#include <algorithm>
#include <vector>
#include "fin_recipes.h"
#include <iostream>

double option_price_call_american_proportional_dividends_binomial(double S, 
								  double X,
								  double r,
								  double sigma, 
								  double time, 
								  int no_steps,
								  vector<double>& dividend_times,
								  vector<double>& dividend_yields) {
    int no_dividends=dividend_times.size();
    if (no_dividends == 0) {
	return option_price_call_american_binomial(S,X,r,sigma,time,no_steps); // price w/o dividends
    };
    double R = exp(r*(time/no_steps));
    double Rinv = 1.0/R;
    double u = exp(sigma*sqrt(time/no_steps));
    double uu= u*u;
    double d = 1.0/u;
    //    cout << "u " << u << " d " << d << endl;
    double pUp   = (R-d)/(u-d);
    double pDown = 1.0 - pUp;
    vector<int> dividend_steps(no_dividends); // when dividends are paid
    for (int i=0; i<no_dividends; ++i) {
	dividend_steps[i] = (int)(dividend_times[i]/time*no_steps);
    };
    vector<double> prices(no_steps+1);
    vector<double> call_prices(no_steps+1);
    prices[0] = S*pow(d, no_steps);
    for (int i=0; i<no_dividends; ++i) { prices[0]*=(1.0-dividend_yields[i]); };
    for (int i=1; i<=no_steps; ++i)  { prices[i] = uu*prices[i-1]; }; // terminal tree nodes
    for (int i=0; i<=no_steps; ++i) call_prices[i] = max(0.0, (prices[i]-X));
    for (int step=no_steps-1; step>=0; --step) {
	for (int i=0;i<no_dividends;++i) {   // check whether dividend paid
	    if (step==dividend_steps[i]) { 
		//		cout << step << endl;
		for (int j=0;j<=step;++j) {
		    prices[j]*=(1.0/(1.0-dividend_yields[i])); 
		};
	    };
	};
	//	for (int i=0; i<=step; ++i)   {
	//	    cout << prices[i] << " ";
	//	};
	//	cout << endl;
	for (int i=0; i<=step; ++i)   {
	    prices[i] = d*prices[i+1];
	    //	    cout << i << " " << prices[i];
	    call_prices[i] = (pDown*call_prices[i]+pUp*call_prices[i+1])*Rinv;
	    call_prices[i] = max(call_prices[i], prices[i]-X);         // check for exercise
	    //	    cout << " " << call_prices[i];
	    //	    cout << endl;
	};
    };
    return call_prices[0];
};