C++ Binomial Option Pricer

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#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

float european_binomial(float s,float k, float r,float v,int t, int N, bool verbose = false){

    int steps = N*t;
    float tree[steps+1];
    float u,d;
    float dt = (float)t/(float)N;
    u=exp(v*sqrt(dt));
    d=1.0/u;



    float p = (exp(r*dt)-d)/(u-d);
    float q = 1.0-p;



    if(verbose){
    cout << "p: " << p << endl;
    cout << "q: " << q << endl << endl;
    }

    for(int n=0;n<steps+1;n++){
        tree[n]=fmax(s*pow(u,steps-n)*pow(d,n)-k,0.0);
        if (verbose) cout << tree[n] << '\n';
    }
    if (verbose) cout << endl;

    for(int i=steps;i>0;i--){
        for(int j=0;j<i;j++){
            tree[j]=p*tree[j]+q*tree[j+1];
        }
    }



return tree[0]*exp(-r*t);
}

int main()
{
    cout << "The European binomial option price is $";
    cout.setf(ios::fixed,ios::floatfield);
    cout.precision(2);
    cout << european_binomial(20.0,17.00,.02,.1,3,10000);
    return 0;
}

#include <iostream>
#include <cmath>
#include <iomanip>


using namespace std;

double american_binomial(double s,double k, double r,double v,int t, int N, bool verbose = false){

    int steps = N*t;
    //cout << steps << endl;
    double dt = (double)t/(double)N;
    //cout << "dt: " << dt << endl;
    double E[steps][steps+1];

    double u,d;
    u=exp(v*sqrt(dt));
    d=1.0/u;
    double disc=exp(r*dt);
    double p = (disc-d)/(u-d);
    double q = 1.0-p;



    if(verbose){
    cout << "p: " << p << endl;
    cout << "q: " << q << endl << endl;
    }

   double temp;
    for(int i=steps-1;i>=0;i--){
        for(int n=0; n<i+1;n++){
         temp=s*pow(u,i-2*n)-k;
            E[i][n]=(temp>0.0)?temp:0.0;
            //cout << E[i][n] << endl;
        }
        //cout << endl;
    }

    for(int i=steps-2;i>=0;i--){
        for(int n=0; n<i+1;n++){
            E[i][n]=fmax(E[i][n],(p*E[i+1][n]+q*E[i+1][n+1])*disc);
            //cout << "E[" << i << "][" << n << "] " << E[i][n] << endl;
        }
        //cout << endl;
    }
double answer=E[0][0];
delete[] E;
return answer;
}

int main()
{
    cout << "The American binomial option price is $";
    cout.setf(ios::fixed,ios::floatfield);
    cout.precision(2);
    cout << american_binomial(20.0,17.00,.02,.1,3,100);
    return 0;
}

#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

double european_binomial(double s,double k, double r,double v,int t, int N, bool verbose = false){

    int steps = N;
    double tree[steps+1];
    double u,d;
    double dt = (double)t/(double)N;
    u=exp(v*sqrt(dt));
    d=1.0/u;
    double disc=exp(-r*dt);

    double p = (exp(r*dt)-d)/(u-d);
    double q = 1.0-p;

    if(verbose){
    cout << "p: " << p << endl;
    cout << "q: " << q << endl;
    cout << "dt: " << dt << endl;
    cout << "disc: " << disc << endl;
    cout << "u: " << u << endl;
    cout << "d: " << d << endl << endl;

    cout << "Value at expiration:" << endl;
    }

    for(int i=0;i<=steps;i++){
        tree[i]=fmax(s*pow(u,steps-2*i)-k,0.0);
        if(verbose) cout << "[" << steps << "][" << i << "] " << tree[i] << endl;
    }
    if(verbose) cout << endl << "Value at time t and node n [t][n]:" << endl;

    for(int i=steps-1;i>=0;i--){
        for(int j=0;j<=i;j++){
                tree[j]=(p*tree[j]+q*tree[j+1])*disc;
            if(verbose) cout << "[" << i << "][" << j << "] " << tree[j] << endl;
        }
        if(verbose) cout << endl;
    }

return tree[0];
}

int main()
{
    cout << "The European binomial option price is $";
    cout.setf(ios::fixed,ios::floatfield);
    cout.precision(2);
    cout << european_binomial(20.0,17.00,.02,.1,1,4);
    return 0;
}

#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

double american_binomial(double s,double k, double r,double v,int t, int N, bool verbose = false){

    int steps = N;
    double tree[steps+1];
    double u,d;
    double dt = (double)t/(double)N;
    u=exp(v*sqrt(dt));
    d=1.0/u;
    double disc=exp(-r*dt);

    double p = (exp(r*dt)-d)/(u-d);
    double q = 1.0-p;

    if(verbose){
    cout << "p: " << p << endl;
    cout << "q: " << q << endl;
    cout << "dt: " << dt << endl;
    cout << "disc: " << disc << endl;
    cout << "u: " << u << endl;
    cout << "d: " << d << endl << endl;

    cout << "Value at expiration:" << endl;
    }

    for(int i=0;i<=steps;i++){
        tree[i]=fmax(s*pow(u,steps-2*i)-k,0.0);
        if(verbose) cout << "[" << steps << "][" << i << "] " << tree[i] << endl;
    }
    if(verbose) cout << endl << "Value at time t and node n [t][n]:" << endl;

    for(int i=steps;i>=0;i--){
        for(int j=0;j<=i;j++){
                tree[j]=fmax(s*pow(u,i-2*j)-k,(p*tree[j]+q*tree[j+1])*disc);
            if(verbose) cout << "[" << i << "][" << j << "] " << tree[j] << endl;
        }
        if(verbose) cout << endl;
    }

return tree[0];
}

int main()
{
    cout << "The American binomial option price is $";
    cout.setf(ios::fixed,ios::floatfield);
    cout.precision(2);
    cout << american_binomial(20.0,17.00,.02,.1,1,4,true);
    return 0;
}