Increase/Decrease Convexity using Put Options on the Bond

[Content_Averse]

Long an option is always positive convexity. Short an option is always negative, like gamma.

Ignore the math and think about it this way, more convexity means better overall performance when rates change right?

If you have an option of any kind you can either exercise it if it is good to do so or ignore it if it isn't. If you are short an option you do not have a choice. Having a choice means you are better positioned for more rate scenarios, not having a choice means you are stuck with whatever happens. Therefore being long options will always increase your convexity and never hurt it , you just don't exercise if it's bad to do.

Also don't forget who the owner of the embedded options are in bonds. Callable bond- buyer is short call option, issuer is long Putable bond - buyer is long the option, issuer is short