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Warnings about future jumps: properties of the exponential Hawkes model

Author

Listed:
  • Rachele Foschi

    (Università di Pisa)

  • Francesca Lilla

    (Banca d'Italia)

  • Cecilia Mancini

    (Department of Economics (University of Verona))

Abstract

Having observed a cluster of jumps produced by an exponential Hawkes process, we study and quantify the residual length of the cluster. We then formalize the stochastic increasingness property of the durations between two consecutive jumps, which strengthens their positive correlation. Finally we consider the case where the process is only observed discretely and provide bounds for the probability of observing a given number of consecutive jumps. As an empirical exercise, we apply our results to a record of JPM's asset prices. First, we show that the identified jumps display dependence and clustering behavior. Second, we find that, under the exponential Hawkes model delivering the best QQ-plot, our formulas indicate a very high probability that an observed cluster of more than 1 jump did not exhaust yet.

Suggested Citation

  • Rachele Foschi & Francesca Lilla & Cecilia Mancini, 2020. "Warnings about future jumps: properties of the exponential Hawkes model," Working Papers 13/2020, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:13/2020
    as

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    clusters of jumps; exponential Hawkes process; residual length of a cluster; conditional probability of a configuration of jumps; financial assets returns; truncation;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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