Abstract
Hawkes processes are a recent theme in the modeling of discrete financial events such as price jumps, trades and limit orders, basing the analysis on a continuous time formalism. We propose to simplify computation in Hawkes processes via a bounded delay density. We derive an Expectation-Maximization algorithm for maximum likelihood estimation, and perform experiments on high-frequency interbank currency exchange data. We find that while simplifying computation, the proposed model results in better generalization.
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References
Bacry, E., Mastromatteo, I., Muzy, J.F.: Hawkes processes in finance. Market Microstruct. Liquidity 1(01), 1550005 (2015)
Bacry, E., Jaisson, T., Muzy, J.F.: Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics. Quant. Financ. 16(8), 1179–1201 (2016)
Bowsher, C.G.: Modelling security market events in continuous time: intensity based, multivariate point process models. J. Economet. 141(2), 876–912 (2007)
Embrechts, P., Liniger, T., Lin, L.: Multivariate Hawkes processes: an application to financial data. J. Appl. Probab. 48(A), 367–378 (2011)
Hawkes, A.G.: Point spectra of some mutually exciting point processes. J. R. Stat. Soc. Ser. B Methodol. 438–443 (1971)
Jaisson, T., Rosenbaum, M.: Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab. 25(2), 600–631 (2015)
Linderman, S., Adams, R.: Discovering latent network structure in point process data. In: International Conference on Machine Learning, pp. 1413–1421 (2014)
Muni Toke, I., Pomponio, F.: Modelling trades-through in a limited order book using Hawkes processes. Economics 6 (2012)
Murphy, K.: Machine Learning a Probabilistic Perspective. The MIT Press, Cambridge (2012)
Rambaldi, M., Filimonov, V., Lillo, F.: Detection of intensity bursts using Hawkes processes: an application to high frequency financial data (2016). arXiv:1610.05383 [q-fin]
Simma, A., Jordan, M.I.: Modeling events with cascades of poisson processes. In: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, pp. 546–555. AUAI Press, Corvallis (2010)
Toke, I.M.: Market making in an order book model and its impact on the spread. In: Econophysics of Order-Driven Markets, pp. 49–64. Springer, Berlin (2011)
Veen, A., Schoenberg, F.P.: Estimation of space-time branching process models in seismology using an EM-type algorithm. J. Am. Stat. Assoc. 103(482), 614–624 (2008)
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Türkmen, A.C., Cemgil, A.T. (2018). Modeling High-Frequency Price Data with Bounded-Delay Hawkes Processes. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_90
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DOI: https://doi.org/10.1007/978-3-319-89824-7_90
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