Which of the following statements about the relationship between yield to maturity and bond prices is FALSE?

A. When the yield to maturity and coupon rate are the same, the bond is called a par value bond.
B. A bond selling at a premium means that the coupon rate is greater than the yield to maturity.
C. When interest rates go up, bond prices go up.
D. A bond selling at a discount means that the coupon rate is less than the yield to maturity.

To determine the false statement about the relationship between yield to maturity and bond prices, let's analyze each option:

A. When the yield to maturity and coupon rate are the same, the bond is called a par value bond.
This statement is true. A par value bond is one where the yield to maturity matches the coupon rate. So, option A is correct.

B. A bond selling at a premium means that the coupon rate is greater than the yield to maturity.
This statement is also true. When a bond sells at a premium, it means that the bond's price is higher than its face value. This happens when the coupon rate of the bond is higher than the prevailing yield to maturity. So, option B is correct.

C. When interest rates go up, bond prices go up.
This statement is false. Bond prices and interest rates generally have an inverse relationship. When interest rates rise, the prices of existing bonds tend to decrease to align with the new, higher-yielding bonds available on the market. Therefore, option C is the false statement.

D. A bond selling at a discount means that the coupon rate is less than the yield to maturity.
This statement is true. When a bond sells at a discount, it means that the bond's price is lower than its face value. This happens when the coupon rate of the bond is lower than the prevailing yield to maturity. So, option D is correct.

Therefore, the false statement about the relationship between yield to maturity and bond prices is option C.

The FALSE statement among the given options is C. When interest rates go up, bond prices go up.

Explanation: When interest rates go up, bond prices actually go down. This is because existing bonds with lower yields become less attractive compared to newly issued bonds with higher yields. As a result, the prices of existing bonds decrease in order to align their yield to maturity with the current market interest rate.

When the yield to maturity and coupon rate are the same, the bond is called a par value bond.