Applying Peaks-Over-Threshold EVT to Financial Returns

Summary

The note asks whether peaks-over-threshold extreme value methods can be applied directly to daily arithmetic returns rather than to portfolio profit and loss. It describes a two-step workflow: use a mean-excess plot to help select a threshold, then fit a generalized Pareto distribution (GPD) to observations beyond that threshold. The question also raises fitting the tail model to residuals from a time-series or volatility model, such as an ARMA or GARCH specification, and asks which approach is preferable.

The response says that applying peaks-over-threshold methods to returns is possible and points to an example of EVT applied to returns. It does not compare returns, PnL, or model residuals, nor does it identify a universally best choice. The evidence provided is a brief reference rather than a detailed empirical analysis. Consequently, the note supports the basic feasibility of fitting a tail model to returns, while leaving practical choices—such as the target measure, threshold selection, dependence, and model diagnostics—unresolved.

Key ideas

• Peaks-over-threshold analysis uses a threshold to isolate tail observations for modeling.
• A mean-excess plot can help assess candidate thresholds before fitting a generalized Pareto distribution.
• The response indicates that EVT can be applied to returns as well as financial losses.
• The note does not compare direct return modeling with PnL or residual-based approaches.
• It provides no universal recommendation or detailed empirical evidence for choosing among those inputs.

Tags

# Extreme Value Theory: GPD application to returns, not losses (PnL)?


# Extreme Value Theory: GPD application to returns, not losses (PnL)?












As it is often presented, Extreme Value Theory (EVT) is applied to financial losses (and gains as well, but always focusing in the tails). By EVT, I especially refer to:

1) Mean excess plot to find an appropriate threshold 2) Generalized Pareto Distribution (GPD) to fit to the data in the tail, beyond the estimated threshold in 1).

My question is: does it make sense to apply steps 1) and 2) to daily (arithmetic) returns, and not to PnL?

I have also seen some cases where steps 1) and 2) are applied to the residuals of a fitted model, e.g. ARMA or GARCH.

Which approach is the best?

Thanks

## Answer by Ami44 (score 1, accepted)

https://quant.stackexchange.com/a/34402

I don't see a reason why it should not be possible to apply peak-over-threshold to the returns.

Also see page 15 of https://www.soa.org/library/newsletters/risk-management-newsletter/2009/september/jrm-2009-iss17-levine.pdf

They use EVT on returns.

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