// my_function.h #include <iostream> #include <vector> const double pi = 3.1415926; const double sqrt_2_pi = sqrt(2 * pi); const double a0 = 2.50662823884; const double a1 = -18.61500062529; const double a2 = 41.39119773534; const double a3 = -25.44106049637; const double b1 = -8.47351093090; const double b2 = 23.08336743743; const double b3 = -21.06224101826; const double b4 = 3.13082909833; const double c0 = 0.3374754822726147; const double c1 = 0.9761690190917186; const double c2 = 0.1607979714918209; const double c3 = 0.0276438810333863; const double c4 = 0.0038405729373609; const double c5 = 0.0003951896511919; const double c6 = 0.0000321767881768; const double c7 = 0.0000002888167364; const double c8 = 0.0000003960315187; int recursiveAdd(int n); void recursivePrint(int a, int b); int fibonacciCal(int n); double normcdf(double x); double my_normcdf(double x); double hornerFunction(double x, double a0, double a1); double hornerFunction(double x, double a0, double a1, double a2); double hornerFunction(double x, double a0, double a1, double a2, double a3); double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4); double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4, double a5); double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4, double a5, double a6); double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4, double a5, double a6, double a7); double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4, double a5, double a6, double a7, double a8); double my_hornerFunction(const double& x, std::vector<double>& a); double norminv(double x); double my_norminv(double x); double my_blackScholesCallPrice(double strike, double timeToMaturity, double spot, double volatility, double riskFreeRate); double blackScholesCallPrice(double strike, double timeToMaturity, double spot, double volatility, double riskFreeRate);
my_function.cpp
#include "my_function.h"
#include <cmath>
int recursiveAdd(int n) {
/*Write a recursive function to compute the sum of the numbers between 1 and n*/
if (n == 1) {
return 1;
}
else {
return n + recursiveAdd(n - 1);
}
}
void recursivePrint(int a, int b) {
if (a == b) {
std::cout << a << std::endl;
}
else if (a < b){
std::cout << a << " ";
recursivePrint(++a, b);
}
else {
std::cout << " the input maybe wrong";
}
}
int fibonacciCal(int n) {
if (n == 0) {
return 1;
}
else if (n == 1) {
return 1;
}
else if (n < 0) {
std::cout << "warnings,input n is wrong, please input n>=0";
return NULL;
}
else {
return fibonacciCal(n - 1) + fibonacciCal(n - 2);
}
}
double normcdf(double x) {
return 0.5 * erfc(-x * sqrt(0.5));
}
double my_normcdf(double x) {
/* 计算标准正太分布的累计概率分布
*/
if (x >= 0) {
x = abs(x);
double pi = 3.1415926;
double k = 1 / (1 + 0.2316419 * x);
double v5 = k * (0.319381530 + k * (-0.356563782 + k * (1.781477937 + k * (-1.821255978 + 1.330274429 * k))));
double temp = 1.0 / sqrt_2_pi * exp(-0.5 * x * x) * v5;
return 1 - temp;
}
else {
x = abs(x);
double pi = 3.1415926;
double k = 1 / (1 + 0.2316419 * x);
double v5 = k * (0.319381530 + k * (-0.356563782 + k * (1.781477937 + k * (-1.821255978 + 1.330274429 * k))));
double temp = 1.0 / sqrt_2_pi * exp(-0.5 * x * x) * v5;
return temp;
}
}
double my_hornerFunction(const double & x, std::vector<double> &a) {
/*std::cout << "a value is " << std::endl;
for (int size_t = 0; size_t < a.size(); size_t++) {
std::cout << " " << a[size_t];
}*/
std::vector<double> a_copy(a);
/*std::cout << "a_copy value is " << std::endl;
for (int size_t = 0; size_t < a_copy.size(); size_t++) {
std::cout << " " << a_copy[size_t];
}*/
//std::cout << std::endl;
if (a_copy.size() == 2) {
return a_copy[0] + x * a_copy[1];
}
else if (a_copy.size() <= 1) {
std::cout << "warnings,input vector or array is wrong" << std::endl;
return NULL;
}
else {
double a_value = a_copy[0];
a_copy.erase(a_copy.begin(), a_copy.begin() + 1);
return a_value + x * my_hornerFunction(x, a_copy);
}
}
double hornerFunction(double x, double a0, double a1) {
//std::cout << "01 normal value is " << a0 + x * a1 << std::endl;
return a0 + x * a1;
}
double hornerFunction(double x, double a0, double a1, double a2) {
//std::cout << "02 a0 = " << a0 << " x = " << x << " result = " << result << std::endl;
return a0 + x * hornerFunction(x, a1, a2);
}
double hornerFunction(double x, double a0, double a1, double a2, double a3) {
return a0 + x * hornerFunction(x, a1, a2, a3);
}
double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4) {
return a0 + x * hornerFunction(x, a1, a2, a3, a4);
}
double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4,
double a5) {
return a0 + x * hornerFunction(x, a1, a2, a3, a4, a5);
}
double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4,
double a5, double a6) {
return a0 + x * hornerFunction(x, a1, a2, a3, a4, a5, a6);
}
double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4,
double a5, double a6, double a7) {
return a0 + x * hornerFunction(x, a1, a2, a3, a4, a5, a6, a7);
}
double hornerFunction(double x, double a0, double a1, double a2, double a3, double a4,
double a5, double a6, double a7, double a8) {
return a0 + x * hornerFunction(x, a1, a2, a3, a4, a5, a6, a7, a8);
}
double norminv(double x) {
// We use Moro's algorithm
double y = x - 0.5;
if (y<0.42 && y>-0.42) {
double r = y * y;
return y * hornerFunction(r, a0, a1, a2, a3) / hornerFunction(r, 1.0, b1, b2, b3, b4);
}
else {
double r;
if (y < 0.0) {
r = x;
}
else {
r = 1.0 - x;
}
double s = log(-log(r));
double t = hornerFunction(s, c0, c1, c2, c3, c4, c5, c6, c7, c8);
if (x > 0.5) {
return t;
}
else {
return -t;
}
}
}
double my_norminv(double x) {
// We use Moro's algorithm
double y = x - 0.5;
if (y<0.42 && y>-0.42) {
double r = y * y;
std::vector<double> a = { a0, a1, a2, a3 };
std::vector<double> b = { 1.0, b1, b2, b3, b4 };
return y * my_hornerFunction(r, a) / my_hornerFunction(r, b);
}
else {
double r;
if (y < 0.0) {
r = x;
}
else {
r = 1.0 - x;
}
double s = log(-log(r));
std::vector<double> c = { c0, c1, c2, c3, c4, c5, c6, c7, c8 };
double t = my_hornerFunction(s, c);
if (x > 0.5) {
return t;
}
else {
return -t;
}
}
}
double my_blackScholesCallPrice(double strike, double timeToMaturity,
double spot, double volatility, double riskFreeRate) {
double numetator = log(spot / strike) + (riskFreeRate + volatility * volatility / 2) * timeToMaturity;
double e_t = volatility * sqrt(timeToMaturity);
double d1 = numetator / e_t;
double d2 = d1 - e_t;
double nd1 = my_normcdf(d1);
//std::cout << "d1 = " << d1 << " my_normcdf(d1) = " << my_normcdf(d1) << std::endl;
double nd2 = my_normcdf(d2);
double c0 = spot * nd1 - strike * nd2 * exp(-riskFreeRate * timeToMaturity);
return c0;
}
double blackScholesCallPrice(double strike, double timeToMaturity,
double spot, double volatility, double riskFreeRate) {
double numerator = log(spot / strike)
+ (riskFreeRate + volatility * volatility * 0.5) * timeToMaturity;
double denominator = volatility * sqrt(timeToMaturity);
double d1 = numerator / denominator;
double d2 = d1 - denominator;
//std::cout << "d1 = " << d1 << " normcdf(d1) = " << normcdf(d1) << std::endl;
double t1 = normcdf(d1) * spot;
double t2 = normcdf(d2) * strike * exp(-riskFreeRate * timeToMaturity);
return t1 - t2;
}
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