Is there a benefit from the issuer's perspective if its bonds are traded at a premium? likewise, is there a disadvantage if the bond starts trading at a discount? Off the top of my head, if a bond is trading at a severe discount, the issuer should be incentivised to buyback the bonds (although i'm sure there are provisions governing the buyback prices).
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there is no effect to the issuer.
however, if the bonds trade at a significant discount, then the issuer could buy back the bonds in the secondary market and retire them for much cheaper than normal. however, if an issuer has the cash to do this...the bonds would not be trading at such a discount, and so it would, in practice, never happen.
No effect on the bonds themselves. However, if they are trading up/down compared to the yield at which they were issued, that implies credit quality or market conditions have changed, which will affect their ability to issue in the future.
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