Quantitative and comparative analyses of limit order books with general compound hawkes processes

Qiyue He and Anatoliy Swishchuk

In this paper, we solve the problem of mid price movements arising in high-frequency and algorithmic trading using real data. Namely, we introduce different new types of General Compound Hawkes Processes (GCHPDO, GCHP2SDO, GCHPnSDO) and find their diffusive limits to model the mid price movements of 6 stocks-EBAY, FB, MU, PCAR, SMH, CSCO. We also define error rates to estimate the models fitting accuracy. Maximum Likelihood Estimation (MLE) and Particle Swarm Optimization (PSO) are used for Hawkes processes and models parameters’ calibration.

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Year of publication:	2019
Authors:	He, Qiyue ; Sviščuk, Anatolij
Subject:	diffusive limit \| error measurements \| general compound Hawkes process \| maximum likelihood estimation (MLE) \| particle swarm optimization (PSO) \| Schätztheorie \| Estimation theory \| Maximum-Likelihood-Schätzung \| Maximum likelihood estimation \| Stochastischer Prozess \| Stochastic process

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