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Hawkes jump-diffusions and finance: a brief history and review

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  • Alan G. Hawkes

Abstract

A brief history of diffusions in Finance is presented, followed by an even briefer discussion of jump-diffusions that involve Poisson or Lévy jumps. The main purpose of the paper is then to discuss applications of self-exciting and mutually-exciting Hawkes point processes. After an outline of the basic properties of this class of processes, there is a review of some recent articles that show how incorporating them as contagious jumps into Financial diffusions may improve model fit, forecasting, pricing, hedging and portfolio management.

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  • Alan G. Hawkes, 2022. "Hawkes jump-diffusions and finance: a brief history and review," The European Journal of Finance, Taylor & Francis Journals, vol. 28(7), pages 627-641, May.
    • Handle: RePEc:taf:eurjfi:v:28:y:2022:i:7:p:627-641
    DOI: 10.1080/1351847X.2020.1755712
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    Cited by:

    1. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "A fractional Hawkes process for illiquidity modeling," LIDAM Discussion Papers ISBA 2023001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Kim, Hyun-Gyoon & Kim, Jeong-Hoon, 2023. "A stochastic-local volatility model with Le´vy jumps for pricing derivatives," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Fan Wu & Yang Shen & Xin Zhang & Kai Ding, 2024. "Optimal Claim-Dependent Proportional Reinsurance Under a Self-Exciting Claim Model," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1229-1255, June.

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