Multivariate General Compound Hawkes and Point Processes with Financial Applications

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dc.contributor.advisorSwishchuk, Anatoliy
dc.contributor.authorGuo, Qi
dc.contributor.committeememberQiu, Jinniao
dc.contributor.committeememberBadescu, Alexandru
dc.contributor.committeememberWare, Antony
dc.contributor.committeememberHyndman, Cody
dc.contributor.committeememberSwishchuk, Anatoliy
dc.date2023-11
dc.date.accessioned2022-10-25T20:18:52Z
dc.date.available2022-10-25T20:18:52Z
dc.date.issued2022-10-20
dc.description.abstractThe Hawkes process (HP) significantly affected the financial modeling area in the past 15 years, especially high-frequency trading. This thesis focuses on various new Hawkes processes and considers their applications in the limit order book (LOB). Preexisting studies of the HP in the LOB showed that the arrivals of orders could be modeled by univariate or multivariate HP because of its long memory property and clustering effect. Therefore, we propose the multivariate general compound Hawkes process (MGCHP), a stochastic model for the mid-price in the LOB. For the MGCHP, we prove the Law of Large Numbers (LLN) and two Functional Central Limit Theorems (FCLT); the latter provides insights into the link between price volatilities and order flows in limit order books with several assets. The parameter estimation for the high-dimensional Hawkes process is always time-consuming. This motivates us to consider a generalization of the MGCHP. We replace the multivariate HP with a more general point process, and we call it the multivariate general compound point process (MGCPP). We also prove limit theorems for the MGCPP and compared numerical simulations for the MGCPP with the MGCHP. The MGCHP model provides us with a perfect framework for the stock price dynamics in the LOB. It’s natural to apply it to other financial applications. We extend the MGCHP to the exponential MGCHP (EMGCHP) and consider the corresponding asset-liability management problem. Risky assets are molded by the EMGCHP while the liability follows a Brownian motion with drift. We derive the Hamilton–Jacobi–Bellman equation and transformed it into a system of PDEs. With the FCLT, we can approximate the EMGCHP to a geometric Brownian motion in the LOB and apply Xie et al.’s results. Numerical simulations for the Hawkes-based model and comparisons with the Poisson-based model are also provided. In the last part of the thesis, we give an option pricing formula under the EMGCHP framework. We believe our study can provide a strong tool for not only researchers but also traders in the high-frequency market.en_US
dc.identifier.citationGuo, Q. (2022). Multivariate general compound Hawkes and point processes with financial applications (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.urihttp://hdl.handle.net/1880/115378
dc.identifier.urihttps://dx.doi.org/10.11575/PRISM/40367
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectHawkes processesen_US
dc.subjectmultivariate general compound Hawkes processesen_US
dc.subjectlimit order booksen_US
dc.subjectpoint processesen_US
dc.subjectfunctional central limit theoremsen_US
dc.subjectlaw of large numbersen_US
dc.subjectasset-liability managementen_US
dc.subjectoption pricingen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.subject.classificationEconomics--Financeen_US
dc.titleMultivariate General Compound Hawkes and Point Processes with Financial Applicationsen_US
dc.typedoctoral thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
ucalgary.item.requestcopytrueen_US
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