Real-time market microstructure analysis: online transaction cost analysis

Motivated by the practical challenge in monitoring the performance of a large number of algorithmic trading orders, this paper provides a methodology that leads to automatic discovery of causes that lie behind poor trading performance. It also gives theoretical foundations to a generic framework for real-time trading analysis. The common acronym for investigating the causes of bad and good performance of trading is transaction cost analysis Rosenthal [Performance Metrics for Algorithmic Traders, 2009]). Automated algorithms take care of most of the traded flows on electronic markets (more than 70% in the US, 45% in Europe and 35% in Japan in 2012). Academic literature provides different ways to formalize these algorithms and show how optimal they can be from a mean-variance (like in Almgren and Chriss [J. Risk, 2000, 3(2), 5–39]), a stochastic control (e.g. Guéant et al. [Math. Financ. Econ., 2013, 7(4), 477–507]), an impulse control (see Bouchard et al. [SIAM J. Financ. Math., 2011, 2(1), 404–438]) or a statistical learning (as used in Laruelle et al. [Math. Financ. Econ., 2013, 7(3), 359–403]) viewpoint. This paper is agnostic about the way the algorithm has been built and provides a theoretical formalism to identify in real-time the market conditions that influenced its efficiency or inefficiency. For a given set of characteristics describing the market context, selected by a practitioner, we first show how a set of additional derived explanatory factors, called anomaly detectors, can be created for each market order (following for instance Cristianini and Shawe-Taylor [An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, 2000]). We then will present an online methodology to quantify how this extended set of factors, at any given time, predicts (i.e. have influence, in the sense of predictive power or information defined in Basseville and Nikiforov [Detection of Abrupt Changes: Theory and Application, 1993], Shannon [Bell Syst. Tech. J., 1948, 27, 379–423] and Alkoot and Kittler [Pattern Recogn. Lett., 1999, 20(11), 1361–1369]) which of the orders are underperforming while calculating the predictive power of this explanatory factor set. Armed with this information, which we call influence analysis, we intend to empower the order monitoring user to take appropriate action on any affected orders by re-calibrating the trading algorithms working the order through new parameters, pausing their execution or taking over more direct trading control. Also we intend that use of this method can be taken advantage of to automatically adjust their trading action in the post trade analysis of algorithms.     

Non-constant rates and over-diffusive prices in a simple model of limit order markets

Abstract

Using simple particle models of limit order markets, we argue that the mid-term over-diffusive price behaviour is due to the variability of market order and limit order rates. Several rules for rate changes are considered. We obtain analytical results for bid-ask spread properties, Hurst plots and price increment correlation functions.     

Exact moments of order statistics from a power-function distribution

Summary

In this note a problem on exact moments of order statistics from a power-function distribution is considered. The characteristic function of the kth order statistic is obtained and moments about the origin of the kth order statistic are expressed in terms of gamma functions. An exact expression for the covariance of any two order statistics Y_i < Y_j is obtained in terms of beta and gamma functions. Various recurrence relations between the expected values of order statistics are also obtained.     

The distributions of the first and second order moments,the partial correlation coefficients and the multiple correlation coefficient in samples from a normal multivariate population

Abstract

1. When the frequency function of a statistical variable is known, one of the most important tasks of Theoretical Statistics is to find the frequency functions of some simple functions of this variable. The most important are the first and second order moments in a sample containing a certain number of values of the variable.     

Another pragmatic loss reserving method or Bornhuetter-Ferguson revisited

Abstract

The efficiency of an approximate credibility method for predicting outstanding claims in reinsurance, is analysed. The advantage of the approximate method is, that it does not require exact knowledge of the model's second order moments.     

Prospect and Markowitz stochastic dominance

Levy and Wiener (J Risk Uncertain 16(2), 147–163, 1998), Levy and Levy (Manage Sci 48(10), 1334–1349, 2002; Rev Fin Stud 17(4), 1015–1041, 2004) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be ‘the opposite of’ or ‘the same as’ their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.     

On Bonus and Bonus Prognoses in Life Insurance

The surplus on a life insurance policy is defined, at any time during the term of the contract, as the difference between the second order retrospective reserve and the first order prospective reserve. General principles for redistribution of the systematic part of the surplus as bonus are formulated, and various special bonus schemes are discussed. Techniques for forecasting future bonuses are worked out in an extended model with stochastic experience basis. Numerical illustrations are provided.     

Corporate investment and earnings surprises

ABSTRACT

We find that firm-level investment is negatively related to the likelihood of meeting or beating analysts’ short-term EPS forecasts. In a 35-year panel dataset of US based companies, we find evidence that suggests firms with the best growth opportunities, opaque firms, and firms with higher than usual bonus compensation, are the ones to alter investment in order to beat benchmarks. Utilizing the passage of Sarbanes-Oxley as a natural experiment we find that firms trade off accruals-based earnings management in lieu of investment cuts. Results are robust to a number of covariates, and endogeneity or reverse causality does not seem to drive our inferences. This study suggests that, consistent with survey results from Graham, Harvey, and Rajgopal [2005. “The Economic Implications of Corporate Financial Reporting.” Journal of Accounting and Economics 40: 3–73], managers may reduce or delay corporate investment to meet or beat short-term earnings benchmarks.     

The role of volume in order book dynamics: a multivariate Hawkes process analysis

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184–2202] can be successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyse interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.     

Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling

We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in the market’s view as in reduced-form credit risk models. However, we show that, in equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider’s trades are inconspicuous.      

Some properties of the ruin function in the collective theory of risk

Abstract

It is well known that the chief aim of all theory of risk is to attain a sort of objective and somehow confirmed opinion of how and to which extent an insurance company ought to reinsure its risks in order that the probability of ruin by random fluctuations of the risk process shall become so small that it can be overlooked in practice.     

Stochastic Orderings of Convex-Type for Discrete Bivariate Risks

New classes of order relations for discrete bivariate random vectors are introduced that essentially compare the expectations of real functions of convex-type of the random vectors. For the actuarial context, attention is focused on the so-called increasing convex orderings between discrete bivariate risks. First, various characterizations and properties of these orderings are derived. Then, they are used for comparing two similar portfolios with dependent risks and for constructing bounds on several multilife insurance premiums.     

T. B. Sprague

1. Introduction.

The object of this work is to show that the effective rate of interest of loans practically can be calculated with so great an accuracy that all practical demands regarding accuracy are more than satisfied. As will be seen from section 5, the effective rate of interest can be very quickly calculated by use of inverse linear interpolation for ordinarily occurring cases with a result which in general is correct with 3, 4 or more figures all according to practical demands. These methods can generally be used for all types of loans.     

Random walks,liquidity molasses and critical response in financial markets

Stock prices are observed to be random walks in time despite a strong, long-term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long-ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative Finance, 2004, 4, 176, where the impact is instead transient, with a power-law decay in time. The exponent of this decay is precisely tuned to a critical value, ensuring simultaneously that prices are diffusive on long time scales and that the impact function is nearly lag independent. We provide new analysis of empirical data that confirm and make more precise our previous claims. We show that the power-law decay of the bare impact function comes both from an excess flow of limit order opposite to the market order flow, and to a systematic anti-correlation of the bid–ask motion between trades, two effects that create a ‘liquidity molasses’ which dampens market volatility.     

Distortion Risk Measures and Economic Capital

Abstract

To provide incentive for active risk management, it is argued that a sound coherent distortion risk measure should preserve some higher degree stop-loss orders, at least the degree-three convex order. Such risk measures are called tail-preserving risk measures. It is shown that, under some common axioms and other plausible conditions, a tail-preserving coherent distortion risk measure identifies necessarily with the Wang right-tail measure or the expected value measure. This main result is applied to derive an optimal economic capital formula.     

Why Do Stock Prices Drop by Less Than the Amount of the Dividend? Evidence from a Unique Environment

Abstract:

This paper investigates the effect of a lack of an automated limit order adjustment mechanism on ex-dividend day stock price behavior in a unique environment in which there are no taxes on dividends and capital gains. It finds that the overnight drop in the ask price is smaller than the overnight drop in the bid price. In addition, the study finds that average price drops are smaller than the dividend amount for all dividend sizes. I also find no evidence of a sawtooth-shaped relationship between the dividend amount and the ex-day price drop. These results are generally consistent with the lack of an automated limit order adjustment mechanism.     

On a family of counting distributions and recursions for related compound distributions

Abstract

This paper considers a family of counting distributions whose densities satisfy certain second order difference equations. Recursions for the evaluation of related compound distributions are developed in the case of severity distributions which are concentrated on the non-negative integers. From these a characterization of the considered counting distributions is obtained, and it is shown that most of these are compound Poisson distributions.     

Order preferencing, adverse-selection costs, and the probability of information-based trading

Although prior studies offer various conjectures on the causes and consequences of order preferencing, there is only limited empirical evidence. In this study, we show that the extent of order preferencing is significantly and negatively related to both the adverse-selection component of the spread and the probability of information-based trading. This result is consistent with the prediction of the clientele-pricing hypothesis that dealers (brokers) selectively purchase (internalize) orders based on information content. Our results suggest that order preferencing may not be as harmful as some researchers have suggested and offer some rationale for its prevalence in securities markets with heterogeneously informed traders. JEL Classification G18 · G19     

Coping with Suicide Attacks: Lessons from Israel

This article describes research on the challenges that suicide attacks and other mass casualty attacks have posed to policy-makers and first responders in Israel. The authors describe a model of response to attacks which focuses on defensive responses to terrorism: prevention, crisis management and reconstruction. The authors draw out the lessons for other countries and discuss the problems that still need to be addressed in order to cope effectively with current and future terrorist attacks.     

Overcoming trade union resistance to local change

As Labour councils throughout the country are discovering, it is not just the Tories who are obsessed by the need for efficiency in the provision of services. And it is not just Margaret Thatcher who has to take on the unions in order to achieve it.