歐洲期權，三叉樹，C++

Question

我試圖爲股票價格的三叉樹模型使用三叉樹模型對股票價格進行定價，並在C++中設置期權。我設法擺脫了錯誤，但在運行命令後，它返回了選項價格的nan。代碼如下：對於選項

#include <iostream> 
#include <cmath> 
using namespace std; 

// contructor to initialise the data member by list 
TriModel(double S0_, double q_, double sigma_, double R_):S0(S0_),q(q_),sigma(sigma_),R(R_) 
{ 
} 

/* member function to work out time interval dt 
T maturity of the option, N number of time steps*/ 
void TriModel::Setdt(double T, int N) 
{ 
    T=1; 
    dt=T/N; 
} 

// risk-neutral probability of going up 
double TriModel::RiskNeutProb_up() 
{ 
    double v=R-q-0.5*sigma*sigma; 
    double dx=sigma*sqrt(3*dt); 
    return 0.5*((sigma*sigma*dt+v*v*dt*dt)/(dx*dx)+v*dt/dx); 
} 

// calculate the risk neutual probability of going down 
double TriModel::RiskNeutProb_down() 
{ 
    double v=R-q-0.5*sigma*sigma; 
    double dx=sigma*sqrt(3*dt); 
    return 0.5*((sigma*sigma*dt+v*v*dt*dt)/(dx*dx)-v*dt/dx); 
} 

// calculate the stock price at time step n and node i 
double TriModel::S(int N, int i) 
{ 
    double dx=sigma*sqrt(3*dt); 
    return S0*exp(i*dx); 
} 

// return the risk free interest rate R 
double TriModel::GetR() 
{ 
    return R; 
} 

// return time interval dt 
double TriModel::Getdt() 
{ 
    return dt; 
} 

頭文件：對於選項

#ifndef Proj1_Options06_h 
#define Proj1_Options06_h 
#include "TriModel01.h" 

class EurOption 
{ 
    private: 
     int N; //steps to expiry 
    public: 
     void SetN(int N_){N=N_;} 
     int getN(){return 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 by a Trinomial Tree model 
     // please implement this function in the accompany Options06.cpp file 
     double PriceByCRR(TriModel Model); 
}; 

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

#endif 

的源代碼：對於三叉樹

源代碼

#include "TriModel01.h" 
#include "Proj1_Options06.h" 
#include <iostream> 
#include <cmath> 
using namespace std; 

double EurOption::PriceByCRR(TriModel Model) 
{ 
    double pu=Model.RiskNeutProb_up(); 
    double pd=Model.RiskNeutProb_down(); 
    double pm=1-pu-pd; 
    double Price[N+1]; 
    for (int i=N; i>=-N;i--) 
    { 
     Price[i]=Payoff(Model.S(N,i)); 
    } 
    for (int n=N-1; n>=0;n--) 
    { 
     for (int i=n; i>=-n; i--) 
     { 
      Price[i]=(pu*Price[i+1]+pm*Price[i]+pd*Price[i-1])*exp(-Model.GetR()*Model.Getdt()); 
     } 
    } 
    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; 
} 

主要功能：

#include "TriModel01.h" 
#include "Proj1_Options06.h" 
#include <iostream> 
#include <cmath> 
using namespace std; 

int main() 
{ 
    double R=0.05; 
    double q=0.03; 
    double sigma=0.2; 
    double S0; 
    cout << "Enter S0: "; cin >> S0; 
    cout << endl; 

    TriModel Model(S0,q,sigma,R); 

    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;*/ 

    return 0; 
} 

任何幫助，將不勝感激！ 謝謝！

Answer 1

在PriceByCRR中，你有幾個錯誤，你正在給一個負數索引寫入到Price數組中，你會導致內存損壞。

for (int i=-N; i<=N;i++) 
{ 
    Price[i]=Payoff(Model.S(N,i)); 
} 

而且在接下來的循環中，您有另一個錯誤，在這裏你將n設爲N-1，然後在for循環迭代步驟中加入1到它。

for (int n=N-1; n>=0;n++) 

這些只是我看到的第一個兩個錯誤......還有兩個，我發現只是看了一眼，但我會離開，你要弄清楚。