求解无风险利率 C语言代码

求解无风险利率

#include <math.h>
#pragma mark - BSModel期权定价模型
// N 函数
double N(double a)
{
   return (1 + erf(a / sqrt(2)))/2;
}

// 看涨期权定价公式
double call_option_price(double L, double S,double T,double r, double v){
    double C, d1, d2;
    d1 = (log(S/L) + (r + 0.5 * v * v) * T)/(v * sqrt(T));
    d2 = d1 - v * sqrt(T);
    C = S * N(d1) - L * exp(-r * T) * N(d2);
    return C;
}
// 看跌期权定价公式
double put_option_price(double L, double S,double T,double r, double v){
    double P, d1, d2;
    d1 = (log(S/L) + (r + 0.5 * v * v) * T)/(v * sqrt(T));
    d2 = d1 - v * sqrt(T);
    P = L * exp(-r * T)* (N(-d2)) - S * (N(-d1));
    return P;
}
/**
 L:期权执行价
 S:标的价格
 T:有效期 ，剩余天数/365
 r:无风险利率
 C:期权价格
 t: 期权类型，0看涨期权，1看跌期权
 d: 精确度
 return: 隐含波动率
 */
double implied_volatility_bs(double L, double S,double T,double r, double OP, int t, double d){
    double h = 100;
    double l = 0;
    double p, op;
    int counter = 0;
    do {
        p = (h + l) / 2;
        op = t == 0 ? call_option_price(L, S, T, r, p/100) : put_option_price(L, S, T, r, p/100);
        op < OP ? (l = p) : (h = p);
        counter += 1;
        if (counter > 20) {
            break;
        }
    } while (fabs(op - OP) > d);
    return p;
}

设置参数

        double v = 0.0;
        double S = 51370;
        double L = 49000;
        double OP = 377;
        double d = 0.01;
        double T = 31.0;
        double iv = implied_volatility_bs(L, S, T/366.0, v, OP, 1, d);
        printf("%.2f\n", iv);

输出结果为：20.78。