Liquidity supply and volatility: futures market evidence

This article examines the provision of liquidity in futures markets as price volatility changes. We find that customer trading costs do not increase with volatility. However, for three of the four contracts studied, the nature of liquidity supply changes with volatility. Specifically, for relatively inactive contracts, customers as a group trade more with each other and less with market makers, on higher volatility days. By contrast, for the most active contract, trading between customers and market makers increases with volatility. We also find that market makers' income per contract decreases with volatility for one of the least active contracts in our sample, but is not significantly affected by volatility for the other contracts. These results are consistent with the idea that, for high‐cost, inactive contracts, market makers react to temporary increases in volatility by raising their bid‐ask spreads significantly, and customers provide increased liquidity through standing limit orders. An implication of our results is that electronic systems, where market maker participation is not required, are able to supply adequate liquidity during volatile periods. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1–17, 2001     

Do designated market makers improve liquidity in open‐outcry futures markets?

On February 1, 2002, the Chicago Board of Trade appointed a designated market maker to enhance liquidity in its 10‐year interest rate swap futures contract. This market‐making program is the first of its kind in the open‐outcry futures industry. We find that introduction of the market maker has increased volume and reduced transaction costs. The market maker has also enhanced the speed and the efficiency of price discovery. Overall, the results suggest that the market‐making program is successful in improving liquidity. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:479–502, 2004     

Optimal contract design: For whom?

In designing a derivative contract, an exchange carefully considers how its attributes affect the expected profits of its members. On November 3, 1997, the Chicago Mercantile Exchange doubled its tick size of its S&P 500 futures contract and halved the denomination, providing a rare opportunity to examine empirically the search for an optimal contract design. This article measures changes in the trading environment that occurred in the days surrounding the contract redesign. We find a discernible change in the incidence of price clustering, an increase in the bid/ask spread, a reduction in trading volume, and no meaningful change in dollar trade size. These results suggest that the contract redesign did not increase accessibility but did increase market maker revenue. Despite the increase, however, the bid/ask spread of the S&P 500 futures contract remains low relative to the costs of market making and the spreads in markets for competing instruments. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:719–750, 2003     

MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.     

Order flow and exchange rate dynamics in electronic brokerage system data

We analyze the association between order flow and exchange rates using a new dataset representing a majority of global interdealer transactions in the two most-traded currency pairs at the one minute frequency over a six-year time period. This long span of high-frequency data allows us to gain new insights about the joint behavior of these series. We first confirm the presence of a substantial association between interdealer order flow and exchange rate returns at horizons ranging from 1 min to two weeks, but find that the association is substantially weaker at longer horizons. We study the time-variation of the association between exchange rate returns and order flow both intradaily and over the long term, and show that the relationship appears to be stronger when market liquidity is lower. Overall, our study supports the view that liquidity effects play an important role in the relationship between order flow and exchange rate changes. This by no means rules out a role for order flow as a channel by which fundamental information is transmitted to the market, as we show that our findings are quite consistent with a recent model by Bacchetta and Van Wincoop (2006: Can information heterogeneity explain the exchange rate determination puzzle? American Economic Review, 96, pp. 552–576.) that combines both liquidity and information effects.     

Illiquidity transmission from spot to futures markets

We develop a model of illiquidity transmission from spot to futures markets that formalizes the derivative hedge theory of Cho and Engle (1999). The model shows that spot market illiquidity does not translate one to one to the futures market but, rather, interacts with price risk, liquidity risk, and the risk aversion of the market maker. The model's predictions are tested empirically with data from the stock market and markets for single-stock futures and index futures. The results support our model and show that the derivative hedge theory provides an explanation for the liquidity link between spot and futures markets.     

LONG HORIZONS,HIGH RISK AVERSION,AND ENDOGENOUS SPREADS

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as the limits of their isoelastic counterparts for high levels of risk aversion. The results are robust with respect to finite horizons, and extend to multiple uncorrelated risky assets. In this setting, we study a Stackelberg equilibrium, led by a risk‐neutral, monopolistic market maker who sets the spread as to maximize profits. The resulting endogenous spread depends on investment opportunities only, and is of the order of a few percentage points for realistic parameter values.     

A Leland model for delta hedging in central risk books

Using a tractable extension of the model of Leland (1985), we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid–ask spreads, and volatilities. The corresponding option price—from which the option can be replicated using market and limit orders—is characterized via a nonlinear PDE. Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced-form models are competitive with “brute force” numerical approaches to market microstructure. Both the estimation of microstructure parameters and the simulation of the optimal trading strategy are made concrete and reconciled with real-life high frequency data.     

Exchange risk premia and firm characteristics

This paper examines the presence and the determinants of exchange risk premia in stock returns using firm level data from South Korea. We conduct empirical asset pricing tests based on cross-sectional data sorted by firm characteristics such as firm size, liquidity, foreign ownership, and industry. Using alternative model specifications and exchange rate measures, our results support the hypothesis of a significant unconditional exchange risk premium in the Korean stock market at firm and industry levels. More specifically, we find that the exchange risk premium is directly related to firm liquidity and inversely related to firm size and foreign ownership.     

A brighter future with lower transactions costs?

Recently, the OMX Nordic Exchange reduced the exchange fee for trading the OMXS 30 index futures with more than 22%. The reduction in exchange fees provides this study with a unique opportunity to investigate the effects of a change in fixed transaction costs on futures market liquidity, trading activity, volatility, futures pricing efficiency, and the futures exchange's revenues. The results show a ceteris paribus increase in futures trading volume with 19%, a 27% decrease in futures bid–ask spread, and a 27% increase in volatility, as a result of the futures exchange fee reduction, whereas the pricing efficiency of the futures contract and the exchange's revenues are unaffected by the change in transaction costs. The exchange fee reduction has improved futures market liquidity at the cost of higher volatility. Moreover, the attractiveness and competitiveness of the futures exchange has increased relative alternative trading venues, without a loss of revenues in the process. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:775–796, 2009     

What Influences Trader Choice of Electronic versus Intermediated Execution?

We examine the determinants of US equity trader choice of electronic versus intermediated execution. While traders exhibit a strong overall preference for automation, when the market is less liquid at order submission time, traders seek market maker automated and human order‐matching services more often. Traders' overall tendency to choose intermediaries is highly correlated with their demand for liquidity. Market maker participation rates are higher for more active and larger size traders. Traders who choose intermediaries more often trade more stocks, execute orders quicker, price orders more aggressively, and disperse their trading over longer periods of time. Although US stock intermediaries continue to lose market share, our results highlight the important role these firms can play in an increasingly automated, electronically driven marketplace.     

Liquidity,exchange listing,and common stock performance

The liquidity of securities—the relationship between volume of trading and changes in market price—has won increasing recognition as an element of investment strategy in recent years. Relatively high liquidity is deemed to be a desirable characteristic of a stock, especially for the institutional investor, who typically trades in large volume. Thus, firms can generally be expected to seek means of enhancing the liquidity of their shares. One of the supposed means of accomplishing this is by listing one's stock on a national securities exchange. This paper examines the relationship of common stock liquidity to both exchange listing and price behavior during major up and down movements in the market. Our conceptual and empirical analyses indicate that liquidity is linked to price behavior; and we suggest that the view held by at least some corporate officers—that exchange listing increases liquidity—may be erroneous. More specifically, it appears that when the amount of firm capitalization is taken into account, exchange listing does not result in greater stock liquidity.     

Volume and Volatility Surrounding Quarterly Redesignation of the Lead S&P 500 Futures Contract

During the last weeks before each quarterly expiration of Standard & Poor's (S&P) 500 futures, the bulk of trading volume begins to shift away from the next‐to‐expire (nearby or lead) contract toward the second‐to‐expire (next out) contract. At some point, the exchange formally redesignates the next out as the new lead contract, and the next out replaces the nearby in the futures pit location designated for the lead contract. This event invariably results in a dramatic increase (decrease) in trading activity in the next out (nearby) contract. This shift in relative trading volumes is due to the microstructure of the futures exchange rather than new information or underlying volatility conditions. The event thus offers us an opportunity to examine how volatility responds to noninformation‐based exogenous changes in volume. This study examines the volatility behavior of nearby and next out S&P 500 futures contracts on the 10 days surrounding quarterly redesignation of the lead contract. Our model measures possible changes in (a) the level of volatility and/or (b) the association between volume and volatility after redesignation of the lead contract. Results indicate that when we account for the association between volume and volatility, the higher volume lead contract consistently experiences a lower level of volatility. This outcome supports the view that the larger population of liquidity providers who trade the more active lead contract fosters greater market depth and lower volatility. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1119–1149, 2001     

MODEL‐INDEPENDENT NO‐ARBITRAGE CONDITIONS ON AMERICAN PUT OPTIONS

We consider the pricing of American put options in a model‐independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process.     

Liquidity effects of trading frequency

In this paper, we present a discrete‐time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). We use the proposed modeling framework to analyze the effects of trading frequency on market liquidity in a very general setting. In particular, we demonstrate the dual effect of high trading frequency. On the one hand, the higher frequency increases market efficiency, if the agents choose to provide liquidity in equilibrium. On the other hand, it also makes markets more fragile, in the sense that the agents choose to provide liquidity in equilibrium only if they are market neutral (i.e., their beliefs satisfy certain martingale property). Even a very small deviation from market neutrality may cause the agents to stop providing liquidity, if the trading frequency is sufficiently high, which represents an endogenous liquidity crisis (also known as flash crash) in the market. This framework enables us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so‐called adverse selection effect.     

How does FX liquidity affect the relationship between foreign ownership and stock liquidity?

This study investigates the roles foreign investors play in a representative emerging market, focusing on the relationship between foreign ownership and stock market liquidity as well as this relationship's response to foreign exchange (FX) liquidity. Our analyses yield three main results. First, the bid–ask spread and price impact of stock trades decrease along with foreign ownership, supporting the view that foreign investors tend to improve stock liquidity. Second, foreign ownership decreases along with a decline in FX liquidity, suggesting that foreign investors care about FX liquidity when determining their stock holdings. Third, stock liquidity increases continuously along with foreign ownership as FX liquidity decreases. Overall, this study's evidence indicates that foreign investors, as liquidity providers, can play a positive role in an emerging economy even when FX liquidity declines.     

DYNAMIC PORTFOLIO OPTIMIZATION WITH A DEFAULTABLE SECURITY AND REGIME‐SWITCHING

We consider a portfolio optimization problem in a defaultable market with finitely‐many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time Markov process. By separating the utility maximization problem into a predefault and postdefault component, we deduce two coupled Hamilton–Jacobi–Bellman equations for the post‐ and predefault optimal value functions, and show a novel verification theorem for their solutions. We obtain explicit constructions of value functions and investment strategies for investors with logarithmic and Constant Relative Risk Aversion utilities, and provide a precise characterization of the directionality of the bond investment strategies in terms of corporate returns, forward rates, and expected recovery at default. We illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economic and numerical analysis.     

Benchmarks in the spotlight: The impact on exchange traded markets

The Fix for precious metals is a global pricing benchmark that provides pricing and liquidity provision for market participants. We exploit the gradual change in the century old auction process to quantify the efficiencies related to more transparent pricing. Our focus is in the market impact of this change on exchange listed products. We find that reforms to the Fix have reduced quoted and effective bid-ask spreads and improved overall market depth. The results imply a positive spillover effect stemming from timelier and more accurate pricing information. The conditions under which we observe the benefits from transparency are related to product liquidity and the degree of market segmentation.     

ON THE TIMING OPTION IN A FUTURES CONTRACT

The timing option embedded in a futures contract allows the short position to decide when to deliver the underlying asset during the last month of the contract period. In this paper we derive, within a very general incomplete market framework, an explicit model independent formula for the futures price process in the presence of a timing option. We also provide a characterization of the optimal delivery strategy, and we analyze some concrete examples.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.