Code Structure
- Class: Option
- Fileds: s, k, r, sigma, t
- Method: d1(), d2()
- derived-class: CallOption
- Method: blackScholesPrice()
- derived-class: PutOption
- Method: blackScholesPrice()
C++
#include <iostream>
#include <cmath>
class Option {
protected:
// Fields
double s; //stock price
double k; //strike price
double r; //continuously compounded risk-free rate
double sigma; //volatility of the stock price per year
double t; //time to maturity in trading years
public:
// Constructor
Option(double s, double k, double r, double sigma, double t) : s(s), k(k), r(r), sigma(sigma), t(t) {}
// Method
// Getter & Setter
double gets() const {
return s;
}
void sets(double s) {
Option::s = s;
}
double getK() const {
return k;
}
void setK(double k) {
Option::k = k;
}
double getR() const {
return r;
}
void setR(double r) {
Option::r = r;
}
double getSigma() const {
return sigma;
}
void setSigma(double sigma) {
Option::sigma = sigma;
}
double getT() const {
return t;
}
void setT(double t) {
Option::t = t;
}
// Construct Black-Scholes Model
double time_sqrt() {
return std::sqrt(t);
}
double d1() {
double d1 = (log(s / k) + r * t) / (sigma * time_sqrt()) + 0.5 * sigma * time_sqrt();
return d1;
}
double d2() {
double d2 = d1() - sigma * time_sqrt();
return d2;
}
// Cumulative Distribution Function
double N(const double &z) {
if (z > 6.0) { return 1.0; }; // this guards against overflow
if (z < -6.0) { return 0.0; };
double b1 = 0.31938153;
double b2 = -0.356563782;
double b3 = 1.781477937;
double b4 = -1.821255978;
double b5 = 1.330274429;
double p = 0.2316419;
double c2 = 0.3989423;
double a = fabs(z);
double t = 1.0 / (1.0 + a * p);
double b = c2 * exp((-z) * (z / 2.0));
double n = ((((b5 * t + b4) * t + b3) * t + b2) * t + b1) * t;
n = 1.0 - b * n;
if (z < 0.0) n = 1.0 - n;
return n;
};
};
// Derived Class
class CallOption : public Option {
public:
CallOption(double s, double k, double r, double sigma, double t) : Option(s, k, r, sigma, t) {}
double blackScholesPrice() {
double bs = s * N(d1()) - k * exp(-r * t) * N(d2());
std::cout << "Black-Scholes Price of Call Option: " << bs << std::endl;
return bs;
}
};
class PutOption : public Option {
public:
PutOption(double s, double k, double r, double sigma, double t) : Option(s, k, r, sigma, t) {}
double blackScholesPrice() {
double bs = k * exp(-r * t) * N(-d2()) - s * N(-d1());
std::cout << "Black-Scholes Price of Put Option: " << bs << std::endl;
return bs;
}
};
int main() {
CallOption Option1(300, 300, 0.03, 0.15, 1);
Option1.blackScholesPrice();
PutOption Option2(300, 300, 0.03, 0.15, 1);
Option2.blackScholesPrice();
return 0;
}
Java
import java.lang.Math;
public class bsTest {
public static void main(String[] args) {
CallOption Option1 = new CallOption(300, 300, 0.03, 0.15, 1);
Option1.blackScholesPrice();
PutOption Option2 = new PutOption(300, 300, 0.03, 0.15, 1);
Option2.blackScholesPrice();
}
}
class Option {
// Fields
public double s; // stock price
public double k; // strike price
public double r; // continuously compounded risk-free rate
public double sigma; // volatility of the stock price per year
public double t; // time to maturity in trading years
// Constructor
public Option(double s, double k, double r, double sigma, double t) {
this.s = s;
this.k = k;
this.r = r;
this.sigma = sigma;
this.t = t;
}
// Method
public double getS() {
return s;
}
public void setS(double s) {
this.s = s;
}
public double getK() {
return k;
}
public void setK(double k) {
this.k = k;
}
public double getR() {
return r;
}
public void setR(double r) {
this.r = r;
}
public double getSigma() {
return sigma;
}
public void setSigma(double sigma) {
this.sigma = sigma;
}
public double getT() {
return t;
}
public void setT(double t) {
this.t = t;
}
// Construct Black-Scholes Model
double time_sqrt() {
return Math.sqrt(t);
}
double d1() {
double d1 = (Math.log(s / k) + r * t) / (sigma * time_sqrt()) + 0.5 * sigma * time_sqrt();
return d1;
}
double d2() {
double d2 = d1() - sigma * time_sqrt();
return d2;
}
// Cumulative Distribution Function
double N(double z) {
if (z > 6.0) {
return 1.0;
}
; // this guards against overflow
if (z < -6.0) {
return 0.0;
}
;
double b1 = 0.31938153;
double b2 = -0.356563782;
double b3 = 1.781477937;
double b4 = -1.821255978;
double b5 = 1.330274429;
double p = 0.2316419;
double c2 = 0.3989423;
double a = Math.abs(z);
double t = 1.0 / (1.0 + a * p);
double b = c2 * Math.exp((-z) * (z / 2.0));
double n = ((((b5 * t + b4) * t + b3) * t + b2) * t + b1) * t;
n = 1.0 - b * n;
if (z < 0.0)
n = 1.0 - n;
return n;
};
};
class CallOption extends Option {
public CallOption(double s, double k, double r, double sigma, double t) {
super(s, k, r, sigma, t);
}
double blackScholesPrice() {
double bs = s * N(d1()) - k * Math.exp(-r * t) * N(d2());
System.out.println("Black-Scholes Price of Call Option: " + bs);
return bs;
}
};
class PutOption extends Option {
public PutOption(double s, double k, double r, double sigma, double t) {
super(s, k, r, sigma, t);
}
double blackScholesPrice() {
double bs = k * Math.exp(-r * t) * N(-d2()) - s * N(-d1());
System.out.println("Black-Scholes Price of Put Option: " + bs);
return bs;
}
};
Python
import numpy as np
import scipy.stats as st
class Option:
def __init__(self, s, k, r, sigma, t):
self.s = s
self.k = k
self.r = r
self.sigma = sigma
self.t = t
def time_sqrt(self):
return np.sqrt(self.t)
def d1(self):
return (np.log(self.s / self.k) + self.r * self.t) / (
self.sigma * self.time_sqrt()) + 0.5 * self.sigma * self.time_sqrt()
def d2(self):
return self.d1() - self.sigma * self.time_sqrt()
def N(z):
return st.norm.cdf(z)
class CallOption(Option):
def __init__(self, s, k, r, sigma, t):
Option.__init__(self, s, k, r, sigma, t)
def blackScholesPrice(self):
bs = self.s * N(self.d1()) - self.k * np.exp(-self.r * self.t) * N(self.d2())
print("Black-Scholes Price of Call Option: ", bs)
return bs
class PutOption(Option):
def __init__(self, s, k, r, sigma, t):
Option.__init__(self, s, k, r, sigma, t)
def blackScholesPrice(self):
bs = self.k * np.exp(-self.r * self.t) * N(-self.d2()) - self.s * N(-self.d1())
print("Black-Scholes Price of Put Option: ", bs)
return bs
Option1 = CallOption(300, 300, 0.03, 0.15, 1)
Option2 = PutOption(300, 300, 0.03, 0.15, 1)
Option1.blackScholesPrice();
Option2.blackScholesPrice();
