Krishnan discusses the use of the valuation model to calculate effective duration and effective convexity with one of Klang Analytics’ developers. The developer makes the following statements to Krishnan:
Statement 1: The effective convexity of a putable bond cannot be less than that of an otherwise identical option-free bond.
Statement 2: The effective convexity of a callable bond can be negative in some circumstances, but the effective convexity of a putable bond is always positive.
Statement 3: The effective duration of a callable bond cannot be greater than that of an otherwise identical option-free bond and the effective duration of a putable bond cannot be less than that of the option-free bond.
Which of the statements made by the Klang Analytics developer is most likely correct?
| Statement 2 | |
| Statement 3 | |
| Statement |
Incorrect.
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)
为什么第一个选项不对，put bond 凸性不是比普通债权高吗
