Affine Point Processes and Portfolio Credit Risk

Errais, Eymen; Giesecke, Kay; Goldberg, Lisa R.

doi:10.2139/ssrn.908045

Cited by 141 publications

(237 citation statements)

References 29 publications

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“…The classical econometric literature, such as [9,32,33,34,35], employ the Hawkes model with the exponential kernel ϕ(t) = α exp(−βt), which is not normalized and require the estimation of the two parameters {α, β}, which just have to obey the conditions α, β > 0. In contrast, the explicit definition of the branching ratio n = α/β (see Eq.…”

Section: Implementation Of the Maximum Likelihood Estimation Methodsmentioning

confidence: 99%

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

Filimonov

Sornette

2015

Quantitative Finance

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We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events. We report the following model biases: (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of outliers, (ii) strong effects on n resulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape. Moreover, we demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n ≃ 1) while the true value is actually n = 0. More generally, regime shifts on the parameters of the Hawkes model and/or on the generating process itself are shown to systematically lead to a significant upward bias in the estimation of the branching ratio. We demonstrate the importance of the preparation of the high-frequency financial data, in particular: (a) the impact of overnight trading in the analysis of long-term trends, (b) intraday seasonality and detrending of the data and (c) vulnerability of the analysis to day-to-day non-stationarity and regime shifts. Special care is given to the decrease of quality of the timestamps of tick data due to latency and grouping of messages to packets by the stock exchange. Altogether, our careful exploration of the caveats of the calibration of the Hawkes process stresses the need for considering all the above issues before any conclusion can be sustained. In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n ≃ 1) cannot be supported. In contrast, our previous results on E-mini S&P 500 Futures Contracts and on major commodity future contracts are upheld.

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Section: Implementation Of the Maximum Likelihood Estimation Methodsmentioning

confidence: 99%

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

Filimonov

Sornette

2015

Quantitative Finance

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“…The decay of g implies that the more recent events have stronger direct effects on the current event intensity than the events in the more remote past. Typical examples of g include the exponential decay function g(t, γ) = exp(−γt) and the polynomial function g(t, γ) = (1 + t) −γ , with γ > 0 (e.g., Errais et al, 2010;Ogata, 1988). The parameter α measures the initial magnitude of the self-exciting effect.…”

Section: The Coxsei(m) Model and The Estimation Proceduresmentioning

confidence: 99%

Modeling Event Clustering Using the m-Memory Cox-Type Self-Exciting Intensity Model

Chen¹,

Chen²

2014

IJSP

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In the analysis of point processes or recurrent events, the self-exciting component can be an important factor in understanding and predicting event occurrence. A Cox-type self-exciting intensity point process is generally not a proper model because of its explosion in finite time. However, the model with m-memory is appropriate to analyze sequences of recurrent events. It assumes the most recent m events multiplicatively affect the conditional intensity of event occurrence. Aside from the interpretability, one advantage is the simplicity of the estimation and inference-the Cox partial likelihood can be applied and the resulting estimator is consistent and asymptotically normal. Another advantage is that the model can be applied to the analysis of case-cohort data via the pseudolikelihood approach. The simulation studies support the asymptotic theory. Application is illustrated with analysis of a bladder cancer dataset and of an Australian stock index dataset, which shows evidence of self-excitation.

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“…Since we had only on process V(t) to start with, expectation E{} is taken with respect to a common process X(t). All Λ i (t)s are considered to be driven by X(t), for instance as Λ i (t) = a i X(t) + b i t for some parameters a i s and b i s. Expression (16) indicates that defaults are independent given a realization of X(t). For the unconditional individual survival probability Q i (t), we now have…”

Section: Finite Heterogeneous Collectionmentioning

confidence: 99%

Levy Subordinator Model: A Two Parameter Model of Default Dependency

Balakrishna¹

2011

SSRN Journal

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Affine Point Processes and Portfolio Credit Risk

Cited by 141 publications

References 29 publications

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

Modeling Event Clustering Using the m-Memory Cox-Type Self-Exciting Intensity Model

Levy Subordinator Model: A Two Parameter Model of Default Dependency

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