Option market making under inventory risk

We propose a mean-variance framework to analyze the optimal quoting policy of an option market maker. The market maker’s profits come from the bid-ask spreads received over the course of a trading day, while the risk comes from uncertainty in the value of his portfolio, or inventory. Within this framework, we study the impact of liquidity and market incompleteness on the optimal bid and ask prices of the option. First, we consider a market maker in a complete market, where continuous trading in a perfectly liquid underlying stock is allowed. In this setting, the market maker may remove all risk by Delta hedging, and the optimal quotes will depend on the option’s liquidity, but not on the inventory. Second, we model a market maker who may not trade continuously in the underlying stock, but rather sets bid and ask quotes in the option and this illiquid stock. We find that the optimal stock and option quotes depend on the relative liquidity of both instruments as well as on the net Delta of the inventory. Third, we consider an incomplete market with residual risks due to stochastic volatility and large overnight moves in the stock price. In this setting, the optimal quotes depend on the liquidity of the option and on the net Vega and Gamma of the inventory.      

Intraday Price Change and Trading Volume Relations in the Stock and Stock Option Markets

This study investigates intraday relations between price changes and trading volume of options and stocks for a sample of firms whose options traded on the CBOE during the first quarter of 1986. After purging the price change series of the effects of bid/ask spreads, multivariate time-series analysis is used to estimate the lead/lag relation between the price changes in the option and stock markets. The results indicate that price changes in the stock market lead the option market by as much as fifteen minutes. The analysis of trading volume indicates that the stock market lead may be even longer.     

Price discovery in the U.S. stock and stock options markets: A portfolio approach

Option prices vary with not only the underlying asset price, but also volatilities and higher moments. In this paper, we use a portfolio of options to seclude the value change of the portfolio from the impact of volatility and higher moments. We apply this portfolio approach to the price discovery analysis in the U.S. stock and stock options markets. We find that the price discovery on the directional movement of the stock price mainly occurs in the stock market, more so now than before as an increasing proportion of options market makers adopt automated quoting algorithms. Nevertheless, the options market becomes more informative during periods of significant options trading activities. The informativeness of the options quotes increases further when the options trading activity generates net sell or buy pressure on the underlying stock price, even more so when the pressure is consistent with deviations between the stock and the options market quotes. JEL Classification C52, G10, G13, G14     

Index Options-Futures Arbitrage: A Comparative Study with Bid/Ask and Transaction Data

We can infer from bid/ask quotations and transaction prices that where options contracts are traded under a competitive open‐outcry market‐making system, the options and futures markets are dynamically efficient. Ex‐ante analysis shows that potential arbitrage opportunities disappear within five minutes. Transaction price data understate both the frequency and magnitude of arbitrage opportunities that are signaled by bid/ask quotes. Quotes stale fast, so opportunities are short‐lived and some of the arbitrage opportunities are deceptive. Nonetheless, the evidence suggests that bid/ask quotes provide valuable trading signals to arbitrageurs. Profitability from exploiting the quotes is negatively related to execution delay and execution risk.     

The Intraday Relation between NYSE and CBOE Prices

I extend the literature regarding price discovery across stock and option markets through an empirical model that allows information to flow through an error‐correction term and volatility. NYSE prices tend to lead CBOE prices by at least thirty minutes over the entire six‐year sample period. In addition, informed trading in the options market is revealed more strongly through persistence in volatility and the spillover of volatility to the stock market than it is through returns.     

Liquidity of the CBOE Equity Options

We examine the CBOE option market depth and bid-ask spreads. Absence of price effects surrounding large option trades suggests excellent market depth. However, bid-ask spreads for the CBOE options and the NYSE stocks are nearly equal, even though an average option is equivalent to less than half a stock plus borrowing. We explain this tradeoff between market depth and bid-ask spreads on the CBOE and the NYSE by differences in market mechanisms. We also show that the adverse-selection component of the option spread, which measures the extent of information-related trading on the CBOE, is very small.     

The liquidity effects associated with addition of a stock to the S&P 500 index: evidence from bid/ask spreads

This study examines changes in stock liquidity, as measured by the bid/ask spread, when a stock is added to the S&P 500 Index. The paper presents evidence of a significant decrease in the bid/ask spread upon S&P 500 addition, however, this effect is limited to only those stocks that were not trading listed options. Further, the decrease in the bid/ask spread for nonoptioned stocks is accompanied by a significant and permanent increase in share price and trading volume. While optioned stocks experience a permanent increase in trading volume, they experience only a temporary increase in share price. The findings for optioned stocks support the hypothesis that the price and volume effects associated with S&P 500 addition derive from temporary price pressure. Findings pertaining to the nonoptioned stocks indicate that the price and volume effects associated with S&P addition reflect enhanced stock liquidity. The decrease in the bid/ask spread for nonoptioned stocks is attributed to informational efficiencies achieved via index arbitrage trading, and it is argued that this effect is mitigated for optioned stocks due to the pre-existence of arbitrage trading between the option and the underlying stock.     

Volatility Information Trading in the Option Market

This paper investigates informed trading on stock volatility in the option market. We construct non-market maker net demand for volatility from the trading volume of individual equity options and find that this demand is informative about the future realized volatility of underlying stocks. We also find that the impact of volatility demand on option prices is positive. More importantly, the price impact increases by 40% as informational asymmetry about stock volatility intensifies in the days leading up to earnings announcements and diminishes to its normal level soon after the volatility uncertainty is resolved.     

Large option trades, market makers, and limit orders

This article focuses on the difference between market makersand limit orders in their role as suppliers of liquidity. Forboth sources of liquidity I analyze the price behavior of stocksand options around large option trades and I estimate the premiumpaid by the initiator of the large trade. My findings suggestthat limit orders for options are 'picked off' after adversechanges in the underlying stock price. Furthermore, I find thatfor these transactions there is a permanent change in quotationsin the direction of the transaction. After transactions wheremarket makers supply liquidity, quotes tend to return to theirpretrade level.     

Price impact and bursts in liquidity provision

This paper analyses brief episodes of high-intensity quote turnover and revision—‘bursts’ in quotes—in the US equity market. Such events occur very frequently, several hundred times a day for actively traded stocks. We find significant price impact associated with these market maker initiated events, about five times higher than during non-burst periods. Bursts in quotes are concurrent with short-lived structural breaks in the informational relationship between market makers and market takers. During bursts, market makers no longer passively impound information from order flow into quotes—a departure from the traditional market microstructure paradigm. Rather, market makers significantly impact prices during bursts in quotes. Further analysis shows that there is asymmetry in adverse selection between the bid and ask sides of the limit order book and only a sub-population of market makers enjoys an informational advantage during bursts. Market makers on the side opposite the burst suffer elevated adverse selection costs, while market makers on the side of the burst realize positive spread, irrespective of the order flow direction. Our results call attention to the need for a new microstructure perspective in understanding modern high-frequency limit order book markets and the quote manipulation strategies at the disposal of the fast market makers.     

The pricing of leverage products: An empirical investigation of the German market for ‘long’ and ‘short’ stock index certificates

This paper describes the first thorough empirical analysis of the pricing of leverage products in the German retail market. These mainly exchange-traded products with an impressive trading volume are frequently advertised as long and short futures contracts, although they are theoretically equivalent to one-sided barrier options. Issuers’ daily quotes for stock index products are compared to (i) theoretical values derived from the prices of Eurex options and to (ii) boundaries obtained from semi-static superhedging strategies. For the vast majority of products, bid and ask quotes significantly exceed both theoretical values and upper hedging boundaries, thus providing almost risk-free profits for the issuers.     

Is there price discovery in equity options?

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.     

Informed Trading in Stock and Option Markets

We investigate the contribution of option markets to price discovery, using a modification of Hasbrouck's (1995) "information share" approach. Based on five years of stock and options data for 60 firms, we estimate the option market's contribution to price discovery to be about 17% on average. Option market price discovery is related to trading volume and spreads in both markets, and stock volatility. Price discovery across option strike prices is related to leverage, trading volume, and spreads. Our results are consistent with theoretical arguments that informed investors trade in both stock and option markets, suggesting an important informational role for options.     

PRICE AND QUANTITY QUOTES ON NASDAQ: A STUDY OF DEALER QUOTATION BEHAVIOR

We show that the majority of quotes posted by NASDAQ dealers are noncompetitive and only 19.5% (18.4%) of bid (ask) quotes are at the inside. The percentage of dealer quotes that are at the inside is higher for stocks with wider spreads, fewer market makers, and more frequent trading, and lower for stocks with larger trade sizes and higher return volatility. These results support our conjecture that dealers have greater incentives to be at the inside for stocks with larger market‐making revenues and smaller costs. Dealers post large depths when their quotes are at the inside and frequently quote the minimum required depth when they are not at the inside. The latter quotation behavior leads to the negative intertemporal correlation between dealer spread and depth.     

Microstructure and reverse stock splits

In this paper we show that, similar to NYSE/AMEX stocks, NASDAQ stocks exhibit significant ex date returns for reverse stock splits. Although the 10-day cumulative return after the ex date is close to –10%, this does not violate market efficiency, because the average bid-ask spread for the reverse split stock is at least double this return. We also document that these large negative returns are mostly due to a drop in the ask price while bid prices barely change at all. Furthermore, the ex date returns are negatively related to trading volume.These results suggest that there is abnormal selling and a significant buildup of market makers' inventories near the ex date. To reduce the inventory buildup, market makers lower ask prices to induce buying by investors, resulting in the observed negative returns. Lowering bid prices, an alternative strategy for reducing inventories, is not attractive to market makers due to competitive factors and the reduction of commissions associated with a smaller number of transactions. Notably, selling investors have no incentives to sell their stocks early to avoid the observed negative ex date return, since this return is largely an ask price phenomenon and does not represent realized returns to sellers.     

Risk sharing in a financial market with endogenous option prices

This article investigates a financial market in which investors may trade in risk-free bonds, stock and put options written on the stock. In each period, stock and option prices are simultaneously determined by market clearing. While the introduction of put options will decrease the systematic risk in the financial market, it will increase the price of risk. Investors with mean-variance preferences will generally hold portfolios containing the primary asset and the put option and may use the option to increase the risk in their wealth position in exchange for higher returns. Aggregate wealth is unaffected by an option market when there are no spillover effects on stock prices, and it is shown that short selling of options will increase the volatility of individual wealth positions. Investors with erroneous beliefs may on average be better off not trading in put options.     

Transactions data tests of efficiency of the Chicago board options exchange

This paper performs lower boundary condition tests based on rational pricing of call options and an implied standard deviation test based on the bid/ask prices of options. These efficiency tests attempt to closely approximate conditions in the option markets to avoid the pitfalls indicated by Phillips and Smith (1980). The tests use transactions data and account for the effects of stock and option bid/ask prices, simultaneity of stock and option prices, depth of market, execution lag and transaction costs. The small and relatively infrequent profits due to market mispricing disappear in the lower boundary tests when transaction costs are taken into account. Frequent violations of the tighter boundary conditions in the implied standard deviation test are reported, but the estimated profits cannot be unambiguously attributed to option market inefficiency.     

Overconfidence among option traders

The investor overconfidence theory predicts a direct relationship between market‐wide turnover and lagged market return. However, previous research has examined this prediction in the equity market, we focus on trading in the options market. Controlling for stock market cross‐sectional volatility, stock idiosyncratic risk, and option market volatility, we find that option trading turnover is positively related to past stock market return. In addition, call option turnover and call to put ratio are also positively associated with the past stock market return. These findings are consistent with the overconfidence theory. We also find that overconfident investors trade more in the options market than in the equity market. We rule out explanations other than investor overconfidence, such as momentum trading and varying risk preferences, for our findings.     

Option trading after the opening bell and intraday stock return predictability

Prior literature finds that information is reflected in option markets before stock markets, but no study has explored whether option volume soon after market open has predictive power for intraday stock returns. Using novel intraday signed option-to-stock volume data, we find that a composite option trading score (OTS) in the first 30 min of market open predicts stock returns during the rest of the trading day. Such return predictability is greater for smaller stocks, stocks with higher idiosyncratic volatility, and stocks with higher bid–ask spreads relative to their options’ bid–ask spreads. Moreover, OTS is a significantly stronger predictor of intraday stock returns after overnight earnings announcements. The evidence suggests that option trading in the 30 min after the opening bell has predictive power for intraday stock returns.     

Why Option Prices Lag Stock Prices: A Trading-based Explanation

While many studies find that option prices lead stock prices, Stephan and Whaley (1990) find that stocks lead options. We find no evidence that options, even deep out-of-the-money options, lead stocks. After confirming Stephan and Whaley's results, we show their results can be explained as spurious leads induced by infrequent trading of options. We show that the stock lead disappears when the average of the bid and ask prices is used instead of transaction prices. Hence, we find no evidence of arbitrage opportunities associated with the stock lead.