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

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

Accessibility Status

Meets minimum standards for ETDs/HUTs

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