Why do we need convexity adjustment (CMS, ...)?

[themarketprofessor]

I'm familiar enough with FRAs vs futures. But that's just because when you trade futures you settle up daily pnl on the exchange, while when you trade a FRA you only settle at expiration. Whether it's worth it or not to be received of a FRA and short the future, or vice versa, is a view on volatility. FRAs get discounted at the prevailing rate at expiration, so just like what I posted above, if you are received of a FRA and rates go down, you are happy that rates have gone down and your winnings are discounted at lower rates, and if you are paid FRAs you are happier than you'd have otherwise been as the money you've lost is discounted at a higher rate. Exactly how much happier or sadder is determined by how far rates have gone up or down. Futures on the other hand are perfectly linear. This is definitely not an arbitrage opportunity, and the convexity adjustment that exists between FRAs and futures is just a function of the implied vol of swaptions, costs of funding for each counterparty, and the amount charged for collateral on the exchange. You can make or lose money going either way on futures vs. FRAs, but it's not an arb at all. The prices are different for very good reason, convexity adjustments to go between futures and FRAs are quoted all day long and are well known among dealers, and they don't necessarily present an amazing market opportunity.

What the crock are you babbling about?! You sounded like you've just done something bad and got caught with pants down, and yet tried to explain your bad deeds.