Find the convexity of a seven-year maturity, 6.6% coupon bond selling at a yield to maturity of 8.4%. The bond pays its coupons annually.

Note: Do not round intermediate calculations. Round your answer to 4 decimal places.





Convexity is a measure of the curvature of the price-yield relationship of a bond, and it can be calculated using the following formula:

\[
\text{Convexity} = \frac{1}{P} \times \sum_{t=1}^{T} \frac{C_t \times t(t + 1)}{(1 + y)^t} + \frac{M \times T(T + 1)}{(1 + y)^T}
\]

Where:
- \( P \) = Current price of the bond
- \( C_t \) = Coupon payment at time \( t \)
- \( M \) = Face value of the bond
- \( y \) = Yield to maturity (in decimal form)
- \( T \) = Maturity of the bond in years

### Given:
- Coupon rate = 6.6% (which implies annual coupon payments of \( C = 66 \) per year for a face value of \( 1000 \))
- Face value \( M = 1000 \)
- Yield to maturity \( y = 8.4\% = 0.084 \)
- Maturity \( T = 7 \) years

The price of the bond \( P \) can be calculated using the present value of the bond's cash flows:

\[
P = \sum_{t=1}^{T} \frac{C_t}{(1 + y)^t} + \frac{M}{(1 + y)^T}
\]

I'll calculate the bond price first, and then use it to determine convexity. Let's begin.The price of the bond is approximately \( 907.5538 \).

Now that we have the bond price, we can calculate the convexity using the following formula:

\[
\text{Convexity} = \frac{1}{P} \times \sum_{t=1}^{T} \frac{C_t \times t(t + 1)}{(1 + y)^t} + \frac{M \times T(T + 1)}{(1 + y)^T}
\]

Let's proceed with this calculation.The convexity of the bond is approximately \( 36.5803 \), rounded to four decimal places.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does convexity affect bond prices when interest rates change?
2. What is the relationship between duration and convexity in bond pricing?
3. How would the convexity change if the bond had semi-annual coupon payments?
4. What happens to the convexity if the yield to maturity increases significantly?
5. How do zero-coupon bonds compare in terms of convexity to coupon bonds?

**Tip**: Convexity helps in understanding the degree of sensitivity of bond prices to interest rate changes beyond what duration predicts!

Find the convexity of a seven-year maturity, 6.6% coupon bond selling at a yield to maturity of 8.4%. The bond pays its coupons annually.

Explore the convexity calculation of a seven-year maturity bond with a 6.6% coupon rate and 8.4% yield to maturity. This detailed solution covers the bond pricing formula and convexity formula, making it ideal for finance students and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation