Littérature scientifique sur le sujet « Elicitabilità »

Risk measures are used not only for financial institutions’ internal risk management but also for external regulation (e.g., in the Basel Accord for calculating the regulatory capital requirements for financial institutions). Though fundamental in risk management, how to select a good risk measure is a controversial issue. We review the literature on risk measures, particularly on issues such as subadditivity, robustness, elicitability, and backtesting. We also aim to clarify some misconceptions and confusions in the literature. In particular, we argue that, despite lacking some mathematical convenience, the median shortfall—that is, the median of the tail loss distribution—is a better option than the expected shortfall for setting the Basel Accords capital requirements due to statistical and economic considerations such as capturing tail risk, robustness, elicitability, backtesting, and surplus invariance.

Le misure di rischio e l’asset allocation sono questioni di fondamentale importanza per i mercati finanziari. Lo studio è suddiviso in due parti. Nella prima parte vengono dimostrate proprietà molto importanti per il Lambda Value at Risk, mentre nella seconda parte vengono utilizzati modelli Markov Switching per modellizzare i rendimenti di serie finanziarie e viene introdotta una regola di trade basata sui regimi. L’ultima crisi finanziaria ha evidenziato le debolezze del Value at Risk. Per questo l’interesse verso misure di rischio alternative è aumentato notevolmente negli ultimi anni. In questo studio viene dimostrato che il Lambda Value at Risk è robuto ed elicitabile in particolari famiglie di distribuzioni ed è anche consistente. Il comportamento dei mercati finanziari è generalmente sottoposto a radicali cambiamenti quando si verificano guerre, crisi politiche o economiche ed altri eventi. Tali cambiamenti non sono permanenti ma possono persistere per periodi più o meno lunghi. Questo si rispecchia in alcune caratteristiche proprie delle serie storiche finanziare come ad esempio l’eccesso di kurtosis, gli effetti di skewness e la volatilità non costante. I modelli Markov Switching riescono a catturare questi cambiamenti che si verificano in maniera non deterministica e possono persistere per alcuni periodi dopo il cambiamento. Più precisamente, utilizziamo misture Markov Switching di distributioni normali fissando il numero di stati a N=2 corrispondenti a Normale Volatilità e Alta Volatilità. Gli obiettivi dello studio sono fondamentalmente due. Prima di tutto i parametri del modello vengono stimati attraverso Gibbs Sampling. Successivamente viene presentata una regola di trade basata sui regimi e confrontata con una semplice strategia buy-and-hold. Il database consiste in rendimenti giornalieri da Gennaio 1997 a Giugno 2018. Vengono analizzate diverse asset class appartenenti a diverse aeree geografiche. Il modello Markov-Switching è stato stimato tanto a livello univariato per le singole serie storiche quanto a livello multivariato trattando i processi correlativi tra le asset class. Per quanto riguarda l’univariato la maggior parte degli indici mostrano due stati nettamente separati con lo stato di Volatilità Normale come stato predominante. In generale le volatilità in Alta volatilità sono doppie rispetto a quella in Volatilità Normale. Il caso multivariato invece mostra che lo stato di Alta Volatilità è caratterizzato da un aumento delle correlazioni. L’esistenza di due regimi con caratteristiche diverse tra loro evidenzia la necessità di utilizzare strategie di trading differenti. Nell’ultima parte dello studio viene analizzata una strategia di trading basata sui regimi.
Risk measures and Asset allocation are a matter of primary concern for the financial market. My study is divided into two parts. In the first part important properties of the Lambda Value at Risk are showed. In the second part Markov Switching models are used to handle the stocks returns and regime-based trade rule is introduced. The last global financial crisis has highlighted the lacks of the Value at Risk. Thus, the interest on alternative risk measures has considerably increased in the last years. In this study we showed that Lambda Value at Risk is robust and elicitable within particular classes of distributions. In addition, it also satisfies the consistency property without any condition on the mechanism generating data. The behavior of financial markets may be changed radically when wars, economical or political crises and other events occur. This changes are generally not permanent but persist for longer or shorter periods of time. This is reflected in certain specific features of financial time series such as the leptokurtosis, the skewness and the heteroskedasticity. Markov Switching models can handle these behavioral changes that occur randomly and persist for several periods after the change. Specifically, we model the returns by a Markov Switching mixture of gaussian distributions and we fix the number of regimes to N=2 corresponding to Normal Volatility and High Volatility. The purpose of the study is twofold. First of all, the model is estimated using Markov Chain Monte Carlo methods. Specifically Gibbs Sampling algorithm is used. Secondly, regime-based trade rule is presented and compared with a buy-and-hold strategy. The data consists of daily returns from Jan 1997 to June 2018. We analyzed different Asset classes across different geographic areas. We estimate both univariate and multivariate Markov Switching models to take into account the correlations among asset classes. In the univariate case, most indices exhibit two states clearly separated and Normal Volatility state is the predominant State. In general, the volatilities in High Volatility are twice those in Normal Volatility. The multivariate case showed that High Volatility state is characterize by an increase of correlations. Thus, the diversification could be only apparent. The existence of two regimes with different features leads to the necessity of different strategies. In the last part of the study a trade rule regime-based is analyzed.

In recent years, the question of whether Expected Shortfall is possible to backtest has been a hot topic after the findings of Gneiting in 2011 that Expected Shortfall lacks a mathematical property called elicitability. However, new research has indicated that backtesting of Expected Shortfall is in fact possible and that it does not have to be very difficult. The purpose of this thesis is to show that Expected Shortfall is in fact backtestable by providing six different examples of how a backtest could be designed without exploiting the property of elicitability. The different approaches are tested and their performances are compared against each other. The material can be seen as guidance on how to think in the initial steps of the implementation of an Expected Shortfall backtest in practice.
De senaste åren har frågan om huruvida det är möjligt att hitta backtester som validerar Expected Shortfall varit ett omdiskuterat ämne efter att Gneiting 2011 visade att Expected Shortfall saknade den matematiska egenskapen som kallas elicitabilitet. Ny forskning tyder på att det går att validera Expected Shortfall och att det inte behöver vara alltför svårt. Syftet med den här uppsatsen är att visa att det går att hitta metoder som backtestar Expected Shortfall. Vi gör det genom att visa utförandet av sex olika metoder som validerar Expected Shortfall utan att använda sig av elicitabilitet. De olika metoderna testas och deras egenskaper jämförs mot varandra. Materialet kan ses som en guide i hur man ska tänka i de första stegen i implementeringen av en metod för att backtesta Expected Shortfall.

AbstractThis chapter is the core theoretical chapter on predictive modeling, forecast evaluation and model selection. The main problem in actuarial modeling is to forecast and price future claims. For this, we build predictive models, and this chapter deals with assessing and ranking these predictive models. We therefore introduce the mean squared error of prediction (MSEP) and, more generally, the expected generalization loss (GL) to assess predictive models. This chapter is complemented by a more decision-theoretic approach to forecast evaluation, it discusses deviance losses, proper scoring, elicitability, forecast dominance, cross-validation, Akaike’s information criterion (AIC) and we give an introduction to the bootstrap simulation method.