Multivariate General Compound Point Processes in Limit Order Books

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.

Limit order books: a systematic review of literature

Purpose This study aims to provide a systematic literature review of the research study in the area of limit order book (LOB) mechanism of trading and its implications for market efficiency. The study attempts to document the recent theoretical developments and empirical findings from the literature exhaustively and identifies the research gaps for future research. Design/methodology/approach The study uses seven reputable databases to select 2,514 research studies spanning over 1981-2018 (finally compressed to a pool of 103 articles, based on relevance and impact). The study uses bibliometric network visualization and text analytics to categorize and examine the literature. The chosen articles are compiled and analyzed to provide a comprehensive account of the current research on LOBs. Findings The recent LOB literature is summarized on various criteria as follows: sub-areas, the types of economies and markets, methodologies and the LOB measures. The review identifies a dearth of studies on the LOBs in emerging markets. It suggests the potential research areas as intraday studies in emerging LOB markets; application of market indicators based on deeper levels of LOB, beyond the best prices; market fragmentation, order routing decision and its impact on order execution quality; optimal display of LOB levels; liquidity dynamics in quote-driven markets vis-à-vis LOB markets; effect of high-frequency trading on market microstructure; application of advanced techniques (e.g. machine learning models, zero-intelligent models); relationship between the trading speed, order aggressiveness, shape and resilience of the order book and informed trading; and information content of the auxiliary order submission strategies, including cancellation, amendments and hidden orders. Originality/value For the past 15 years, to the best of the knowledge, a comprehensive review of the literature on LOBs has not been published. The financial markets have transformed significantly over this period, driven by the adoption of LOBs, low latency trading and technological advancements in information dissemination. This article provides an extensive collection and classification of the literature on LOBs. This would be useful for the practitioners, future researchers and academics in the area of financial markets.

General Compound Hawkes Processes in Limit Order Books

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.