Central limit theorem for the realized volatility based on tick time sampling

A central limit theorem for the realized volatility estimator of the integrated volatility based on a specific random sampling scheme is proved, where prices are sampled with every ‘continued price change’ in bid or ask quotation data. The estimator is shown to be robust to market microstructure noise induced by price discreteness and bid–ask spreads. More general sampling schemes also are treated in case that the price process is a diffusion.     

Arbitrage and deflators in illiquid markets

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid–ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints.     

Does Anonymity Matter in Electronic Limit Order Markets?

We develop a model in which limit order traders possess volatilityinformation. We show that in this case the size of the bid–askspread is informative about future volatility. Moreover, ifvolatility information is in part private, we establish that(i) the size of the bid–ask spread and (ii) its informativenessabout future volatility should change in the same directionwhen limit order traders' identifiers stop being disclosed.We test these predictions using data from the Paris Bourse.As expected, we find that the average quoted spread and itsinformativeness are significantly smaller when limit order traders'identifiers are concealed. These findings suggest that the limitorder book is a channel for volatility information.     

Trades and Quotes: A Bivariate Point Process

This article formulates a bivariate point process to jointlyanalyze trade and quote arrivals. In microstructure models,trades may reveal private information that is then incorporatedinto new price quotes. This article examines the speed of thisinformation flow and the circumstances that govern it. A jointlikelihood function for trade and quote arrivals is specifiedin a way that recognizes that an intervening trade sometimescensors the time between a trade and the subsequent quote. Modelsof trades and quotes are estimated for eight stocks using Tradeand Quote database (TAQ) data. The essential finding for thearrival of price quotes is that information flow variables,such as high trade arrival rates, large volume per trade, andwide bid–ask spreads, all predict more rapid price revisions.This means prices respond more quickly to trades when informationis flowing so that the price impacts of trades and ultimatelythe volatility of prices are high in such circumstances.     

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.     

Optimal execution of open-market stock repurchase programs

This paper formalizes the following intuition about open-market share repurchases. Firms do open-market share repurchases to return free cash, which would otherwise be wasted. However, when the firm goes to buy its own shares with this cash, it has inside information and hence the actual execution is characterized by adverse selection. The market knows that the firm has inside information, and consequently the ask price is high to compensate for this adverse selection problem. This implies that, all else equal, the greater the adverse selection problem compared to the cash waste problem, the higher the ask price, and, therefore, the wider the bid–ask spread and the lower the share repurchase completion rate. We test this implication on a sample of U.S. firms and report evidence consistent with the model.     

The manipulation of closing prices

Before the introduction of a call auction at the close, the last minute of trading at the Paris Bourse was the most active of the whole day. Even though the bid–ask spread increased substantially, the probability of large and aggressive orders increased, as did price volatility. In addition, both the one-minute returns and the proportion of partially hidden orders increased. In this paper, we develop an agency-based model of closing price manipulation, which can account for these phenomena. In addition, we discuss the optimal closing price mechanism under manipulation.     

Dynamics of Trade-by-Trade Price Movements: Decomposition and Models

In this article we introduce a decomposition of the joint distributionof price changes of assets recorded trade-by-trade. Our decompositionmeans that we can model the dynamics of price changes usingquite simple and interpretable models which are easily extendedin a great number of directions, including using durations andvolume as explanatory variables. Thus we provide an econometricbasis for empirical work on market microstructure using timeseries of transaction data. We use maximum likelihood estimationand testing methods to assess the fit of the model to one yearof IBM stock price data taken from the New York Stock Exchange.     

The role of trading intensity estimating the implicit bid–ask spread and determining transitory effects

In this paper, we investigate the information content of trading intensity applying the Madhavan, Richardson and Roomans (1997) structural model to express trading intensity as trading momentum in duration and volume. Using both transactions and intraday data from the Helsinki Stock Exchange Limit Order Bookmarket, we find that momentum in duration and volume enhances the information effect. We reach this conclusion based on the parametric effect determined by the sign and the magnitude of the coefficients associated with the trading intensity variables, the trading effect determined by the ratio of transitory effects to permanent effects, and the economic effect determined by the size of the implicit bid–ask spread. While we find that the implicit bid–ask spread and transitory effects are decreasing toward the end of the trading day in consistency with information models in the literature, there is a surge of trades at the market close, most probably due to information uncertainty at market opening in New York.     

Foreign institutional ownership and stock market liquidity: Evidence from Indonesia

From January 2002 to August 2007, foreign institutions held almost 70% of the free-float value of the Indonesian equity market, or 41% of the total market capitalization. Over the same period, liquidity on the Jakarta Stock Exchange improved substantially with the average bid–ask spread more than halved and the average depth more than doubled. In this study we examine the Granger causality between foreign institutional ownership and liquidity, while controlling for persistence in foreign ownership and liquidity measures. We find that foreign holdings have a negative impact on future liquidity: a 10% increase in foreign institutional ownership in the current month is associated with approximately 2% increase in the bid–ask spread, 3% decrease in depth, and 4% rise in price sensitivity in the next month, challenging the view that foreign institutions enhance liquidity in small emerging markets. Our findings are consistent with the negative liquidity impact of institutional investor ownership in developed markets.     

The fundamental theorem of asset pricing under transaction costs

This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The RNFLVR condition implies that admissible strategies are predictable processes of finite variation. The Appendix develops an extension of the familiar Stieltjes integral for càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices.     

A super-replication theorem in Kabanov’s model of transaction costs

We prove a general version of the super-replication theorem, which applies to Kabanov’s model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued càdlàg bid-ask process evolving in continuous time. We propose a new definition of admissible portfolio processes as predictable (not necessarily right- or left- continuous) processes of finite variation related to the bid-ask process by economically meaningful relations. Under the assumption of existence of a strictly consistent price system (SCPS), we prove a closedness property for the set of attainable vector-valued contingent claims. We then obtain the super-replication theorem as a consequence of that property, thus generalizing to possibly discontinuous bid-ask processes analogous results obtained by Kabanov (Financ. Stoch. 3, 237–248, 1999), Kabanov and Last (Math. Financ. 12, 63–70, 2002) and Kabanov and Stricker (Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, pp 125–136, 2002). Rásonyi’s counter-example (Lecture Notes in Mathematics 1832, 394–398, 2003) served as an important motivation for our approach.     

Excess demand and equilibration in multi-security financial markets: the empirical evidence

Price dynamics are studied in a dataset of more than 11,000 transactions from large-scale financial markets experiments with multiple risky securities. The aim is to determine whether a few simple principles govern equilibration. We first ask whether price changes are driven by excess demand. The data strongly support this conjecture. Second, we investigate the presence of cross-security effects (the excess demands of other securities influence price changes of a security beyond its own excess demand). We find systematic cross-security effects, despite the fact that transactions in one market cannot be made conditional on events in other markets. Nevertheless, stability is not found to be compromised in our data. A curious relationship emerges between the signs of the cross-effects and the signs of the covariances of the payoffs of the corresponding securities. It suggests a link between price discovery in real markets and the Newton procedure in numerical computation of general equilibrium. Next, we investigate whether the book (the set of posted limit orders) plays a role in the process by which excess demand becomes reflected in transaction price changes. We find strong correlation between excess demands and a weighted average of the quotes in the book. The correlation is far from perfect, and we document that our weighted average of the quotes in the book explains part of the variance of transaction price changes that is unaccounted for by excess demands.     

Intraday dynamics of volatility and duration: Evidence from Chinese stocks

We propose a new joint model of intraday returns and durations to study the dynamics of several Chinese stocks. We include three U.S. stocks for comparison. Flexible innovation distributions are used for durations and returns, and the total variance of returns is decomposed into different volatility components associated with different transaction horizons. The new model provides strong improvements in density forecasts for duration and returns and only modest gains for points forecasts of the variance of returns. The conditional hazard functions are non-monotonic and there is strong evidence for different volatility components. Although diurnal patterns, volatility components, and market microstructure implications are similar across the markets, there are interesting differences. Durations for lightly traded Chinese stocks tend to carry more information than heavily traded stocks. Chinese investors usually have longer investment horizons, which may be explained by the specific trading rules in China.     

Valuation of default-sensitive claims under imperfect information

We propose a valuation method for financial assets subject to default risk, where investors cannot observe the state variable triggering the default but observe a correlated price process. The model is sufficiently general to encompass a large class of structural models and can be seen as a generalization of the model of Duffie and Lando (Econometrica 69:633–664, [2001]). In this setting we prove that the default time is totally inaccessible in the market’s filtration and derive the conditional default probabilities and the intensity process. Finally, we provide pricing formulas for default-sensitive claims and illustrate in particular examples the shapes of the credit spreads.      

Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model

The paper develops a general discrete-time framework for asset pricing and hedging in financial markets with proportional transaction costs and trading constraints. The framework is suggested by analogies between dynamic models of financial markets and (stochastic versions of) the von Neumann–Gale model of economic growth. The main results are hedging criteria stated in terms of “dual variables” – consistent prices and consistent discount factors. It is shown how these results can be applied to specialized models involving transaction costs and portfolio restrictions.     

Determinants of bid and ask quotes and implications for the cost of trading

Financial transaction costs are time varying. This paper proposes a model that relates transaction cost to characteristics of order flow. We obtain qualitatively consistent model results for different stocks and across different time periods. We find that an unusual excess of buyers (sellers) relative to sellers (buyers) tends to increase the ask (bid) price. Hence, the ask and bid components of spread change asymmetrically about the efficient price. For a fixed order imbalance surprise these effects are muted when unanticipated total volume is high. Unexpected high volatility in the transaction price process tends to widen the spread symmetrically about the efficient price. Our findings are consistent with predications from market microstructure theory that the cost of market making should depend on both the risk of trading with better-informed traders and inventory risk. We also find that order flow surprises have a significant impact on the efficient price and can also explain a substantial amount of persistence in the volatility of the efficient price. This dependence does not violate the efficient market hypothesis since the surprises, by definition, are not predictable.     

Trading activity and bid–ask spreads of individual equity options

We empirically examine the impact of trading activities on the liquidity of individual equity options measured by the proportional bid–ask spread. There are three main findings. First, the option return volatility, defined as the option price elasticity times the stock return volatility, has a much higher power in explaining the spread variations than the commonly considered liquidity determinants such as the stock return volatility and option trading volume. Second, after controlling for all the liquidity determinants, we find a maturity-substitution effect due to expiration cycles. When medium-term options (60–90 days maturity) are not available, traders use short-term options as substitutes whose higher volume leads to a smaller bid–ask spread or better liquidity. Third, we also find a moneyness-substitution effect induced by the stock return volatility. When the stock return volatility goes up, trading shifts from in-the-money options to out-of-the-money options, causing the latter’s spread to narrow.     

Adverse selection costs for NASDAQ and NYSE after decimalization

NYSE and NASDAQ completed their decimalization on January 29, 2001 and on April 9, 2001 respectively. In this paper, we compare adverse selection component of the bid–ask spread for NASDAQ and NYSE stocks after decimalization using the data from May 2001 and July 2001. We find that the adverse selection component of the bid–ask spread is significantly lower on NASDAQ than on NYSE, and these differences cannot be attributed to the differences in the characteristics of the stocks traded in the two markets. In addition, we find that the adverse selection costs increase with trade size on NYSE, however there is no monotonic pattern observed for NASDAQ stocks. Lastly, we report that although the order flows arrived in the two markets are significantly different, they can at best explain a small portion of the observed differences in adverse selection costs.     

Comparison of Option Prices in Semimartingale Models

In this paper we generalize the recent comparison results of El Karoui et al. (Math Finance 8:93–126, 1998), Bellamy and Jeanblanc (Finance Stoch 4:209–222, 2000) and Gushchin and Mordecki (Proc Steklov Inst Math 237:73–113, 2002) to d-dimensional exponential semimartingales. Our main result gives sufficient conditions for the comparison of European options with respect to martingale pricing measures. The comparison is with respect to convex and also with respect to directionally convex functions. Sufficient conditions for these orderings are formulated in terms of the predictable characteristics of the stochastic logarithm of the stock price processes. As examples we discuss the comparison of exponential semimartingales to multivariate diffusion processes, to stochastic volatility models, to Lévy processes, and to diffusions with jumps. We obtain extensions of several recent results on nontrivial price intervals. A crucial property in this approach is the propagation of convexity property. We develop a new approach to establish this property for several further examples of univariate and multivariate processes.