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Theses

Pro-cyclicality of risk measurements. Empirical quantification and theoretical confirmation

Abstract : This thesis examines, empirically and theoretically, the pro-cyclicality of risk measurements made on historical data. Namely, the effect that risk measurements overestimate the future risk in times of crisis, while underestimating it in quiet times. As starting point, we lay down a methodology to empirically evaluate the amount of pro-cyclicality when using a sample quantile (Value-at-Risk) process to measure risk. Applying this procedure to 11 stock indices, we identify two factors explaining the pro-cyclical behavior: The clustering and return-to-the-mean of volatility (as modeled by a GARCH(1,1)) and the very way of estimating risk on historical data (even when no volatility dynamics are present). To confirm these claims theoretically, we proceed in two steps. First, we derive bivariate (functional) central limit theorems for quantile estimators with different measure of dispersion estimators. We establish them for sequences of iid random variables as well as for the class of augmented GARCH(p,q) processes. Then, we use these asymptotics to theoretically prove the pro-cyclicality observed empirically. Extending the setting of the empirical study, we show that no matter the choice of risk measure (estimator), measure of dispersion estimator or underlying model considered, pro-cyclicality will always exist.
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Submitted on : Friday, April 30, 2021 - 2:42:08 PM
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Marcel Bräutigam. Pro-cyclicality of risk measurements. Empirical quantification and theoretical confirmation. Statistics [math.ST]. Sorbonne Université, 2020. English. ⟨NNT : 2020SORUS100⟩. ⟨tel-03213594⟩

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