表述1

问题如下：

Which of the statements made by the Klang Analytics developer is most likely correct?

选项：

A.

Statement 2

B.

Statement 1

C.

Statement 3

解释：

A is correct. Statement 2 is correct. The convexity of a callable bond turns negative when the call option is near the money, because the upside for the bond is much smaller than the downside (because the value is capped at the call price). The convexity of a putable bond is always positive because when the option is near the money, the upside for the bond is much larger than the downside (because the floor value is the put price).

B is incorrect because the statement is false. The value of a putable bond cannot fall below the put price, whereas the value of the option-free bond can. Therefore the effective duration of the option-free bond can be larger than that of the putable bond.

C is incorrect because at high interest rates, the value of the putable bond is equal to the floor price, so the effective duration is very low and the effective convexity is close to zero. The effective convexity of the option-free bond is higher because its value continues to decrease, albeit at an ever decreasing rate (convexity gets smaller).