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.      

END‐OF‐DAY PRICING IN THE U.S. TREASURY MARKET: A COMPARISON OF GovPX AND THE FEDERAL RESERVE BANK OF NEW YORK

We compare end‐of‐day indicative U.S. Treasury prices from GovPX and the Federal Reserve Bank of New York (FRBNY). We find that the two sources rarely quote identical prices, and differences are not simply due to noise or rounding. The average bid price differential is 2 cents for notes and bonds, but it is only ¹/₁₀ of 1 cent for bills. Bid‐ask spreads in both sources appear to be largely artificial and contain limited information. Finally, we find that the end‐of‐day indicative FRBNY bid prices are closer to true intraday GovPX market quotes than end‐of‐day indicative quotes provided by GovPX itself.     

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 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.     

Adverse selection and the presence of informed trading

We combine two concepts of informed trading – contrarian trades and stealth trading – to develop proxies for the probability of informed trading. These proxies are used to test the link between informed trading and adverse selection as measured by bid–ask spreads and stock illiquidity. The estimation results show that these proxies, which are based on the probability of contrarian trading (PC) and progressively refined thereon, are all highly significantly positive in various empirical specifications of the cross-sectional determinants of spreads and illiquidity across stocks, and after controlling for important firm characteristics and trading factors. The robustness of our PC-based proxies for informed trading in these analyses, especially for the further refined measures, suggests that they successfully capture the adverse selection component of bid–ask spreads and illiquidity due to information asymmetry.     

On the Distribution of CBOE Option Trade Prices Occurring Between Consecutive Stock Trades

This paper examines the volume distribution of option trade prices that occurs when the underlying stock price remains constant. The width of these option trade price bands provides direct evidence on the law of one price and the redundancy of options assumed in many option models. We find that index option bands are narrower than equity option bands. Furthermore, for both equity and index options, puts have narrower bandwidths than calls. In general, option price bandwidth is narrow and can be explained by the minimum price movement allowed by the Chicago Board Options Exchanges (CBOE). This supports the single price law and the redundancy assumption. The existence of bid/ask quotes on the option does not materially affect the above results although it does alter the frequency of multiple option trade prices for a given underlying stock price. We note that over 53% of option trading volume occurs without bid/ask quotes on the CBOE compared to less than 15% a decade ago. Our results suggest that the effective bid/ask spread on options is probably no larger than the minimum price movements allowed by the CBOE. Furthermore, the need for the liquidity services of market makers may be declining if the decline in quoting activity stems from cross trading (i.e. trades not involving market makers).     

Dealer Bid-Ask Quotes and Transaction Prices: An Empirical Study of Some AMEX Options

This paper, utilizing dealer's “trading book” information, presents some empirical evidence supporting the validity of a dealer pricing model. It shows that much of the transaction prices variation may be explained by the specialist's optimal determination of his bid and ask quotes. Furthermore, it demonstrates that the dealer's bid-ask spread is an important explanatory variable in the observed transaction return. Finally, it indicates that the dealer's inventory level may affect his quotes and thus the transaction prices and order arrivals. The paper provides insights into the relationship between transaction prices and equilibrium prices, which will permit more extensive use of transaction data in empirical investigations. It also provides a better understanding of optimal dealer pricing strategies, suggesting that the proposed empirical model may be used to evaluate a dealer's trading performance.     

Institutional trading and stock resiliency: Evidence from the 2007–2009 financial crisis

We examine the impact of institutional trading on stock resiliency during the financial crisis of 2007–2009. We show that buy-side institutions have different exposure to liquidity factors based on their trading style. Liquidity supplying institutions absorb the long-term order imbalances in the market and are critical to recovery patterns after a liquidity shock. We show that these liquidity suppliers withdraw from risky securities during the crisis and their participation does not recover for an extended period of time. The illiquidity of specific stocks is significantly affected by institutional trading patterns; participation by liquidity supplying institutions can ameliorate illiquidity, while participation by liquidity demanding institutions can exacerbate illiquidity. Our results provide guidance on why some stocks take longer to recover in a crisis.     

A new methodology for studying intraday dynamics of Nikkei index futures using Markov chains

The empirical study of intraday patterns of stock trading volatilities and bid–ask spreads in the literature depends on assumptions of specific price generating process and may therefore not be robust to distributional assumptions. By creating discrete states that conform more naturally to the way prices are actually quoted in the derivatives and assets markets, we employ a new methodology of Markov chains for studying the intraday dynamics of derivative prices. We apply the method to study the intraday behavior of the Nikkei index futures prices, trading volumes, and spreads. We find some interesting results such as higher probabilities of transitions between larger volatilities at the opening and closing times. The volatility at lunch break is strikingly low. Contrary to most of the literature, the Nikkei intraday bid–ask spread does not show a U-shaped pattern. We offer some explanations.     

Specialists,Limit‐Order Traders,and the Components of the Bid‐Ask Spread

This study compares the components of the bid‐ask spread estimated from quotes that reflect the trading interest of specialists with those estimated from limit‐order quotes and all available quotes for a sample of New York Stock Exchange (NYSE) stocks. The results show that the adverse selection component of the spread estimated from specialist quotes is significantly smaller than the corresponding figures from limit‐order quotes and entire quotes. We interpret this as evidence that NYSE specialists transfer at least a part of adverse selection costs to outsiders through the discretionary use of limit orders. Our results show that the estimation/interpretation of the components of the spread using quote data that include both specialist and limit‐order interests is problematic.     

Information asymmetry of fair value accounting during the financial crisis

We examine whether US banks’ fair value net assets, measured according to the three-level hierarchy introduced in SFAS 157, are associated with information asymmetry during the 2008 financial crisis. Our results show that bid–ask spread, a proxy for information asymmetry, is positively associated with fair value net assets, and the degree of association is contingent upon the three-level hierarchy, with bid–ask spreads being lowest for Level 1 (the most transparent valuation inputs) and highest for Level 3 (the least observable). Also, there is some evidence that SFAS 157 led to a reduction in bid–ask spread, and we find that quarterly changes in Level 1 and Level 2 fair value net assets are significantly associated with changes in bid–ask spread in 2008 when the spread was rapidly rising, but not in 2009 when it was falling. Our findings suggest that the three-level hierarchy under SFAS 157 provides investors with useful information, and fair value is associated with uncertainty, as measured by bid–ask spread, before and during the financial crisis.     

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.     

Subjective evaluation of delayed risky outcomes for buying and selling positions: the behavioral approach

This paper analyzes time discounting as a function of risk, using reservation prices. Based on experimental data, we compare bidder reservation prices for riskless assets with those for risky assets. The experiments rely on a second price auction with real monetary incentives and real delay in payoffs. We estimate the pure time discount rate for different maturities, considering riskless assets (bonds) and risky assets (delayed lotteries). An innovation in the experimental design allows disentangling pure time from pure risk discounting effects. If subjects bid for assets, we find implied discount rates for risky assets to be uniformly lower than those for riskless assets, across all maturities (the risk moderation effect). However, there is no risk moderation effect if subjects quote ask prices. We argue that delaying a payoff has a stronger effect on the price of bonds than on the price of risky assets since, in the case of bonds, the investor moves from a position of certainty to a position of risk, or uncertainty. Our findings on the risk moderation effect may be used to explain the attractiveness of compensation contracts with options, as commonly used in the financial industry.     

Conditions on option prices for absence of arbitrage and exact calibration

Under the assumption of absence of arbitrage, European option quotes on a given asset must satisfy well-known inequalities, which have been described in the landmark paper of Merton [Merton, R., 1973. Theory of rational option pricing. Bell Journal of Economics and Management Science 4 (1), 141–183]. If we further assume that there is no interest rate volatility and that the underlying asset continuously pays deterministic dividends, cross-maturity inequalities must also be satisfied by the bid and ask option prices.     

An evolutionary multi‐objective optimization of trading rules in call markets

We evaluate an agent‐based model featuring near‐zero‐intelligence traders operating in a call market with a wide range of trading rules governing the determination of prices and which orders are executed, as well as a range of parameters regarding market intervention by market makers and the presence of informed traders. We optimize these trading rules using a multi‐objective population‐based incremental learning algorithm seeking to maximize the trading volume and minimize the bid–ask spread. Our results suggest that markets should choose a small tick size if concerns about the bid–ask spread are dominating and a large tick size if maximizing trading volume is the main aim. We also find that unless concerns about trading volume dominate, time priority is the optimal priority rule. Copyright © 2011 John Wiley & Sons, Ltd.     

A Regime-Level Empirical Model of the Specialist Quote Revision Process

NYSE trading is a continuous auction process distinguished by order flow imbalances and non-coincident revision of the bid and the ask. To deal with the aggregation problem presented by non-coincident revision of the quotes, we propose a regime-level empirical model and use it to test the Brock and Kleidon queuing theory of a continuous auction. Using transactions data for IBM for calendar year 1988, Harris, McInish, and Chakravarity (1995) performed a Hausman-type specification test that confirmed the exogeneity of order flow volumes at the bid and the ask. Extending their work, this paper estimates two simultaneous autoregressive ask and bid equations for 50 randomly selected stocks and contrasts thinly traded and volatile stocks. The results support Brock and Kleidon's distinguishing implication—namely, exogenous increases in trading volume raise the ask and lower the bid. Although some queuing system characteristics prove endogenous in thinly traded stocks and in especially volatile stocks, exogenous order flow volume continues to increase spreads across the 50 stock sample. The paper draws conclusions about the appropriate specification of endogeneity, cross-equation disturbances from the bid to the ask, and cross-equation queuing information flows.     

Minimum Price Variations,Time Priority,and Quote Dynamics

We analyze price competition between dealers in a security market where the bidding process is sequential. The model provides an interpretation for the evolution of the best ask and bid prices, in between transactions. We find that convergence to the competitive ask and bid prices can take time. The speed of convergence is determined by the frequency with which dealers check their offers and by the tick size. This creates a relationship between the expected trading cost and the timing of offers posted by the dealers. We also find that a zero minimum price variation never minimizes the expected trading cost. Finally, we study the role of time priority. Journal of Economic Literature Classification Numbers: D43, G10.     

Impacts of trades in an error-correction model of quote prices

In this paper we analyze and interpret the quote price dynamics of 100 NYSE stocks stratified by trade frequency. We specify an error-correction model for the log difference of the bid and the ask price with the spread acting as the error-correction term, and include as regressors the characteristics of the trades occurring between quote observations, if any. From this model we are also able to extract the implied model for the spread and the mid-quote. We find that short duration and medium volume trades have the largest impacts on quote prices for all one hundred stocks. Further, we find that buys have a greater impact on the ask price than on the bid price, while sells have a greater impact on the bid price than on the ask price. Both buys and sells increase spreads in the short run, but in the absence of further trades, the spreads mean revert. Trades have a greater impact on quotes for the infrequently traded stocks than for the more actively traded stocks.     

Effect of the ban on short selling on market prices and volatility

We examine the effects of the short‐selling ban, imposed by Australian regulators in the wake of the global financial crisis, on the trading of financial stocks. Our findings argue against commonly stated reasons for imposing short‐sale bans. We find no evidence that short‐sale restrictions provide support for stock prices or that they reduce volatility. Moreover, stocks subject to the short‐selling ban suffered a severe degradation in market quality. Controlling for the adverse effects of the financial crisis on markets, we show that short‐selling restrictions increase intraday volatility, reduce trading activity and increase bid–ask spreads.     

The Illiquidity of Corporate Bonds

This paper examines the illiquidity of corporate bonds and its asset‐pricing implications. Using transactions data from 2003 to 2009, we show that the illiquidity in corporate bonds is substantial, significantly greater than what can be explained by bid–ask spreads. We establish a strong link between bond illiquidity and bond prices. In aggregate, changes in market‐level illiquidity explain a substantial part of the time variation in yield spreads of high‐rated (AAA through A) bonds, overshadowing the credit risk component. In the cross‐section, the bond‐level illiquidity measure explains individual bond yield spreads with large economic significance.