Abstract
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.
Highlights
We introduced a new class of stochastic models, which can be considered as a generalization of the multivariate general compound Hawkes process (MGCHP) in
We provided the numerical comparisons of the multivariate general compound point process (MGCPP) and MGCHP by real high-frequency trading data and we found that results of the new generalized model are as good as the MGCHP
We proposed a MGCPP model for the mid-price modeling in limit order book
Summary
We introduced a new class of stochastic models, which can be considered as a generalization of the multivariate general compound Hawkes process (MGCHP) in. We called this model the multivariate general compound point processes (MGCPP). FCLTs of the MGCPP can be viewed as a link between price volatility and the order flow We applied this asymptotic method to study the mid-price modeling in the limit order book (LOB). In Guo and Swishchuk (2020), they applied the multivariate Hawkes process to model the order flow of several stocks in limit order market and proved limit theorems for the MGCHP. We proposed a new mid-price model which is a generalization of the MGCHP and we called it the multivariate general compound point process (MGCPP). We proposed a multivariate stochastic model for the mid-price in the limit order book This is a generalization for models in Cont and De Larrard (2013), Guo and Swishchuk (2020), and Swishchuk (2017). H where λ(t) ≥ 0 and F N (t) is the corresponding natural filtration
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