ABSTRACT I show that the inventory risk faced by market‐makers has a first‐order effect on option prices. I introduce a simple approach that decomposes the price impact of trades into inventory risk and asymmetric information components. While both components are large for option trades, the inventory risk component is larger. Using the full panel of daily option returns, I find that option order imbalances attributable to inventory risk have five times larger impact on option prices than previously thought. Finally, I find that past order imbalances have greater predictive power than any other commonly used predictor of option returns.

Average delta hedged returns for Standard & Poor's 500 index options are large: −0.7% per day. When we decompose these option returns into intraday and overnight components, average close-to-open returns are −1% per day and open-to-close returns are positive, 0.3%. A similar return pattern holds for all maturity and moneyness categories and equity options. These positive intraday returns are particularly difficult to explain. However, our results are consistent with option prices’ failing to account for the well-known fact that stock volatility is substantially higher intraday than overnight. These findings help explain price formation in the options market.

Abstract We study how the market return depends on the time of the day using E-mini S&P 500 futures actively traded around the clock. Strikingly, 4 hours around European open account for the entire average market return. This period’s returns have a 1.6 Sharpe ratio and remain high after transaction costs. Average returns are a noisy zero during the remaining 20 hours. High returns are consistent with European investors processing information accumulated overnight and thus resolving uncertainty. Indeed, uncertainty reflected by VIX futures prices rises overnight and falls around European open. The results are stronger during the 2020 COVID crisis.

We use tick-by-tick quote data for 39 liquid US stocks and options on them, and we 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.

ABSTRACT We train a machine learning method on a class of informed trades to develop a new measure of informed trading, informed trading intensity (ITI). ITI increases before earnings, mergers and acquisitions, and news announcements, and has implications for return reversal and asset pricing. ITI is effective because it captures nonlinearities and interactions between informed trading, volume, and volatility. This data‐driven approach can shed light on the economics of informed trading, including impatient informed trading, commonality in informed trading, and models of informed trading. Overall, learning from informed trading data can generate an effective informed trading measure.

ABSTRACT Recent research argues that uncertainty about future stock borrowing fees hinders short‐selling, and this risk explains the performance of short strategies. One possible mechanism is that borrowing fee risk carries a risk premium. Since the present value of the uncertain borrowing fee is reflected in options prices, the difference between option‐implied and realized fees estimates this premium. We find that the risk premium is small. Moreover, if the risk premium is substantial, it should be reflected in the returns to short‐selling stock after adjusting for stock borrowing fees. However, borrowing fee risk does not predict fee‐adjusted returns.