Asset market equilibrium with liquidity risk

This paper derives an equilibrium asset pricing model with endogenous liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a strong set of assumptions, we prove that a unique equilibrium liquidity cost process and a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. We derive a generalized intertemporal CAPM and consumption CAPM for these markets. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.     

The “make or take” decision in an electronic market: Evidence on the evolution of liquidity

This paper uses experimental asset markets to investigate the evolution of liquidity in an electronic limit order market. Our market setting includes salient features of electronic limit order markets, as well as informed traders and liquidity traders. We focus on the strategies of the traders and how these are affected by trader type, characteristics of the market, and characteristics of the asset. We find that informed traders use more limit orders than do liquidity traders. Our main result is that liquidity provision shifts as trading progresses, with informed traders increasingly providing liquidity in markets. The change in the behavior of the informed traders seems to be in response to the dynamic adjustment of prices to information; they take (provide) liquidity when the value of their information is high (low). Thus, a market-making role emerges endogenously in our electronic markets and is ultimately adopted by the traders who are least subject to adverse selection when placing limit orders.     

The implications of liquidity and order flows for neoclassical finance

While liquidity and order flows are microstructure constructs, we show that they have profound implications for all of finance. In particular, liquidity is intimately connected with the fundamental building blocks of finance, namely, the pricing of risk, the powerful no-arbitrage theorems, and market efficiency. Large-sample studies of liquidity show that both liquidity and liquidity risk are priced in the cross-section of stock returns, the law of one price is more likely to hold in more liquid markets, and liquidity enhances market efficiency. Hence policies to enhance liquidity encourage efficiency and reduce costs of raising capital. Furthermore, order flows are powerful predictors of returns as well as the real economy.     

Reprint of: Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality

We examine the dynamics and the drivers of market liquidity during the financial crisis, using a unique volume-weighted spread measure. According to the literature we find that market liquidity is impaired when stock markets decline, implying a positive relation between market and liquidity risk. Moreover, this relationship is the stronger the deeper one digs into the order book. Even more interestingly, this paper sheds further light on so far puzzling features of market liquidity: liquidity commonality and flight-to-quality. We show that liquidity commonality varies over time, increases during market downturns, peaks at major crisis events and becomes weaker the deeper we look into the limit order book. Consistent with recent theoretical models that argue for a spiral effect between the financial sector’s funding liquidity and an asset’s market liquidity, we find that funding liquidity tightness induces an increase in liquidity commonality which then leads to market-wide liquidity dry-ups. Therefore our findings corroborate the view that market liquidity can be a driving force for financial contagion. Finally, we show that there is a positive relationship between credit risk and liquidity risk, i.e., there is a spread between liquidity costs of high and low credit quality stocks, and that in times of increased market uncertainty the impact of credit risk on liquidity risk intensifies. This corroborates the existence of a flight-to-quality or flight-to-liquidity phenomenon also on the stock markets.     

Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality

We examine the dynamics and the drivers of market liquidity during the financial crisis, using a unique volume-weighted spread measure. According to the literature we find that market liquidity is impaired when stock markets decline, implying a positive relation between market and liquidity risk. Moreover, this relationship is the stronger the deeper one digs into the order book. Even more interestingly, this paper sheds further light on so far puzzling features of market liquidity: liquidity commonality and flight-to-quality. We show that liquidity commonality varies over time, increases during market downturns, peaks at major crisis events and becomes weaker the deeper we look into the limit order book. Consistent with recent theoretical models that argue for a spiral effect between the financial sector’s funding liquidity and an asset’s market liquidity, we find that funding liquidity tightness induces an increase in liquidity commonality which then leads to market-wide liquidity dry-ups. Therefore our findings corroborate the view that market liquidity can be a driving force for financial contagion. Finally, we show that there is a positive relationship between credit risk and liquidity risk, i.e., there is a spread between liquidity costs of high and low credit quality stocks, and that in times of increased market uncertainty the impact of credit risk on liquidity risk intensifies. This corroborates the existence of a flight-to-quality or flight-to-liquidity phenomenon also on the stock markets.     

Liquidity Provision of Limit Order Trading in the Futures Market Under Bull and Bear Markets

Abstract:  This study investigates how limit orders affect liquidity in a purely order-driven futures market. Additionally, the possible asymmetric relationship between market depth and transitory volatility in bull and bear markets and the effect of institutional trading on liquidity provision behavior are examined as well. The empirical results demonstrate that subsequent market depth increases as transient volatility increases in bull markets. Market depth exhibits significantly positive relationship to subsequent transient volatility in bull markets. Additionally, although trading volume positively influences transient volatility in bull markets, no such relationship exists in bear markets. Liquidity provision decreases when institutional trading activity intensifies during bear markets. Thus, liquidity provision for limit orders differs between bull and bear markets.     

Optimal Dynamic Order Submission Strategies in Some Stylized Trading Problems

This study derives optimal dynamic order submission strategies for trading problems faced by three stylized traders: an uninformed liquidity trader, an informed trader and a value-motivated trader. Separate solutions are obtained for quote- and order-driven markets. The results provide practicable rules for how to trade small orders and how to manage traders. Transaction cost measurement methods based on implementation shortfall are proven to dominate other methods.
Since investors demand liquidity when they submit market orders and supply liquidity when they submit limit orders, the results improve our understanding of market liquidity. In particular, the models illustrate the role of time in the search for liquidity by characterizing the demand for and supply of immediacy.     

Discrete-time option pricing with stochastic liquidity

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant liquidity model of Madan (2010). With this extension, we can replicate the term and skew structures of bid-ask spreads typically observed in option markets. We show how to implement such a stochastic liquidity model within our framework using multidimensional binomial trees and we calibrate it to call and put options on the S&P 500.     

A market-clearing role for inefficiency on a limit order book

Limit order markets with stationary dynamics attract equal volumes of market orders and uncanceled limit orders, equalizing the supply and demand for liquidity and immediacy. To maintain this balance, market orders must share any benefit obtained by limit order traders from more efficient trading conditions, such as better order queuing policies. Therefore an efficient market places a low price on immediacy, producing small bid–ask spreads. Furthermore, when price-discreteness leads to a mainly constant spread, cutting the price tick raises surplus. This is modeled with a stochastic sequential game, using stationarity considerations to bypass direct analysis of traders’ intricate market forecasts.     

Uncovering the time-varying relationship between commonality in liquidity and volatility

This study examines the dynamic linkages between commonality in liquidity in international stock markets and market volatility. Using a recently proposed liquidity measure as input in a variance decomposition exercise, we show that innovations to liquidity in most markets are induced predominately by inter-market innovations. We also find that commonality in liquidity peaks immediately after large market downturns, coinciding with periods of crisis. The results from a dynamic Granger causality test indicate that the relationship between commonality in liquidity and market volatility is bi-directional and time-varying. We show that while volatility Granger-causes commonality in liquidity throughout the entire sample period, market volatility is enhanced by commonality in liquidity only in sub-periods. Our results are helpful for practitioners and policy makers.     

The world price of liquidity risk

This paper empirically tests the liquidity-adjusted capital asset pricing model of Acharya and Pedersen (2005) on a global level. Consistent with the model, I find evidence that liquidity risks are priced independently of market risk in international financial markets. That is, a security’s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity, as well as the covariance of its own liquidity with local and global market returns. I also show that the US market is an important driving force of global liquidity risk. Furthermore, I find that the pricing of liquidity risk varies across countries according to geographic, economic, and political environments. The findings show that the systematic dimension of liquidity provides implications for international portfolio diversification.     

Liquidity shocks and real GDP growth: Evidence from a Bayesian time-varying parameter VAR

We examine the dynamic impact of liquidity shocks resonating in stock and housing markets on real GDP growth. We fit a Bayesian time-varying parameter VAR model with stochastic volatility to US data from 1970 to 2014. GDP becomes highly sensitive to house market liquidity shocks as disruptions in the sector start to emerge, yet more resilient to stock market liquidity shocks throughout time. We provide substantial evidence in favour of asymmetric responses of GDP growth both across the business cycle, and among business cycle troughs. Stock and house market liquidity shocks explain, on average, 17% and 35% of the variation in GDP during the Great Recession, respectively.     

Limit order books and trade informativeness

In the microstructure literature, information asymmetry is an important determinant of market liquidity. The classic setting is that uninformed dedicated liquidity suppliers charge price concessions when incoming market orders are likely to be informationally motivated. In limit order book (LOB) markets, however, this relationship is less clear, as market participants can switch roles, and freely choose to immediately demand or patiently supply liquidity by submitting either market or limit orders. We study the importance of information asymmetry in LOBs based on a recent sample of 30 German Deutscher Aktienindex (DAX) stocks. We find that Hasbrouck's (1991) measure of trade informativeness Granger causes book liquidity, in particular that required to fill large market orders. Picking-off risk due to public news-induced volatility is more important for top-of-the book liquidity supply. In our multivariate analysis, we control for volatility, trading volume, trading intensity and order imbalance to isolate the effect of trade informativeness on book liquidity.     

Internalisation by electronic FX spot dealers

Dealers in over-the-counter financial markets provide liquidity to customers on a principal basis and manage the risk position that arises out of this activity in one of two ways. They may internalise a customer's trade by warehousing the risk in anticipation of future offsetting flow, or they can externalise the trade by hedging it out in the open market. It is often argued that internalisation underlies much of the liquidity provision in the currency markets, particularly in the electronic spot segment, and that it can deliver significant benefits in terms of depth and consistency of liquidity, reduced spreads, and a diminished market footprint. However, for many market participants, the internalisation process can be somewhat opaque, data on it are scarcely available, and even the largest and most sophisticated customers in the market often do not appreciate or measure the impact that internalisation has on their execution costs and liquidity access. This paper formulates a simple model of internalisation and uses queuing theory to provide important insights into its mechanics and properties. We derive closed form expressions for the internalisation horizon and demonstrate—using data from the Bank of International Settlement's triennial FX survey—that a representative tier 1 dealer takes on average several minutes to complete the internalisation of a customer's trade in the most liquid currencies, increasing to tens of minutes for emerging markets. Next, we analyse the costs of internalisation and show that they are lower for dealers that are willing to hold more risk and for those that face more price-sensitive traders. The key message of the paper is that a customer's transaction costs and liquidity access are determined both by their own trading decisions as well as the dealer's risk management approach. A customer should not only identify the externalisers but also distinguish between passive and aggressive internalisers, and select those that provide liquidity compatible with their execution objectives.     

Price dispersion in OTC markets: A new measure of liquidity

In this paper, we model price dispersion effects in over-the-counter (OTC) markets to show that, in the presence of inventory risk for dealers and search costs for investors, traded prices may deviate from the expected market valuation of an asset. We interpret this deviation as a liquidity effect and develop a new liquidity measure quantifying the price dispersion in the context of the US corporate bond market. This market offers a unique opportunity to study liquidity effects since, from October 2004 onwards, all OTC transactions in this market have to be reported to a common database known as the Trade Reporting and Compliance Engine (TRACE). Furthermore, market-wide average price quotes are available from Markit Group Limited, a financial information provider. Thus, it is possible, for the first time, to directly observe deviations between transaction prices and the expected market valuation of securities. We quantify and analyze our new liquidity measure for this market and find significant price dispersion effects that cannot be simply captured by bid-ask spreads. We show that our new measure is indeed related to liquidity by regressing it on commonly-used liquidity proxies and find a strong relation between our proposed liquidity measure and bond characteristics, as well as trading activity variables. Furthermore, we evaluate the reliability of end-of-day marks that traders use to value their positions. Our evidence suggests that the price deviations from expected market valuations are significantly larger and more volatile than previously assumed. Overall, the results presented here improve our understanding of the drivers of liquidity and are important for many applications in OTC markets, in general.     

Option market liquidity: Commonality and other characteristics

This study examines option market liquidity using Ivy DB's OptionMetrics data. We establish convincing evidence of commonality for various liquidity measures based on the bid–ask spread, volumes, and price impact. The commonality remains strong even after controlling for the underlying stock market's liquidity and other liquidity determinants such as volatility. Smaller firms and firms with a higher volatility exhibit stronger commonalities in option liquidity. Aside from commonality, we also uncover several other important properties of the option market's liquidity. First, information asymmetry plays a much more dominant role than inventory risk as a fundamental driving force of liquidity. Second, the market-wide option liquidity is closely linked to the underlying stock market's movements. Specifically, the options liquidity responds asymmetrically to upward and downward market movements, with calls reacting more in up markets and puts reacting more in down markets.     

Implied liquidity: Model sensitivity

The concept of implied liquidity originates from the conic finance theory and more precisely from the law of two prices where market participants buy from the market at the ask price and sell to the market at the lower bid price. The implied liquidity λ of any financial instrument is determined such that both model prices fit as well as possible the bid and ask market quotes. It reflects the liquidity of the financial instrument: the lower the λ, the higher the liquidity. The aim of this paper is to study the evolution of the implied liquidity pre- and post-crisis under a wide range of models and to study implied liquidity time series which could give an insight for future stochastic liquidity modeling. In particular, we perform a maximum likelihood estimation of the CIR, Vasicek and CEV mean-reverting processes applied to liquidity and volatility time series. The results show that implied liquidity is far less persistent than implied volatility as the liquidity process reverts much faster to its long-run mean. Moreover, a comparison of the parameter estimates between the pre- and post-credit crisis periods indicates that liquidity tends to decrease and increase for long and short term options, respectively, during troubled periods.     

Multimarket trading and corporate bond liquidity

Global bonds are international securities traded and settled efficiently in multiple markets. This paper examines global bonds to evaluate the effects of multimarket trading on corporate bond liquidity and pricing. The results show that global bonds are significantly more liquid than similar-sized domestic bonds of the same issuers, and their liquidity advantage is reflected in higher market valuations. These findings support microstructure models that predict a positive relation between the number of potential investors and liquidity in over-the-counter markets, and help explain the increasing use of global bonds by corporate issuers.     

Does high-frequency trading actually improve market liquidity? A comparative study for selected models and measures

The increasing volume of messages sent to the exchange by algorithmic traders stimulates a fierce debate among academics and practitioners on the impacts of high-frequency trading (HFT) on capital markets. By comparing a variety of regression models that associate various measures of market liquidity with measures of high-frequency activity on the same dataset, we find that for some models the increase in high-frequency activity improves market liquidity, but for others, we get the opposite effect. We indicate that this ambiguity does not depend only on the stock market or the data period, but also on the used HFT measure: the increase of high-frequency orders leads to lower market liquidity whereas the increase in high-frequency trades improves liquidity. We hypothesize that the observed decrease in market liquidity associated with an increasing level of high-frequency orders is caused by a rise in quote volatility.     

Market microstructure

It is assumed that a collection of market agents can be treated as a statistical ensemble. Their market activities are depicted as the stochastic generation of market orders according to a Poisson process. The objective is to effectively describe the ‘temporal microstructure’, or moment-to-moment trading activities in asset markets. Two basic models, ‘dealership’ vs. ‘auction’ markets (and their variants) are put forth. Implications are drawn from each model. The implications include several testable hypotheses regarding the aggregate behavior of markets and market-makers as well as some qualitative insight into the transaction-to-transaction nature of realistic exchange processes.