Warnings About Future Jumps: Properties of the Exponential Hawkes Model

41 Pages Posted: 6 Oct 2019

See all articles by Rachele Foschi

Rachele Foschi

University of Pisa - Department of Economics

Francesca Lilla

Bank of Italy

Cecilia Mancini

University of Verona - Department of Economics

Multiple version iconThere are 4 versions of this paper

Date Written: September 25, 2019

Abstract

Having observed a cluster of jumps in the discrete prices of a financial asset, and modeling the jump arrival times with an exponential Hawkes process, we study and quantify the probability that the cluster is going to produce further jumps. We also provide bounds for the probability of observing a given number of consecutive jumps and formalize the stochastic increasingness property of the durations between two consecutive jumps.

As an empirical exercise, we apply our results to a record of the JPM asset prices. Firstly we show that the identified jumps display dependence and clustering behavior. Secondly, we find that, under the exponential Hawkes model delivering the best QQplot, our formulas indicate that the probability that a cluster of more than 1 jump produces a further jump is mostly close to 1.

Keywords: financial assets returns, truncation, clusters of jumps, conditional probability of a jump, exponential Hawkes process

JEL Classification: C02, C52, C58

Suggested Citation

Foschi, Rachele and Lilla, Francesca and Mancini, Cecilia, Warnings About Future Jumps: Properties of the Exponential Hawkes Model (September 25, 2019). Available at SSRN: https://ssrn.com/abstract=3459443 or http://dx.doi.org/10.2139/ssrn.3459443

Rachele Foschi (Contact Author)

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

Francesca Lilla

Bank of Italy ( email )

Via Nazionale 91
Rome, 00184
Italy

Cecilia Mancini

University of Verona - Department of Economics ( email )

via Cantarane 24
Verona, I-37129
Italy

HOME PAGE: http://https://www.dse.univr.it/?ent=persona&id=55236

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