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Summary

We developed a simple method to estimate the Hawkes branching ratio, a key measure for financial markets. This approach uses readily available data, simplifying analysis of market endogeneity and critical dynamics in S&P futures.

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Area of Science:

  • Quantitative Finance
  • Statistical Modeling
  • Point Processes

Background:

  • Hawkes self-exciting point processes model event occurrences.
  • The branching ratio is crucial for understanding market endogeneity.
  • Estimating the branching ratio traditionally requires complex numerical methods.

Purpose of the Study:

  • To introduce a model-independent approximation for the Hawkes branching ratio.
  • To simplify the estimation of the Hawkes branching ratio using empirical data.
  • To support findings on the critical nature of Hawkes models for S&P futures.

Main Methods:

  • Developed a model-independent approximation for the Hawkes branching ratio.
  • Utilized mean and variance of event counts in a large time window for estimation.
  • Compared the new method with numerical likelihood maximization.

Main Results:

  • The proposed estimator simplifies branching ratio estimation.
  • The method requires only mean and variance of event counts.
  • Empirical application supports critical dynamics in S&P futures price changes.

Conclusions:

  • The new approximation offers an efficient way to estimate the Hawkes branching ratio.
  • Financial markets, like S&P futures, exhibit critical behavior indicated by the branching ratio.
  • This method facilitates analysis of market endogeneity and long memory effects.