# 計算零波動率價差(Static Spread)
:::info
給定每一期的yield rate、期數、債息，跟yield spread差等訊息來計算static spread
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## 程式碼 (by C++)

### 輸入需要的資訊
yield rate、期數、債息，跟 yield spread

# include <iostream>
# include <string>
# include <cmath>

using namespace std;
// static spread

int main(){
    float coupon_rate, yield_spread, bond_value, bond_price;
    int n, face_value = 100;

    printf("Enter number of years: \n");
    scanf("%d", &n);
    float yield_rate[n], zero_rate[n];
    printf("Enter yield rate: \n");
    for(int i = 0; i < n; i++){
        printf("第 %d 期: ", i+1);
        scanf("%f", &yield_rate[i]);    //輸入每期的yield_rate
    }
    printf("Enter coupon rate: \n");
    scanf("%f", &coupon_rate);
    printf("Enter yield spread: \n");
    scanf("%f", &yield_spread);
    int coupon = face_value * coupon_rate;

### 計算zero rate

    for(int i = 1; i <= n-1; i++){  // i+1期的zero rate
        bond_value = 0;
        for(int j = 0; j <= i; j++){
            float discount = 1;
            for(int k = 0; k <= j; k++){
                discount /= (1 + yield_rate[i]);  // discount factor
            }
            bond_value += discount*coupon;
            if(j == i){
                bond_value += face_value*discount;
            }
        }
        // printf("bond price01: %f\n", bond_value);
        for(int j = 0; j < i; j++){
            float PV = coupon;
            for(int k = 0; k <= j; k++){
                PV /= (1 + zero_rate[j]);
            }
            bond_value -= PV;
        }
        // printf("bond price: %f\n", bond_value);
        zero_rate[i] = pow((coupon + face_value)/bond_value, 1.0/(i+1))-1;
        // printf("i = %d\n", i);
    }
    for(int i = 0; i < n; i++){
        printf("第%d期 zero rate = %f\n", i+1, zero_rate[i]);
    }

### 計算債券價格
含 yield spread

    bond_value = 0;
    for(int i = 1; i <= n; i++){
        float discount = 1;
        for(int j = 1; j <= i; j++){
            discount /= (1 + yield_rate[n-1] + yield_spread);  // discount factor + yield_sprade
        }
        printf("discount (price) = %f\n", discount);
        bond_value += discount * coupon;
        if(i == n){
            bond_value += face_value * discount;
        }
    }
    bond_price = bond_value;

### 找出 static spread
使用二分法

    float High = 1, Low = 0, discount = 1; // 代0為正，代1為負

    while(High - Low > 0.0001){
    	float Middle = (Low + High)/2;
		float value = 0;
		for(int i=1;i<=n;i++){
			discount = 1;
			for(int j=1 ; j<=i; j++){
				discount /= (1 + zero_rate[i-1] + Middle); //要折現幾次就乘幾次 
			}
            printf("discount = %f\n", discount);
			value += discount * coupon;	//並將折現乘上cash payment 
            if(i == n){
                value += (face_value * discount);
            }
		}
        printf("value01 = %f\n", value);
		value -= bond_price;
        printf("value = %f\n", value); 
        printf("bond price: %f\n", bond_price);
		if(value > 0){
            Low = Middle;
            printf("Low = %f\n", Low);
        }	
		else{
            High = Middle;
            printf("High = %f\n", High);
        }
		printf("%f \n", Middle); //可以看到收斂的過程 
	}
	printf("Static spread = %f. \n", High);
    return 0;
}

### 執行畫面
######

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###### tags: `財務工程`、`期貨與選擇權`、`債券`、`數值方法`、`二分法`、`C++`