In most established rates markets, swaps are discounted using risk-free reference rates, such as Sonia in the GBP market and Eonia in the EUR market, as opposed to Libor.
Because of the way zero-coupon Libor swaps are valued (i.e. forward cash flows compounded up to the maturity date of the swap vs Libor, and then discounted back vs Sonia), this creates a convexity adjustment that needs to be accounted for when pricing them.
In other words, a dealer will need to charge a client more if the client wants receive fixed on the zero-coupon swap, and does not need to charge anything more if the client wants to pay fixed on the zero-coupon swap. So not accounting for any extra 'convexity' charges, it is desirable to receive fixed on a zero-coupon swap, but undesirable to pay fixed.
The below was explained to me by someone, but I'm not entirely sure I understand exactly why/how this works from a mathematical point of view. Would it be the other way around if the Libor curve happened to lie below the Sonia curve?
I'm essentially looking for a more concise/clear explanation of this phenomenon.