Abstract
In this paper, we further study various new Hawkes processes, namely, so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLN) and Functional Central Limit Theorems (FCLT) for these processes. The latter two FCLTs are applied to limit order books where we use these asymptotic methods to study the link between price volatility and order flow in our two models by studying the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes.
Highlights
The Hawkes process (HP) is named after its creator, Hawkes (1971); Hawkes and Oakes (1974).The Hawkes Processes (HPs) is a simple point process equipped with a self-exciting property, clustering effect and long run memory
We study various new Hawkes processes, namely general compound Hawkes processes to model the price process in limit order books
The main contribution and novelty of. He and Swishchuk (2019) paper consists of considering different types of general compound Hawkes processes and their diffusive limits to model the mid-prices of six different stocks
Summary
The Hawkes process (HP) is named after its creator, Hawkes (1971); Hawkes and Oakes (1974). Self-exciting point processes have recently been applied to high frequency data for price changes Bacry et al (2011) or order arrival times Embrechts et al (2011). We study various new Hawkes processes, namely general compound Hawkes processes to model the price process in limit order books. He and Swishchuk (2019) paper consists of considering different types of general compound Hawkes processes and their diffusive limits to model the mid-prices of six different stocks. The paper Swishchuk et al (2017) deals with compound and regime-switching Hawkes processes to model the mid-price processes in limit order books. Dassios and Zhao (2011), and Hawkes processes with generation dependent kernels Mehrdad and Zhu (2014), to name a few
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