A bothersome empirical finding in the options market microstructure literature is that in a small but significant percentage of the cases, market prices for a call and for its underlying stock move in opposite directions. For example, the stock price falls, but the call goes up, which is a violation of options’ monotonicity property. Using detailed intraday data on the Taiwan TAIEX index and its options, the authors find violations of monotonicity in about one third of the trades. They consider two possible factors that might push the call (put) price in a different (the same) direction as the stock: stochastic volatility, which introduces a second variable with its own dynamics into option pricing, and demand pressure from trades like covered calls, which can have opposite impacts on the stock and the option. The two factors together can explain all but 18% of the monotonicity violations in the data.