The square-root impact law also holds for option markets
  Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of option trades. We find that the square-root law indeed holds in that case. This finding supports the argument for a universal underlying mechanism. 
Bence Toth, Zoltan Eisler, Jean-Philippe Bouchaud
q-fin.TR