This thesis consists of three essays that examine various problems in empirical derivatives. In the first essay, we use “tick-by-tick” quote data for 39 liquid U.S. stocks and options on them, and focus on events when the two markets disagree about the stock price in the sense that the option-implied stock price obtained from the put-call parity relation is inconsistent with the actual stock price.Option market quotes adjust to eliminate the disagreement, while the stock market quotes behave normally, as if there were no disagreement. The disagreement events are typically precipitated by stock price movements, and display signed option volume in the direction that tends to eliminate the disagreements.These results show that option price quotes do not contain economically significant information about future stock prices beyond what is already reflected in current stock prices, i.e. no economically significant “price discovery” occurs in the option market.We also find no option market price discovery using a much larger sample of disagreement events based on a weaker definition of a disagreement, which verifies that the findings for the primary sample are not due to unusual or unrepresentative market behavior during the put-call parity violations.The second essay examines trading costs and price impact in the options market. Conventional measures of trading costs and price impact rely on the quote midpoint as an estimate of a true security value. However, investors use a more precise estimate of the true value which takes advantage of public information as well as best quotes. Investors buy when the public information midpoint is above the quote midpoint and vice versa. As a result, conventional measures have a substantial upward bias. The execution timing bias is particularly large in the options market. Effective and average quoted spreads overestimate actual trading costs by 50% and 100% respectively.Less than half of the price impact is caused by trades; the remainder is expected changes in the quote midpoint. The timing bias varies across stocks and has been increasing over time. Trades of non-round size pay smaller spreads. We suggest a general approach to adjusting conventional measures for the timing bias. Our results indicate that the usage of the adjusted measures is crucial for making inferences about liquidity and informed trading.The third essay shows that inventory considerations play a first order role in determining expected option returns. This point is supported by three main results. First, position rollover during the expiration period creates large selling pressure which leads to a 5.7% drop in prices for non-expiring options. Expiration dates create exogenous variation in order imbalance, which in turn can explain the “abnormal” expiration returns. Second, as implied by the inventory channel, individual and market-wide order imbalances predict future option returns primarily through future order imbalances. The past imbalances are the most significant predictors of future returns controlling for a large battery of observable variables. One standard deviation increase in the inventory-related order imbalance corresponds to 1% higher expected option returns on the next day. Finally, we develop a microstructure method to decompose the price impact of trades into inventory and information components. Inventory has a bigger price impact than information for any trade size.
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