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The most extreme events, such as economic crises, are rare but often have a great impact. It is difficult to precisely determine the likelihood of such events because the sample is small.

Modeling and estimating persistent discrete data can be challenging. In this paper, we use an autoregressive panel probit model where the autocorrelation in the discrete variable is driven by the autocorrelation in the latent variable. In such a non-linear model, the autocorrelation in an unobserved variable results in an intractable likelihood containing high-dimensional integrals.

Worst-case analysis is used among financial regulators in the wake of the recent financial crisis to gauge the tail risk. We provide insight into worst-case analysis and provide guidance on how to estimate it. We derive the bias for the non-parametric heavy-tailed order statistics and contrast it with the semi-parametric extreme value theory (EVT) approach.

We explore properties of asymmetric generalized autoregressive conditional heteroscedasticity (GARCH) models in the threshold GARCH (GTARCH) family and propose a more general Spline-GTARCH model, which captures high-frequency return volatility, low-frequency macroeconomic volatility as well as an asymmetric response to past negative news in both autoregressive conditional heteroscedasticity (ARCH) and GARCH terms.

This paper estimates potential exposures, netting benefits and settlement gains by merging retail and wholesale payments into batches and conducting multiple intraday settlements in this hypothetical model of a single "calibrated payments system." The results demonstrate that credit risk exposures faced by participants in the system are largely dependent on their relative activity in the retail and wholesale payments systems.

The increasing importance of risk management in payment systems has led to the development of an array of sophisticated tools designed to mitigate tail risk in these systems. In this paper, we use extreme value theory methods to quantify the level of tail risk in the Canadian retail payment system (ACSS) for the period from 2002 to 2015.

This paper shows that changes in market participants’ fear of rare events implied by crude oil options contribute to oil price volatility and oil return predictability. Using 25 years of historical data, we document economically large tail risk premia that vary substantially over time and significantly forecast crude oil futures and spot returns.

The recent financial crisis has led to the development of new regulations to control risk in designated payment systems, and the implementation of new credit risk management standards is one of the key issues. In this paper, we study various credit risk management schemes for the Canadian retail payment system (ACSS) that are designed to cover the exposure of a defaulting member.

We measure systemic risk in the network of financial market infrastructures (FMIs) as the probability that two or more FMIs have a large credit risk exposure to the same FMI participant.

This paper proposes new measures of the integrated variance, measures which use high-frequency bid-ask spreads and quoted depths. The traditional approach assumes that the mid-quote is a good measure of frictionless price.