Black Scholes Pricing Model European Option on Dividend paying Stock

Transcription

1 Black Scholes Pricing Model European Option on Dividend paying Stock This is a C++ implementation of the famous Black Scholes options pricing model for a European option on a dividend paying stock. The model calculates the price, as well as the hedging parameters ( the Greeks ). The price for a call option is calculated as, For a put option, where, S is the price of the underlying stock, K is the strike price, q is the dividend yield, T is the time until maturity (in years), σ is the volatility of the underlying stock, r is the risk-free interest rate, and N(z) represents the cumulative standard normal probability distribution function and is given by, and N (z) is given by, The hedge parameters, also known as the Greeks, are given by Delta Theta Call Put Gamma Vega Rho

2 The interface file for the class EuropeanOption //EuropeanOption.h #ifndef EuropeanOption_h #define EuropeanOption_h #include<string> using namespace std; class EuropeanOption public: EuropeanOption(); EuropeanOption(const double& _S0, const double& _K, const double& _r, const double& _q, const int& _T, const double& vol, const string& type); EuropeanOption(const EuropeanOption& euroopt2); virtual ~EuropeanOption(); EuropeanOption& operator = (const EuropeanOption& euroopt2); //cumulative normal distribution functions double N(double z) const; double Nprime(double z) const; //helper functions double callprice() const; double putprice() const; //helper functions for sensitivities double calldelta() const; double putdelta() const; double calltheta() const; double puttheta() const; double Gamma() const; double Vega() const; double callrho() const; double putrho() const; //functions that contain price, sensitivities double NPV() const; double delta() const; double theta() const; double gamma() const; double vega() const; double rho() const;

3 ; private: double S0; double K; double r; double q; int T; double sigma; string opttype; //underlying stock price //strike price //risk-neutral interest rate; //dividend yield //time to maturity (in years) //volatility //option type (call, put) #endif The implementation of the class EuropeanOption. //EuropeanOption.cpp #ifndef EuropeanOption_cpp #define EuropeanOption_cpp #include<string> #include<math.h> #include "EuropeanOption.h" using namespace std; EuropeanOption::EuropeanOption() S0 = 50.0; K = 50.0; r = 0.04; q = 0.1; T = 2; sigma = 0.35; opttype = "call"; EuropeanOption::EuropeanOption(const double& _S0, const double& _K, const double& _r, const double& _q, const int& _T, const double& vol, const string& type) : S0(_S0), K(_K), r(_r), q(_q), T(_T), sigma(vol), opttype(type) EuropeanOption::EuropeanOption(const EuropeanOption& eopt2) S0 = eopt2.s0; K = eopt2.k;

4 r = eopt2.r; q = eopt2.q; T = eopt2.t; sigma = eopt2.sigma; opttype = eopt2.opttype; EuropeanOption::~EuropeanOption() EuropeanOption& EuropeanOption::operator = (const EuropeanOption& euroopt2) if (this == &euroopt2) return *this; S0 = euroopt2.s0; K = euroopt2.k; r = euroopt2.r; q = euroopt2.q; T = euroopt2.t; sigma = euroopt2.sigma; opttype = euroopt2.opttype; return *this; double EuropeanOption::N(double z) const if (z > 6.0) return 1.0; if (z < -6.0) return 0.0; double b1 = ; double b2 = ; double b3 = ; double b4 = ; double b5 = ; double p = ; double c = ; double a = fabs(z); double t = 1.0/(1.0+a*p); double b = c*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 = n; return n;

5 double EuropeanOption::Nprime(double z) const return (1.0/sqrt(2* ))*exp((pow(-z,2))/2); double EuropeanOption::callPrice() const return S0*exp(-q*T)*N(d1)-K*exp(-r*T)*N(d2); double EuropeanOption::putPrice() const return K*exp(-r*T)*N(-d2)-S0*exp(-q*T)*N(-d1); double EuropeanOption::callDelta() const return exp(-q*t)*n(d1); double EuropeanOption::putDelta() const return exp(-q*t)*(n(d1)-1); double EuropeanOption::callTheta() const return (-(S0*Nprime(d1)*sigma*exp(-q*T))/(2*sqrt(T)))+ (q*s0*n(d1)*exp(-q*t))-(r*k*exp(-r*t)*n(d2)); double EuropeanOption::putTheta() const

6 return (-(S0*Nprime(d1)*sigma*exp(-q*T))/(2*sqrt(T)))- (q*s0*n(-d1)*exp(-q*t))+(r*k*exp(-r*t)*n(-d2)); double EuropeanOption::Gamma() const return (Nprime(d1)*exp(-q*T))/(S0*sigma*sqrt(T)); double EuropeanOption::Vega() const return S0*sqrt(T)*Nprime(d1)*exp(-q*T); double EuropeanOption::callRho() const return K*T*exp(-r*T)*N(d2); double EuropeanOption::putRho() const return -K*T*exp(-r*T)*N(-d2); double EuropeanOption::NPV() const return callprice(); return putprice(); double EuropeanOption::delta() const return calldelta();

7 return putdelta(); double EuropeanOption::theta() const return calltheta(); return puttheta(); double EuropeanOption::gamma() const return Gamma(); double EuropeanOption::vega() const return Vega(); double EuropeanOption::rho() const return callrho(); return putrho(); #endif