Keywords
Limit order book, Hawkes process, rough volatility, Volterra integral equations, high frequency trading
Abstract
We introduce a financial model for limit order book with two main features: First, the limit orders and market orders for the given asset both appear and interact with each other. Second, the high frequency trading (HFT, for short) activities are allowed and described by the scaling limit of nearly-unstable multi-dimensional Hawkes processes with power law decay. The model eventually becomes a stochastic partial differential equation (SPDE, for short) with the diffusion coefficient determined by a Volterra integral equation governed by a Hawkes process, whose Hurst exponent is less than 1/2, which makes the volatility path of the stochastic PDE rougher than that driven by a Brownian motion. We have further established the well-posedness of such a system so that a foundation is laid down for further studies in this direction.
Completion Date
2024
Semester
Spring
Committee Chair
Yong, Jiongmin
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematics
Format
application/pdf
Identifier
DP0028289
URL
https://purls.library.ucf.edu/go/DP0028289
Language
English
Rights
In copyright
Release Date
May 2024
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
Campus Location
Orlando (Main) Campus
STARS Citation
Chen-Shue, Yun S., "A Limit Order Book Model for High Frequency Trading with Rough Volatility" (2024). Graduate Thesis and Dissertation 2023-2024. 120.
https://stars.library.ucf.edu/etd2023/120
Accessibility Status
Meets minimum standards for ETDs/HUTs