C++ Program to Implement Binomial Tree

This C++ Program demonstrates the implementation of Binomial Tree.

Here is source code of the C++ Program to demonstrate Binomial Tree. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
/*
```

 * C++ Program to Implement Binomial Tree

```
 */
```
```
#include <iostream>
```
```
#include <cstdio>
```
```
#include <cmath>
```
```
using namespace std;
```
```
/*
```
```
 * Node Declaration
```
```
 */
```
```
struct Node
```
```
{
```
```
    double price, time, optionvalue;
```
```
};
```
```
/*
```
```
 * Class Declaration
```
```
 */
```
```
class BinomialTree
```
```
{
```
```
    private:
```
```
        Node **tree;
```
```
        int n;
```

        double S, volatility, upfactor, tfin, tstep;

        double getValue(int level, int node, double K, double R);

        void initNode (int level, int node);

```
    public:
```

        BinomialTree(double S, double volatility, int n, double tstep);

        double getValue(double K, double R);

```
        void print();
```
```
};
```
```
/*
```
```
 * Constructor
```
```
 */
```

BinomialTree::BinomialTree(double price , double vol, int _n, double _tstep)

```
{
```
```
    n = _n;
```
```
    S = price;
```
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    volatility = vol;
```
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    tstep = _tstep;
```
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    tfin = n * tstep;
```

    upfactor = exp (volatility * sqrt (tstep));

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    tree = new Node * [n];
```
```
    for (int i = 0; i < n; i++)
```
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        tree[i] = new Node [i+1] ;
```
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    tree[0][0].price = S;
```
```
    tree[0][0].time = 0.0;
```
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    double currtime = 0.0;
```
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    for (int i = 1; i < n; i++)
```
```
    {
```
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        Node * currnode = tree[i];
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        currtime += tstep;
```

        for (int j = 0; j <= i; j++, currnode++)

```
        {
```
```
            if (!j)
```
```
            {
```

                currnode->price = tree[i-1][j].price / upfactor ;

                currnode->time = currtime;

```
            }
```
```
            else
```
```
            {
```

                currnode->price = tree[i-1][j-1].price * upfactor ;

                currnode->time = currtime;

```
            }
```
```
        }
```
```
    }
```
```
}
```
```
/*
```
```
 * Get Value Function
```
```
 */
```

double BinomialTree::getValue(int l, int node, double K, double df)

```
{
```
```
    if (l == (n-1))
```
```
    {
```
```
        if (K < tree[l][node].price)
```

            return tree[l][node].optionvalue = tree[l][node].price - K;

```
        else
```

            return tree[l][node].optionvalue = 0.0;

```
    }
```
```
   else
```
```
   {
```

      double g1 = getValue(l + 1, node + 1, K, df);

      double g2 = getValue(l + 1, node, K, df);

      return tree[l][node].optionvalue = 0.5 * df * (g1 + g2);

```
   }
```
```
}
```
```
 
```
```
/*
```
```
 * Get Value Function
```
```
 */
```

double BinomialTree::getValue(double K, double R)

```
{
```

    double discountfactor = exp (-R * tstep);

    return getValue(0, 0, K, discountfactor);

```
}
```
```
/*
```
```
 * Display optimal values
```
```
 */
```
```
void BinomialTree::print()
```
```
{
```
```
    for (int i = 0; i < n; i++)
```
```
    {
```
```
        for( int j = 0; j <= i; j++ )
```
```
        {
```

            cout<< "[" << tree[i][j].price << "," << tree[i][j].time << ",";

            cout<< tree[i][j].optionvalue << "]\t";

```
        }
```
```
        cout <<endl;
```
```
   }
```
```
}
```
```
/*
```
```
 * Main Contains Menu
```
```
 */
```
```
int main()
```
```
{
```
```
    double S, V, K, T, R, N;
```
```
    cout<<"Enter Security Price: ";
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```
    cin>>S;
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```
    cout<<"Enter Volatility: ";
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```
    cin>>V;
```
```
    cout<<"Enter Call Strike Price: ";
```
```
    cin>>K;
```
```
    cout<<"Enter Time To Expiry: ";
```
```
    cin>>T;
```
```
    cout<<"Enter Risk Free Rate: ";
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```
    cin>>R;
```
```
    cout<<"Enter levels: ";
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    cin>>N;
```
```
    BinomialTree bt(S, V, N, T / N);
```
```
    double value = bt.getValue(K, R);
```
```
    bt.print();
```

    cout<< "OPTION VALUE = " << value <<endl;

```
    return 0;
```
```
}
```

$ g++ binomailtree.cpp
$ a.out
 
Enter Security Price: 10
Enter Volatility: 0.5
Enter Call Strike Price: 100
Enter Time To Expiry: 5
Enter Risk Free Rate: 0.6
Enter levels: 3
[10,0,0]
[5.24402,1.66667,0]     [19.0693,1.66667,0]
[2.74997,3.33333,0]     [10,3.33333,0]  [36.364,3.33333,0]
OPTION VALUE = 0
 
------------------
(program exited with code: 0)
Press return to continue

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