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A marked point process model for intraday financial returns: modeling extreme risk

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Abstract

Forecasting the risk of extreme losses is an important issue in the management of financial risk and has attracted a great deal of research attention. However, little attention has been paid to extreme losses in a higher frequency intraday setting. This paper proposes a novel marked point process model to capture extreme risk in intraday returns, taking into account a range of trading activity and liquidity measures. A novel approach is proposed for defining the threshold upon which extreme events are identified taking into account the diurnal patterns in intraday trading activity. It is found that models including covariates, mainly relating to trading intensity and spreads offer the best in-sample fit, and prediction of extreme risk, in particular at higher quantiles.

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Notes

  1. Other functional forms of returns are possible to capture the intraday behavior, for instance, squared returns. However, according to preliminary results, the choice of absolute values is preferred.

  2. We tried higher orders, but little is gained in the results observed.

  3. The objective of this random variable \(\epsilon \) with small variance is to help to break ties between test values.

  4. For instance, a risk manager could be more interested in the iid property of the exceptions during crisis period by choosing a lower level of a, instead of a correct unconditional coverage.

  5. From a risk management perspective, using different values of \(\delta \) reflects different levels of risk-aversion. For instance, \(\delta =0.5\) gives a weight around \((0.6-\alpha )\) to the observations for which \(X_{t}<\hbox {VaR}_{\alpha }^{t}\), while that \(\delta =2.5\) and \(\delta =5\) give a weight around \((0.8-\alpha )\) and \((1-\alpha )\), respectively.

  6. This is the check function introduced by Koenker and Bassett Jr (1978) and is defined as \(\ell \left( X_{t},\hbox {VaR}_{\alpha }^{t}\right) =\left( \mathbf {1}\left\{ X_{t}>\hbox {VaR}_{\alpha }^{t}\right\} -\alpha \right) \left( X_{t}-\hbox {VaR}_{\alpha }^{t}\right) \), where \(\mathbf {1}\left\{ X_{t}>\hbox {VaR}_{\alpha }^{t}\right\} \) is an indicator function that takes the value 1 when the return observed is larger than the VaR estimated for the day t at the given confidence level \(\alpha \) and the value 0 otherwise.

  7. A Newey–West heteroskedasticity and autocorrelation-consistent (HAC) estimator is used to obtain the covariance matrix for these statistics.

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Acknowledgements

Herrera acknowledges the Chilean CONICYT funding agency for financial support (FONDECYT 1180672) for this project.

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Authors and Affiliations

  1. Facultad de Economía y Negocios, Universidad de Talca, Talca, Chile

    Rodrigo Herrera

  2. School of Economics and Finance, Queensland University of Technology, Brisbane, Australia

    Adam Clements

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  1. Rodrigo Herrera
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  2. Adam Clements
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Correspondence to Rodrigo Herrera.

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Herrera, R., Clements, A. A marked point process model for intraday financial returns: modeling extreme risk. Empir Econ 58, 1575–1601 (2020). https://doi.org/10.1007/s00181-018-1600-y

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