I've observed that the repo rate implied from options on Euro Stoxx 50 is significantly higher than the repo rate implied from options on individual stocks that are constituents of the index. This is especially pronounced for the short-end tenors (<0.5y) Why this occurs? Shouldn't the repo of the index be approximately equal to the average of the repo of its constituent stocks?
Repo is a supply and demand dynamic, the reason you have people doing index arbitrage and synthetic financing on the index because you can easily trade large derivative sizes, it's a reliable proxy for secured financing and you can easily get in and out.
However, by the sheer size of the bid ask spread and the limited liquidity on single stock options, you cannot realistically buy 10 MM USD shares, do a synthetic forward using call puts for 40 bps, lend the shares to someone for 50 bps and expect to make a 10 bps profit. I used to work on a secured financing desk and no one even looked at the implied repo on single stock options due to bid/ask + limited liquidity.
Overall, I would say that for special shares with high repo options and OTC repo should be in the same area because short sellers would compare at synthetic forward through put/call. However below a certain level everything is considered GC and you're unlikely to be charged differently if the single name implied repo is 40 bps or 50 bps. If GC is considered 40 it's going to be 40.
In other factors, you could also consider the fact that your options are probably american and thus for dividend paying stocks the "repo duration" would be shorter, while your index options are european.