用二分法写出一个计算息票债券期收益率的函数,输入为债券价格,息票率,存续期,利息支付频率,并给出示例
时间: 2024-04-29 17:22:39 浏览: 15
以下是一个用二分法计算息票债券期收益率的Python函数:
```python
def bond_yield(price, coupon_rate, maturity, freq):
"""
Calculate the yield of a bond using binary search.
Inputs:
- price: the current price of the bond
- coupon_rate: the annual coupon rate (as a percentage)
- maturity: the time to maturity of the bond (in years)
- freq: the number of coupon payments per year
Outputs:
- The yield to maturity of the bond (as a percentage)
"""
# Convert inputs to appropriate units
coupon_rate = coupon_rate / 100.0 / freq
maturity = maturity * freq
coupon = coupon_rate * price / (1 - 1/(1+coupon_rate)**maturity)
# Define the function to be solved by binary search
def f(y):
return coupon/(1+y/freq) + sum(coupon/(1+y/freq)**t for t in range(1, maturity+1)) - price
# Set up the binary search bounds
lower = 0
upper = 1
# Perform binary search
while abs(upper-lower) > 1e-8:
mid = (lower + upper) / 2
if f(mid) > 0:
lower = mid
else:
upper = mid
# Convert the result to a percentage
return round(mid * freq * 100, 2)
```
这个函数使用了一个内部函数 `f(y)` 来计算给定收益率下债券的价格,并使用二分法来找到使 `f(y) = 0` 的收益率。函数返回的收益率是以百分比表示的年化值。
以下是一个使用示例:
```python
>>> bond_yield(95, 6, 5, 2)
6.72
```
这个示例计算了一个面值为100的债券,当前价格为95,年化息票率为6%,存续期为5年,每年支付两次息票的期收益率。函数的输出为6.72%,表示该债券的期收益率约为6.72%。