Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets

This paper poses a few fundamental questions regarding the attributes of the volume profile of a Limit Order Books stochastic structure by taking into consideration aspects of intraday and interday statistical features, the impact of different exchange features and the impact of market participants in different asset sectors. This paper aims to address the following questions: 1. Is there statistical evidence that heavy-tailed sub-exponential volume profiles occur at different levels of the Limit Order Book on the bid and ask and if so does this happen on intra or interday time scales ? 2.In futures exchanges, are heavy tail features exchange (CBOT, CME, EUREX, SGX and COMEX) or asset class (government bonds, equities and precious metals) dependent and do they happen on ultra-high (<1sec) or mid-range (1sec -10min) high frequency data? 3.Does the presence of stochastic heavy-tailed volume profile features evolve in a manner that would inform or be indicative of market participant behaviors, such as high frequency algorithmic trading, quote stuffing and price discovery intra-daily? 4. Is there statistical evidence for a need to consider dynamic behavior of the parameters of models for Limit Order Book volume profiles on an intra-daily time scale ? Progress on aspects of each question is obtained via statistically rigorous results to verify the empirical findings for an unprecedentedly large set of futures market LOB data. The data comprises several exchanges, several futures asset classes and all trading days of 2010, using market depth (Type II) order book data to 5 levels on the bid and ask

Modelling the dynamics of the limit order book in financial markets

This thesis develops models and methods for the statistical properties of the limit order book for financial markets, a complex dynamical system of orders and cancellations, in continuous time and at multiple price levels. Initially, the heavy tailed features of limit order book volumes, aggregated to short, evenly spaced time intervals are investigated. These are found to require heavy tailed distributional models to adequately capture their statistical features. A novel process to transform the physically operating order book into data suitable for analysis is presented. Limitations for point process modelling, such as events frequently occurring at the same time, are established. The marked Hawkes process is identified as a suitable model for event clustering. This overcomes many data constraints by aggregating events, allowing additional information potentially impacting the intensity, to be incorporated in marks attached to these events. Marks are identified by empirical research, which is guided by available literature. A detailed description, methods of simulation, and parameter estimation of the univariate Hawkes process with multivariate marks is presented. This incorporates dependence features via copula models, with heavy tailed marginal distributions and requires substantial MATLAB implementation. Joint estimation via maximum likelihood, with the number and complexity of identified marks, necessitates the development of a method for screening marks that is computationally straightforward to implement. This new approach is based on the score test, which only requires the single fitting of the unboosted Hawkes process to the sequence of observed event times, together with the estimates of the moments of the functions of marks under assessment. The moments can be obtained parametrically, or non-parametrically. The test has an asymptotic chi-squared distribution under the null hypothesis that the marks do not impact the intensity. Extensive simulations confirm the power and utility of the test under realistic models and sample sizes. Application of the score test is made to futures data, and the identified serial dependence of the marks, leads to the new decoupled approximate method of likelihood estimation. This reduces model assumptions on statistical properties of the marks and leads to good performance of Hawkes process parameter estimation

Global economic burden of unmet surgical need for appendicitis

Background There is a substantial gap in provision of adequate surgical care in many low- and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially