Hi, we know that a callable bond has negative convexity, and the way we usually describe it is by saying that when rates fall, a callable bond’s price increases less than a straight bond. What about when the rates rise, does a callable bond price still decrease at a slower rate? I’d think so.
I feel that whenever we talk about callable bonds and negative convexity, we associates them with rates falling ; whereas when talking about puttable bonds and positive convexity, we associate them with rates rising. Is there a reason for doing that? Or we can describe them in either rates rising or falling?
A callable bond only has negative convexity at specific times (at rates below that of which the bond will likely be called) if rates are rising the bond has positive convexity
Does what you said above apply to putable bonds as well?
Putable bonds don’t have negative convexity.
They have extra positive convexity as yields rise.
Also, just so ya know, the negative convexity hitting the callable bond curve only applies post-call date. If rates are low and the firm can’t call yet to “refinance,” the price is not yet capped. Pre-call date, I believe the option decreases positive convexity. Still a smiley face, just less smiley. Post-call, that smiley face turns frowny face as market rates fall.
So bascially putable bonds always have positive convexity, whereas callable bonds have negative convexity post-call date, but positive convexity pre-call date??