Thumthiti P.

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Bull Spread and Bear Spread Option Pricer. (C++)

Thumthiti Pinto
3–5 minutes
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The implementation, in c++, of bull spread and bear spread option pricer can be as followed:

Files
2 Header file
3 cpp file

Header file 1: BinModel02.h

#pragma once

class BinModel
{
private:
	double S0;
	double U;
	double D;
	double R;
public:
	//computing tisk neurtal prob
	double RiskNeutProb();
	//computing the stock price at node n,i 
	double S(int n, int i);
	//inputing, displaying and checking model data
	int GetInputData();
	double GetR();

};

Header file 2: Options06.h

#pragma once
#include "BinModel02.h"
class EurOption {
private:
	int N; //steps to expiry
public:
	void SetN(int N_) { N = N_; }
	//Payoff defined to return 0.0
	//for pedagogical purposes.
	//To use a pure virtual function replace by
	//virtual double Payoff(double z)=0;
	virtual double Payoff(double z) { return 0.0; }
	//pricing European option
	double PriceByCRR(BinModel Model);
};


class Call : public EurOption {
private:
	double K; //strike price
public:
	void SetK(double K_) { K = K_; }
	int GetInputData();
	double Payoff(double z);
};
class Put : public EurOption {
private:
	double K; //strike price
public:
	void SetK(double K_) { K = K_; }
	int GetInputData();
	double Payoff(double z);
};


class BullSpread : public EurOption {
	private:
		double K1;
		double K2;
	public:
		void SetK1(double K1_) { K1 = K1_; }
		void SetK2(double K2_) { K2 = K2_; }
		int GetInputData();
		double Payoff(double z);
};


class BearSpread : public EurOption {
	private:
		double K1;
		double K2;
	public:
		void SetK1(double K1_) { K1 = K1_; }
		void SetK2(double K2_) { K2 = K2_; }
		int GetInputData();
		double Payoff(double z);
	};

Cpp file 1: BinModel02.cpp

#include "BinModel02.h"
#include <iostream>
#include <cmath>
using namespace std;


int BinModel::GetInputData()
{
	//entering data
	cout << "Enter S0: "; cin >> S0;
	cout << "Enter U:  "; cin >> U;
	cout << "Enter D:  "; cin >> D;
	cout << "Enter R:  "; cin >> R;
	cout << endl;
	//making sure that 0 < s0 , -1 < D <U , -1 <R
	if (S0 <= 0 || -1 >= D || -1 >= U || D >= U || -1 >= R)
	{
		cout << "illegal data ranges" << endl;
		cout << "Terminating program" << endl;
		return 1;
	}
	//check for arbitrage
	if (R >= U || R <= D)
	{
		cout << "Arbitrage exists" << endl;
		cout << "Terminating program" << endl;
		return 1;

	}
	cout << "Input data checked" << endl;
	cout << "There is no arbitrage" << endl;

	return 0;
}





double BinModel::RiskNeutProb()
{
	return (R - D) / (U - D);
}
double BinModel::S(int n, int i)
{
	return S0 * pow(1 + U, i) * pow(1 + D, n - i);

}





double BinModel::GetR()
{
	return R;
}

Cpp file 2: Options06.cpp

#include "Options06.h"
#include "BinModel02.h"
#include <iostream>
#include <cmath>
using namespace std;

double EurOption::PriceByCRR(BinModel Model)
{
	double q = Model.RiskNeutProb();
	double Price[100];
	for (int i = 0; i <= N; i++) { Price[i] = Payoff(Model.S(N, i)); }
	for (int n = N - 1; n >= 0; n--)
	{
		for (int i = 0; i <= n; i++)
		{
			Price[i] = (q * Price[i + 1] + (1 - q) * Price[i]) / (1 + Model.GetR());
		}
	}
	return Price[0];
}


int Call::GetInputData()
{
	cout << "Enter Call option data:" << endl;
	int N;
	cout << "Enter steps to expiry N:"; cin >> N;
	SetN(N);
	cout << "Enter strike price K: "; cin >> K;
	cout << endl;
	return 0;
}


double Call::Payoff(double z)
{
	if (z > K) return z - K;
	return 0.0;
}




int Put::GetInputData()
{
	cout << "Enter Call option data:" << endl;
	int N;
	cout << "Enter steps to expiry N:"; cin >> N;
	SetN(N);
	cout << "Enter strike price K: "; cin >> K;
	cout << endl;
	return 0;
}


double Put::Payoff(double z)
{
	if (z < K) return K - z;
	return 0.0;
}




int BullSpread::GetInputData()
{
	cout << "Enter Call option data:" << endl;
	int N;
	cout << "Enter steps to expiry N:"; cin >> N;
	SetN(N);
	cout << "Enter strike price K1: "; cin >> K1;
	cout << endl;
	cout << "Enter strike price K2: "; cin >> K2;
	cout << endl;
	return 0;
}


double BullSpread::Payoff(double z) {
	if (K2 <= z) {
		return K2 - K1;
	}
	else if (K1 < z) {
		return z - K1;
	}
	return 0.0;
}






int BearSpread::GetInputData()
{
	cout << "Enter Call option data:" << endl;
	int N;
	cout << "Enter steps to expiry N:"; cin >> N;
	SetN(N);
	cout << "Enter strike price K1: "; cin >> K1;
	cout << endl;
	cout << "Enter strike price K2: "; cin >> K2;
	cout << endl;
	return 0;
}


double BearSpread::Payoff(double z) {
	if (K2 <= z) {
		return 0.0;
	}
	else if (K1 < z) {
		return K2 - z;
	}
	return K2 - K1;
}

/////////////////////////////////////////////////////
/////////////////////////////////////////////////////

cpp file 3 : Main.cpp

#include "BinModel02.h"
#include "Options06.h"
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
	BinModel Model;
	if (Model.GetInputData() == 1) return 1;
	Call Option1;
	Option1.GetInputData();
	cout << "European call option price = " << Option1.PriceByCRR(Model) << endl << endl;
	Put Option2;
	Option2.GetInputData();
	cout << "European put option price = " << Option2.PriceByCRR(Model) << endl << endl;

	BullSpread Bull;
	Bull.GetInputData();
	cout << "European BullSpread Price = " << Bull.PriceByCRR(Model) << endl << endl;
	BearSpread Bear;
	Bear.GetInputData();
	cout << "European BearSpread Price = " << Bear.PriceByCRR(Model) << endl << endl;
	return 0;


}



/*

Enter S0 : 106
Enter U : 0.15125
Enter D : -0.13138
Enter R : 0.00545

Input data checked
There is no arbitrage
Enter Call option data :
Enter steps to expiry N : 8
Enter strike price K : 100

European call option price = 21.6811

Enter Call option data :
Enter steps to expiry N : 8
Enter strike price K : 100

European put option price = 11.4261

Enter Call option data :
Enter steps to expiry N : 8
Enter strike price K1 : 100

Enter strike price K2 : 110

European BullSpread Price = 4.71584

Enter Call option data :
Enter steps to expiry N : 8
Enter strike price K1 : 100

Enter strike price K2 : 110

European BearSpread Price = 4.85866

*/

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