I understand that callable bonds are like an option free bond and a short call, hence when yields fall the embedded call become more valuable and hence it has negative convexity. I dont get the link to interest rate vol and spreads?
Also is it wrong to say in a putable bond it has positive convexity?
Volatility relationship is same as options… Since short call = inverse relationship
Putable will hv direct relationship. Yes, they hv pos convexity.
Thanks that is really helpful!
Sorry last thing on this, in the below answer to a question. I understand it all now based on your help. But why does the nominal spread increase on the callable? Is it because it is now more risky than the option-free due to the short call moving by more?
A callable bond is a bond with an embedded short call option. The value of a callable bond is equal to the value of an option-free bond less the value of the embedded option. The value of the embedded call option owned by the issuer will increase as volatility rises, reducing the value of the bond versus a similar option-free bond, thus causing nominal spreads to increase.
It is only saying you value of callable reduces as vol increases= price down = yield up.
I think.
That makes sense! Thanks!